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Electrical Technology Grade 11 Learner Book
Sample copy
© Future Managers 2012 All rights reserved. No part of this book may be reproduced in any form, electronic, mechanical, photocopying, or otherwise, without prior permission of the copyright owner. ISBN 978-1-920540-46-3 First published 2012 To copy any part of this publication, you may contact DALRO for information and copyright clearance. Any unauthorised copying could lead to civil liability and/or criminal sanctions.
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Please note that this is a sample draft copy and may still undergo minor changes.
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[email protected] Website: www.futuremanagers.net
Contents Chapter 1 – Safety...............................................................................................................1 Chapter 2 – Tools and measuring instruments ............................................................15 Chapter 3 – Single-phase AC generation ......................................................................39 Chapter 4 – Single-phase transformers .........................................................................51 Chapter 5 – Protective devices........................................................................................71 Chapter 6 – Single-Phase Motors ...................................................................................89 Chapter 7 – RCL .............................................................................................................101 Chapter 8 – Semiconductors.........................................................................................139 Chapter 9 – Power supplies ...........................................................................................179 Chapter 10 – Amplifiers ................................................................................................201 Chapter 11 – Logic .........................................................................................................225 Chapter 12 – Communication ......................................................................................261
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Description Key word
Did you know?
Take note
Activity
Case study
Chapter 1 Safety
A
Safety and the OHS Act
B Ergonomics
A
B Signage
Personal safety
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Electrical Technology
Introduction Workshops and laboratories are places where workers are constantly designing, making, manufacturing or repairing industrial tools or equipment. It is in these places that safety and first aid are of the utmost importance to both the employer and the employee. We must remember that safety is the responsibility of every single person, not just of the employer or factory owner. Many accidents occur in the workplace because of negligence on the part of the worker and, sometimes, the employer. In South Africa about 230 000 serious accidents occur every year. It is the aim of the Occupational Health and Safety Act (OHS Act) to eliminate, prevent or reduce such accidents so as to make our workshops accident-free and safe places to work in. According to the Act, an accident is an unplanned, uncontrolled event caused by unsafe acts and conditions. It is the aim of this chapter to look at general safety and first aid in the workplace and how to make the workshops and laboratories safer for everybody.
Safety and the OHS Act Safety can generally be described as: the condition of being safe; free from danger, risk, or injury. Working in electrical workshops can be very dangerous as carelessness and neglect can lead to serious injury or even death. When working with electrical equipment, care must be taken to adhere to all possible safety measures for personal safety and protection. It is commonly agreed that, if unsafe acts and unsafe conditions can be eliminated, 98% of all accidents could be prevented. A workshop is only as safe as the persons operating in it make it. One must ensure proper workshop safety, since ultimately the safety in any workshop is the responsibility of everybody in the workshop, including visitors. Figure 1.1: Safety signs
According the OHS Act both the employer and the employee are responsible for safety in the workshop. The OHS Act states that: “every employer shall provide and maintain, as far as is reasonably practicable, a working environment that is safe and without risk to the health of his employees.” To maintain safe working conditions in the workplace, the employer must ensure he does the following: • Provide and maintain systems of work, plant and machinery that are safe and without risks to health. • Take steps to eliminate or reduce any danger or potential hazard to the safety or health of employees. • Make arrangements to ensure the safety and absence of risks to the health of employees in connection with the production, processing, use, handling, storage or transport of articles or substances. • Provide training and supervision as may be necessary to ensure the health and safety at work of the employees. • Ensure that work is performed and that plant or machinery is used under the general supervision of a person trained to understand the hazards associated with it and who has the authority to ensure that precautionary measures taken by the employer are implemented.
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The employee, on the other hand, must also adhere to certain conditions to maintain safety in the workplace. Each employee has the following responsibilities: • Ensure the health and safety of themselves and of other persons who may be affected by their acts. • As regards any duty or responsibility imposed on the employer or any other person by this Act, co-operate with such employer or person to enable that duty or responsibility to be performed or complied with. • Carry out any official order given to them, and obey the health and safety rules and procedures laid down by the employer or by anyone authorised by their employer, in the interest of health or safety. • If any situation which is unsafe or unhealthy comes to their attention, report such situation to their employer or to the health and safety representative as soon as possible. • If they are involved in any incident which may affect their health or which has caused an injury to themselves, report such incident to their employer or to anyone authorised by the employer, or to their health and safety representative, as soon as possible. The general safety in the electrical workshop can also be improved by having workshop rules to ensure proper conduct in the workshop. It is important not only to post your workshop safety rules, but to enforce them to reduce accidents and injuries. The following rules will ensure that your workshop is a safer place: • No horseplay in workshop. • No eating and drinking in workshop. • Wear protective clothing and equipment when using dangerous tools and machines. • NEVER operate machines without supervision and permission. • Never use any tools or machines unless you have been properly instructed by the teacher. • Tools that have sharp edges should be carried with sharp edges pointing downwards. • Always clean the work area after the completion of a task. • Make sure all machine guards are kept in place. • No bags allowed the workshop, as people can trip over them. • Keep hands away from moving/rotating machinery. • No unauthorised persons allowed in workshops. • No smoking in workshop. The OHS Act compels the employer to ensure that the workplace meets safety standards by appointing health and safety representatives. The main task of such representatives it is to monitor the safety in the workplace. These health and safety representatives need to • regularly review health and safety measures in the workplace; • identify dangerous and hazardous conditions; • investigate incidents in the workplace in partnership with the employer; • investigate complaints of employees regarding health and safety issues; and • do regular inspection of the workplace, including tools and equipment. Such health and safety representatives can be held responsible and be punished if machinery or working conditions are found to be unsafe. To maintain high safety standards in the workplace we can all ensure that: • the workshop remains clean and neat. • equipment and materials are stored in their proper places. • the first-aid kit is easily accessible and contains the necessary medical items. • fire extinguishers are maintained and in good working order. • warning signs are visible and easily understood. • areas containing machinery are demarcated and clean.
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Electrical Technology • • • • • • •
walking paths are clearly indicated and obstacle-free. poisonous materials are safely stored and used. sharp tools are used with caution. games and jokes have no place in the workplace. smoking and drinking are prohibited in the workplace. any materials or liquids that are spilled are immediately cleared. any damaged or broken tools or machinery are immediately reported.
Unsafe acts As mentioned earlier, most accidents are caused by human carelessness. However, accidents also occur when workers are too complacent and then take risks, because they think nothing will happen to them. Below are some of the unsafe acts responsible for most accidents in workshops: • Failure to wear protective clothing and eye wear • The unsafe placement of tools • Horseplay in the workshop (running around and playing the fool) • The unsafe use of equipment or incorrect use of equipment • Trying to do adjustments or working on moving equipment • Taking up unsafe positions • Working at an unsafe speed. Figure 1.2: Safety equipment
Unsafe conditions This is also a major contributor to many accidents in the workplace. The following are unsafe conditions: • Inadequate guarding • Bad ventilation – high temperatures and a lack of clean fresh air can lead to tiredness and breathing problems • Rough or slippery floors • No personal protective equipment • A disorganised workshop • Overcrowding in a workshop • Badly planned workshop • Loose-hanging clothing and long hair • Insufficient light in workplace.
Ergonomics “Ergonomics” means using scientific information regarding humans to design objects, systems and the environment for human use in order to optimise human comfort and overall system performance. Ergonomics is about improving employee comfort, reducing chances for occupational injuries, improving productivity, and improving employee job satisfaction. The goal of ergonomics is to design jobs to fit people. Something is ergonomically designed if it is optimised to fit people. This means taking into account differences such as size, strength and ability to handle information for a wide range of users. Ergonomics is concerned with the reduction of one or more of the following risk factors: • Uncomfortable posture: If a job/task looks uncomfortable, it probably is and this increases the chances of injury. Whenever possible, strive to arrange the work environment or work processes to allow employees to work from a comfortable, neutral posture. Excessive bending, reaching and awkward neck, back, and arm positions should be eliminated.
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• High repetition: Repetition can be controlled by using equipment that reduces repetition, allowing employees to rotate tasks, assuring adequate staffing, and ensuring that employees take regular breaks away from highly repetitive tasks. • Extreme force: The need to exert too much force should be controlled through use of proper equipment, ensuring that equipment is operating properly, and getting adequate help when needed. • Contact stresses: Contact with sharp, abrupt edges, whether from a fixed piece of furniture or from a tool, should be avoided. • Vibration: Vibration can be reduced at the source through tool or equipment selection or by padding the body against vibration, e.g. wearing padded gloves. • Excessive temperatures: The temperature in the workplace should be controlled whenever possible. The improvement of the thermal environment – air circulation, ventilation, room temperature and humidity – can ensure a healthier place to work. Remember, the way one works and the conditions in which one works will definitely affect one’s effectiveness and efficiency as an employee. Controlling stress, both physical and psychological, following a balanced daily diet, resting and “recharging batteries” and working in a well-organised office or workshop environment are major factors in a person’s work life. Workplaces may take either the reactive or proactive approach when applying ergonomics practices. Reactive ergonomics is when something needs to be fixed, and corrective action is taken. Proactive ergonomics is the process of looking for areas that could be improved and fixing them before they become a bigger problem. Problems may be fixed through equipment design, task design, or environmental design. Equipment design changes the devices used by people, whereas task design changes what people do with the equipment. Environmental design changes the environment in which people work, and not the equipment they use. In conclusion, ergonomics can help reduce expenses of companies by improving safety. This would decrease the money paid out in workers’ compensation.
Housekeeping principles Good housekeeping in a workshop simply means an orderly arrangement of tools, equipment, operations, storage facilities and materials. To put it in simpler words, housekeeping can be defined as everything in its place and a place for everything. The simple principle of housekeeping is that an orderly, clean, tidy and bright workshop is far safer than one that is none of these things. One of the key factors to good housekeeping is making sure it involves everybody and that everybody understands its necessity – from the factory owner to the cleaner. It is, therefore, important to educate the entire workforce about the methods and desirability of the highest standards of housekeeping, which includes fostering an awareness of danger and having a code of safety practices in place. Organisation is one of the keys to an effective workplace. It seems like such a simple thing, but the fact is that when one takes the time to organise the workplace, one becomes more efficient.
Figure 1.3: Safety signs
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Electrical Technology A number of years ago, a major vehicle manufacturing company identified five housekeeping principles for ensuring an organised work area. These principles are simply good housekeeping practices, but they can have a major impact on any organisation. The five principles are: • Sort: Remove all items that are not immediately needed for the job at hand from the work area. This includes tools, documents, containers and equipment. • Set in order: Everything left in the work area should have a designated place. There are many ways to designate locations, including marked lines on the floor, signs hung from above and labels on all storage devices. • Shine: Consistently clean up the area to make it look good. Everyone prefers to work in a clean area, and this will lead to improved morale and better productivity. • Standardise: Develop procedures that will keep things like new. Formal procedures for housekeeping and preventative maintenance are essential components of this principle. • Sustain: Follow the procedures developed for maintaining an orderly workplace. This requires discipline to ensure that corners are not cut. These principles are not complicated, but they require commitment. To avoid a position in which one has to decide between production and housekeeping, one should clean and organise as one works. Do not wait until a job is finished before cleaning up chips or sweeping around a machine. Practicing housekeeping principles on an ongoing basis means the tasks are easier and less time-consuming. It is, therefore, clear that a neat and organised workplace is a safer workplace, and a safer working environment allows for better profits, a happier workforce and saves time.
Signs in the workshop
Figure 1.4: Signs found in the workshop
The use of signage in workshops and laboratories has become a legal requirement and it acts as a universal language when it comes to promoting safety. Safety signs and signals are the main means of communicating health and safety information. Proper signage will help reduce accidents and will help make the workplace safer. In view of the importance of signs, it is critical that all safety signs and signals be easily understood. Safety signs should be provided where necessary to warn of hazards, to prevent dangerous practices, and to indicate safe exit routes and safe practices. All safety signs must be placed where they can be easily seen and provide the best warning of the presence of a hazard. Generally, they are best placed above eye level at a height above two metres. If the natural light is not enough to light up the sign properly, artificial light must be used. It is important to note that any defective or faded sign must be replaced as soon as possible and unfamiliar signs must be explained to employees, including the action to be taken in connection with them. It is important that everybody using the workshop knows the different types of signs that are being used and their meanings. It must also be noted that different types of signs are printed in different colours. The International Standards Organisation, of which South Africa is a member, has published recommendations on the use of symbolic safety signs. With this information as guide, the South African Bureau of Standards (SABS) has designed the range of safety signs. These signs are recommended for use throughout South Africa.
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Safety signs Safety signs should be provided where necessary to warn of hazards, to prevent dangerous practices, and to indicate safe exit routes and safe practices. Specific types of signs should be used in dangerous locations, e.g. where there is a risk of slipping, falling from heights, or where there is low headroom.
Figure 1.5: Safety signs
The signs are divided into five categories. Each type is recognisable by colour and, with one exception, also by shape.
Colours Category
Colour – Border/oblique diagonal
Background
Symbol
P – Prohibitive
Signal Red (All)
White
Black
M – Mandatory
------------------
Ultramarine (type of blue)
White
I – Informative
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Emerald green
White
F – Fire
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White
Signal red (All)
W – Warning
Black
Golden yellow
Black
Figure 1.6: The five categories of safety signs
Information signs An information sign informs the user of a workshop or area of certain facts or knowledge or conditions. A sign indicating an emergency exit in a room can be referred to as an information sign. An information sign is a rectangular or square sign with a white picture on a green background. The colour green indicates ‘access’ or ‘permission’.
Figure 1.7: Information signs
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Prohibition signs A prohibition sign is a sign that orders or forbids something. A sign indicating no eating or drinking is a prohibition sign. Prohibition signs have a red, circular outline and crossbar running from top left to bottom right on a white background. The symbol displayed on the sign must be black and placed centrally on the background, without obliterating the crossbar. The colour red is associated with ‘stop ’or ‘do not’.
Figure 1.8: Prohibition signs
Warning signs Warning signs are signs that warn of a hazardous condition that may exist and that special care must be taken when entering a specific area or working with specific equipment. Warning signs are normally triangular with a black picture on a yellow background and black edging. This combination of black and yellow signifies ‘caution’.
Figure 1.9: Warning signs
Mandatory signs Mandatory signs indicate that a specific course of action is to be taken, or that a specific behaviour is required. Mandatory signs are round with a blue background and a white picture. An example of a mandatory sign is: wear protective headgear.
Figure 1.10: Mandatory signs
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Designated areas The risk of accidents happening in workshops can also be reduced by focusing on non-obvious risk areas such as walkways, storage areas and other related areas. In all workshops there are special designated areas where machines are kept, materials stored and where the person using the workshop can walk freely. It is, therefore, important that these areas are clearly marked on the workshop floor and with special signs. Normally the walkways are painted green with yellow lines on both sides, indicating the width of the walkway. Work/machinery areas and storage areas are also indicated by special floor markings and are sometimes segregated by barriers. For these walkways and designated areas to be effective in contributing to keeping the workshop safe, all walkways and designated areas must be kept clean and clutter-free. These areas must be kept dry and free from spillage and trip hazards. It is, therefore, important that these surfaces be cleaned regularly. Care must be taken that these floor surfaces are sound and have an easily maintainable, non-slip finish. The storage and work areas must be kept separate. All storage areas must be kept neat and tidy, and boxes must not be stored too high as this may pose a risk of falling. Other areas of special interest in any workshop that need to be highlighted are emergency exit doors and pathways, fire extinguishers and first-aid boxes. Emergency doors, fire extinguishers and first-aid boxes must be clearly marked. Emergency doors must be clear of obstacles, both inside and outside, for free movement in and out. Exit doors must be able to open from the inside. Fire extinguishers and first-aid boxes must be clearly marked and easy accessible.
Personal safety Eye protection Eye injuries are very common in workshop environments where hand tools and machinery are used. Many eye injuries occur because of workers forgetting or just not using the protective gear given to them. Injuries also occur when people are wearing the wrong eye protection for the job they are doing (e.g. wearing safety glasses instead of goggles or a full face shield when pouring chemicals, or wearing low-impact resistance glasses where a high-impact design is best). Eye wear that does not fit the contours of the face is also a source of injury. Workers select and use the recommended design but, because it does not fit the facial contours, particles get into the eye. It is, therefore, of the utmost importance that the correct eye protection be used depending on the tool or machine being used. In the electrical workshop, good quality safety goggles are needed specifically for grinding and drilling. Coveralls/Overalls As with eye protection, the overall/coverall/apron is used to protect the user from harm that may be caused by sparks or spillage of toxic or harmful liquids. The aim is to protect the clothes and body. Many expensive school uniforms have been damaged by sparks or chemical spills because of learners neglecting to put on their overalls/coveralls/aprons. For general grinding and drilling work in the electrical workshop, a woven cotton overall/coverall or apron is required, but when working with chemicals during PCB manufacturing, a rubber apron is required. It is important to note that specific overalls/coveralls/aprons must be used for specific jobs: it is not a one fit for all.
Figure 1.11: Safety goggles
Figure 1.12: Overall
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Did you know?
It is believed that exposure to noise levels at 85 decibels (db) or higher for eight hours or more per day puts your hearing at risk.
Hearing protection In today’s busy and noisy world one simply cannot afford not to safeguard one of our most delicate senses. Once one has lost one’s hearing, it is gone forever. It is, therefore, very important that one protect one’s hearing whenever exposed to high noise levels. Regular use of hearing protection will help protect against long-term hearing loss. In electrical workshops, one of two types of hearing protection can be used: earmuffs and earplugs. Either will provide an acceptable level of hearing protection and, depending on the noise level, some people may even use both types at the same time. Earmuffs Earmuffs look a lot like a large pair of headphones. Typically, the earpieces completely cover the ears to try to form a tight seal and keep out as much sound as possible. While they tend to provide a bit better sound reduction than earplugs, they also are quite bulky and cumbersome. Figure 1.13: Ear muffs
Earplugs Ear plugs are much smaller and less cumbersome than their earmuff counterparts, but do not provide the same level of protection. Earplugs are typically made of a type of memory foam that the user compresses, inserts into the outer ear cavity and waits for the foam to expand to form a tight fit. Many users find these more comfortable than earmuffs, particularly when working in warm weather. Always remember, no matter which type of hearing protection you prefer to be sure to use hearing protection when using power tools. Your ears will thank you for your foresight in future years. Below is a table indicating the estimated noise level from different types of sources: Figure 1.14: Ear plugs
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Noise Source
Db
Watch ticking
20
Quiet street noise
40
Normal conversation
60
Ringing telephone
80
Aircat impact wrench
82
Motorcycle
85-90
Rock concert
80-100
Hairdryer
90
Hand drill
95-105
Chainsaw
110
Jackhammer (3’)
120
Jet engine (100’)
130
Shotgun blast
140
Figure 1.15: Different noise sources
Safety
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Protective gear for machinery Besides the user of machines wearing protective clothing and all sorts of other protection, industrial machines are big and can be hazardous to those working around them if they need protective gear too. These machines have not been made safe for the user. Blades, flying objects and loose belts are all items that could present a safety risk to the persons working around these types of industrial machinery. Some of the protective gear for machinery can include the following safety requirements: Anchors It is important for all industrial machines used in a workshop or factory to be fastened securely to the ground, preventing them from moving during operation. It also prevents them from being placed in prohibited areas, such as in front of a fire escape, etc. when they are not in use. Protective shields/guards Protective guards/shields are required on all pieces of equipment and machinery. These guards/shields will prevent pieces of the machinery from coming loose and hitting the workers who are near the machines. Protective guards/shields can also prevent workers from falling into the machines or getting too close to dangerous blades and belts that could injure them severely. Guarding/shielding is commonly used with machinery and equipment to prevent access to • rotating end drums of belt conveyors; • moving augers (a corkscrew-shaped thread), or auger conveyors and rotating shafts; • moving parts that do not require regular adjustment; • machine transmissions, such as pulley and belt drives, chain drives, exposed drive gears; and • any dangerous moving parts, machines or equipment. There are three types of guarding/shielding: fixed, removable or adjustable guarding/shielding. If no access is required to parts of a machine, the guarding/shield can be permanently fixed. Removable guards/shields are used when parts of the machine can be removed for a short period to do some repairs to the machine. It is important that the guard/shield can only be removed with a special tool which is not normally available to the operator. Adjustable guarding/shields incorporate movable sections or panels of the guard and allow for material or parts to be fed into the guarded area while still preventing bodily contact.
Figure 1.16: Machine guards
Interlock guarding Interlock guarding occurs when the act of moving the guard (opening, sliding or removing) to allow access stops the action of the dangerous mechanism. Interlock guarding works by • mechanically disconnecting the drive mechanism, • isolating the power source of the drive mechanism (stops the motor), or • a combination of mechanical and power disconnection. Interlock guarding is generally achieved via mechanical or electrical means, but may also include hydraulic or pneumatic control systems.
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Electrical Technology Stopping mechanism Some industrial machines have areas or parts that can easily grip hands and fingers. If the machine has such an area, it must be shielded. However, it must also have a stopping mechanism so that workers can safely stop the machines should any part of the worker be caught in the machine. Simultaneous two-handed operation Where a machine has only one operator, the use of simultaneous two-handed operation buttons can serve as a risk control. This ensures that operation of the dangerous mechanism cannot occur until both hands are clear of the danger area. The two buttons must be pushed at the same time and are located at a distance from each other, which prevents simultaneous operation using one hand. The operation should be designed so that if either or both of the buttons are released, the hazardous action of the machine or equipment cannot be reached; or when it can be reached, the mechanism has returned to a safe state. A two-handed control option may be suitable for ensuring that a machine cannot be operated until both hands of the operator are clear of the hazardous area. Presence sensing systems If physical guards/shields are not reasonably practicable, then a presence sensing system can be used as a control to reduce risk. Presence sensing systems can be used where people enter areas shared by moving production equipment. Presence sensing systems are capable of providing a high degree of flexibility with regard to access. These systems detect when a person is in the identified danger area, and stop or reduce the power or speed of the mechanism at the time of entry to provide for safe access. Presence sensing systems can rely on foot pressure pads, infra-red sensing, light beams or laser scanning.
Figure 1.17: Presence sensing system
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Activity 1 1. 2. 3. 4. 5. 6. 7. 8. 9.
What do you understand by the concept of safety? What is the significance of the OHSA with regard to safety? Name THREE things that the employer must put in place to maintain safe working conditions. Safety in the electrical workshop must receive the highest priority. Write down at least five rules that will make the workshop a safer place. Unsafe conditions are the cause of many accidents. Name FIVE unsafe conditions in an electrical workshop. Briefly explain, in your own words, what you understand by the term ergonomics, with reference to the electrical workshop. Why is it so important to have good housekeeping in place? The South African Bureau of Standards (SABS) has designed the range of safety signs. Name the five main categories of these safety signs. Identify the following safety signs.
10. Why is it important that emergency exits be clearly marked? 11. Name the type of protection you will use when doing the following: • Working with a grinding wheel. • Drilling a hole. • Etching of a PCB. 12. Name TWO types of hearing protection that can be used in a workshop and give the main difference between them. 13. What do you understand by a pro-active approach to ergonomics? 14. Name at least THREE aspects of good housekeeping and give a brief explanation of each. 15. What do you understand to be the main reason why safety signs are used? 16. What is the best height at which safety signs should be displayed in workshops? 17. What is the significance of warning signs? 18. Mandatory signs indicate that a specific course of action is to be taken, or that a specific behaviour is required. Name THREE mandatory signs. 19. What is the importance of using protective guards/shields for big machines? 20. Name THREE types of guarding/shielding used on machines. 21. Name THREE safety features used on big machinery to help prevent injuries. 22. Briefly explain what you understand by simultaneous two-handed operation.
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Chapter 2 Tools and measuring instruments
A Oscilloscope
A
Soldering and desoldering
Safe use of power tools
B
B Housekeeping 15
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Electrical Technology
Introduction This chapter deals with the basic test instruments used in an electronics workshop: a digital multimeter, an insulation tester, a function generator and the oscilloscope. It will also deal with the safe use and care of special tools such as the crimping tool and bending spring, as well as the safe use of power tools such as the drill, grinder and jigsaw. After the principles of soldering, the chapter provides a step-by-step guide to designing and making a PCB and ends with a section on housekeeping.
Digital multimeter One of the most common and versatile measuring instrument used in all electrical/ electronic workshops is the electronic multimeter – more specifically the digital multimeter. This is a multifunctional measuring device that is most commonly used for the measurement of voltage, current and resistance. However, as technology has advanced, digital multimeters have been developed that can even measure capacitance, frequency and temperature, as well as test semiconductor devices such as transistors and diodes. There is such a wide range of multimeters that it is important to read the operating instructions before using some of the more sophisticated digital multimeters. The pictures below show examples of simple digital multimeters: one with a manual ranging and the other with an auto ranging selection. With the manual ranging multimeter it is always important to select the correct range within a selected function before taking any measurement, while with the auto ranging multimeter, you can simply select the function and the multimeter will automatically select the appropriate range to take the most accurate reading. This means that once the function is selected (volts, amps, ohms, etc.), the meter will select the range or scale automatically. 1
1
2
2
3
3
4 Figure 2.1: A manual ranging multimeter
Figure 2.2: Auto ranging multimeter
1. Digital display: The digital display displays the reading of whatever measurement is being taken. 2. Selector switch: This switch is used to select the correct function for the task to be performed, e.g. measuring volts, measuring resistance, or even testing a diode. One must always be sure that the multimeter is on the correct setting before taking any measurements. Selecting an incorrect setting can damage the multimeter. 3. Measuring lead connector sockets: These are the inputs for the measuring leads (red and black). It is important to put the leads into the correct sockets.
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For standard use of the multimeter, the red lead is put into the socket marked “V/Ω/mA” and the black lead is put into the socket marked “Com”. Only for the measurement of very high currents is the red lead put into the socket marked “10A/DC”. 4. Transistor tester: This is a socket for connecting a transistor (NPN or PNP) in order to measure the hFE (gain) of the transistor.
Principle of operation Unlike the analog multimeter that makes use of a moving coil meter to display any measurements taken, the digital multimeter makes use of a liquid crystal digital (LCD) display to display the information measured. The basic operating principle is that the multimeter makes use of a simple digital voltmeter to take the basic measurements. This digital voltmeter is made up of three major parts: • an unknown input voltage, • an analog to digital converter (A/D converter), and • a digital output display. For voltage measurements, the unknown analog signal is measured and converted to a digital signal by the A/D converter. This digital signal is then displayed on the digital output display of the multimeter. The digital output display will constantly change with the change in input voltage being measured. For current measurements, a precision-fixed, low-value resistor is connected across the input leads. The unknown current measured will thus flow through the resistor, creating a voltage drop across the resistor which, in turn, is measured by the digital voltmeter, as explained in the previous paragraph. This voltage measured would be proportional to the current being measured. For resistance measurement, a known amount of current is sent through the unknown resistor, once again creating a voltage drop across the unknown resistor. This voltage drop is measured by the digital voltmeter and displayed on the digital output display. This voltage measured would be proportional to the resistance of the unknown resistor being measured.
Applications Digital multimeters are very versatile measuring instruments and are widely used in electrical/electronic workshops. As mentioned previously, digital multimeters can be used for measuring voltage, current, resistance, frequency and temperature, as well as for testing diodes and transistors. Always remember that when one does a voltage measurement, the probes must be across the points to be measured (in parallel). The red lead must be connected to the positive side of the circuit and the black lead to the negative side of the circuit. For current measurements, the probes must be in series in the circuit. (The circuit must be broken and the digital multimeter must complete the circuit.) The red lead must be connected to the positive side of the circuit and the black lead to the negative side of the circuit.
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Electrical Technology For resistance measurement, the circuit must first be switched off. The resistor must then be removed completely, or one lead must be removed completely, before a resistance reading can be taken. The probes must be connected across the resistor (in parallel).
Care and maintenance Digital multimeters are very sensitive electronic devices and must always be handled with care. The following points are very important: • Always put the multimeter in a protective cover if possible. • Store the multimeter in a dust-free area. • Never allow the meter to be dropped on the floor. This can damage the display. • Ensure that the leads are connected to the right input sockets (red and black). • Always select the highest range on the function select input if you are not certain about the quantity being measured. • Always make sure that the multimeter is on the correct setting before taking any measurements. Selecting an incorrect setting can damage the multimeter. • Never roll up the test leads tightly, as this may cause a break in the leads. Rather let them hang loosely in the storeroom. • Always keep the terminals and terminal posts clean, as dirt on the posts may lead to incorrect readings. • Follow the correct operational instructions/procedures for the specific instrument. • Always use the right equipment for the right job. • Equipment must always be stored in a secure place.
Insulation tester (Megger)
Did you know? This famous brand name MEGGER dates back to 1889, when the first portable insulation tester was introduced with the MEGGER brand name on it.
The insulation tester is a portable instrument used to measure the insulation resistance of electrical machinery or systems. It is an instrument that tests the safe operation of electrical installations, motors, transformers, generators and other electrical appliances. Regular insulation testing is one of the most cost-effective methods of identifying aging in any type of electrical equipment. The insulation and continuity tester is also commonly known as a ‘Megger’. It is a tester that must be able to measure very high resistances of up to 200 megohm at test voltages of up to ±1 000 V (DC), as well as very low resistance, as low as 0,01 ohm. The device must be very accurate, especially at very low resistance readings. The older type of meters comprised two parts: a hand-driven direct current (DC) generator capable of producing different test voltages, such as 6 V for the testing of continuity and ±500 V DC for the testing of insulation resistance; and a direct driven ohmmeter. Currently more and more people are using the more modern digital insulation and continuity tester because it is easier to operate and more accurate. According to Regulation 8.7.8: Insulation resistance in SANS 10142-1 2003 Wiring code as amended, a single phase installation must be tested with an insulation tester (500 V DC or AC) at twice the operating voltage. When this test is carried out, the reading should not be less than 1 megaohm.
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Tools and measuring instruments 1. Measuring lead connector sockets (on top of Megger): These are the inputs for the measuring leads (red and black). It is important to put the leads into the correct sockets. 2. Digital/Analog display: The digital/analog display displays the reading of whatever measurement is being taken. The digital display gives a numeric representation of the reading, while the analog reading is given by means of a pointer moving across a calibrated scale. 3. Selector switch: This switch is used to select the correct function for the task to be performed, Figure 2.3: Megger e.g. measuring high or low resistances. One must always ensure that the insulation tester is on the correct setting before taking any measurements. 4. Test button: Press TEST to initiate the selected test or to repeat the selected test. The test button is used when insulation testing is done. Zero adjust: (Analog meters only) To ensure that readings are accurate, the analog multimeter must always be zero-adjusted manually. This is done by turning the selector switch to the ohm scale, shorting the two test leads and adjusting the zero adjust setting on the front of meter until the pointer is exactly on zero ohms on the analog scale.
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Principle of operation
Figure 2.4: Circuit representing a Megger
An insulation tester (Megger) consists of the following basic parts: 1. Control and deflection coil: These are normally mounted at a right angle to each other and connected parallel to the generator. The polarities are such that the torque produced by them is in opposite directions. 2. Permanent magnet: These permanent magnets with north and south poles produce a magnetic effect for the deflection of the pointer. 3. Pointer and scale: A pointer is attached to the coils and the end of the pointer floats on a scale which is in the range from “zero” to “infinity”. The unit for this is “ohms”. 4. DC generator or battery connection: The testing voltage is supplied by a handoperated DC generator for a manually operated Megger and a set of batteries and electronic voltage charger for an automatic Megger.
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Electrical Technology • The current carrying coil (deflection coil) is connected in series and carries the current taken by the circuit under test. The pressure coil (control coil) is connected across the circuit. • Current limiting resistors are connected in series with the pressure coil (control coil) and the current carrying coil (deflection coil) to prevent damage in case of a low resistance in the external circuit. • In hand-generator units, the armature moves in the field of the permanent magnet or vice versa, to generate a test voltage by electromagnetic induction effect. • As the potential increases across the outside circuit, the deflection of the pointer will increase; and as the current increases, the deflection of the pointer decreases so that the resultant torque on the movement is directly proportional to the potential difference and inversely proportional to the resistance. • When the external resistance is infinity, i.e. the insulation measured is very good, the pointer will read infinity (α). When there is a short circuit in the circuit, the pointer will read 0 ohm.
Applications The insulation and continuity tester can be used to test • for open circuits. • for short circuits. • earth continuity. • insulation resistances between conductors. • insulation resistances between conductors and earth. • the polarity of switches.
Care and maintenance All electronic test instruments are very sensitive devices and must always be handled with care. The following points are very important to remember when using an insulation tester: • If battery operated, always ensure batteries are in good order (fully charged). • Keep the insulation tester in a protective cover if possible. • Always make sure the test leads are in good condition. • If the deflection type insulation tester is used, be careful not to damage the deflection coil as this may lead to incorrect readings. • Always store in a dust-free area, because dust can be harmful to the instrument. • Follow the correct operational instructions/procedures for the specific instrument. • The circuit connections and exposed metalwork of an installation or the equipment being tested must not be touched. • Do not allow anybody to touch the leads while a test for insulation is in progress (they will get a shock). • Do not move the rotary selector switch position while a test is in progress. • Replacement fuses must be of the correct type and rating. • Equipment must always be stored in a secure place. • When doing measurements, ensure that you use the correct scale.
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Function generator The function generator is a waveform generating instrument that is also widely used within the electronics industries. The function generator is an electronic instrument responsible for generating different types of signals or waveforms (sine, square and triangular (sawtooth) waves) to help with the design, testing, or troubleshooting of electrical devices. It also allows the user to change the frequency and the amplitude of such waveforms. The frequency can range from a few Hz into the MHz scale, and the amplitude can vary from a few mV up to about 10 V, depending on the type of function generator. As with multimeters, there is also a huge variety of function generators, from very simple ones to very complicated and sophisticated ones. Some function generators have a digital display to display the frequency being generated. For the purposes of this book we will focus on the very simple, basic function generator. 1
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4 5 6 Figure 2.5: Function generator
1. Digital output display: The digital display provides a numeric display of the frequency being generated by the function generator. This make for easy reading and accurate setting of the frequency needed. 2. Function selector: This facility allows one to select the type of waveform required (square, sine or triangular (sawtooth)). 3. Frequency range selector: The frequency selection function enables one to select the frequency range to be generated, e.g. 100 Hz, 1 kHz or 10 kHz. 4. Amplitude selector: This function is used to set or adjust the amplitude of the waveform that is being generated. This can range from a few mV to about 10 V, depending on what amplitude value is required. 5. BNC output socket(50 Ω): The 50 ohm BNC connector is used for connecting the function generator to other equipment. The most common connection used is a cable with a BNC connector at one end and two croc clips (red and black) at the other end. Always ensure that the cable is connected correctly to the circuit being tested. The function generator is polarity conscious, i.e. the ground lead of the function generator must be connected to the ground of the circuit being tested. 6. Frequency adjustment knob: This control allows one to set or adjust the frequency to a specific value.
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Principle of operation Waveform generator
Amplitude and frequency adjustment
Output
Power supply
Figure 2.6: Simple block diagram of a function generator
A function generator generally provides an AC signal of variable amplitude and frequency. Because of the wide range of function generators, each one will have a unique principle of operation. In general, the three basic waveforms can be generated by a simple 14 pin 8038 waveform-generated IC. This IC is capable of generating sine, square and triangular (sawtooth) waveforms. With the correct additional circuitry connected to the IC, one can adjust both the frequency and the amplitude of the selected waveform. The function switch will allow one to select the desired output waveform, which is then transferred to the BNC output socket.
Applications The function generator can be used to help with the design of electronic equipment and apparatus and with the testing and troubleshooting of electrical and electronic devices.
Care and maintenance The function generator is a very sensitive and delicate piece of electronic equipment and must be handled with care at all times. Haphazard operation or improper setting of the controls can damage the electronic equipment. The following points are very important to remember when using a function generator: • Always store in a dust-free area, because dust can be harmful to the instrument. • Follow the correct operational instructions/procedures for the specific instrument. • Always make sure the test leads are in good working order. • Make sure the BNC sockets on the function generator are in good condition and rust-free.
The oscilloscope The oscilloscope is a measuring instrument that is also widely used within the electronics industry. The oscilloscope is a tool commonly used by engineers and technicians to analyse and troubleshoot electronic systems. An oscilloscope is an electronic measuring device which makes use of a cathoderay tube (CRT) to display a two-dimensional visual representation of a signal. Because the oscilloscope allows the user to see the signal(s), the characteristics of the signal(s) can be easily measured and observed. The oscilloscope displays a graph of voltage (on the vertical axis) over time (on the horizontal axis). Most electrical circuits can be connected to the oscilloscope using probes without difficulty. Most standard oscilloscopes will have the facility to connect two oscilloscope probes. As with multimeters, there is a wide variety of oscilloscopes from very simple ones to very complicated and sophisticated ones. In some modern workshops one might
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even see digital oscilloscopes. Instead of displaying a signal by deflecting an electron beam that is traced across a CRT, the digital oscilloscope uses a processor to sample, digitise and display the incoming analog signal on the display screen. For the purposes of this book we will focus on the very simple, basic analog oscilloscope. 1
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Figure 2.7: An oscilloscope
1. Horizontal position control: This is used to move the waveform horizontally (from side to side) across the screen. 2. Time/Div control: The time per division setting allows one to select the rate at which the waveform is drawn across the screen (also known as the timebase setting or sweep speed). This setting is a scale factor. For example, if the setting is 1 ms, each horizontal division represents 1 ms and the total screen width represents 10 ms (ten divisions). Changing the time/div setting enables one to look at longer or shorter time intervals of the input signal. 3. Trigger mode: The trigger mode determines whether or not the oscilloscope will draw a waveform if it does not detect a trigger. Common trigger modes include normal and auto. In normal mode the oscilloscope only sweeps if the input signal reaches the set trigger level; otherwise (on an analog oscilloscope) the screen is blank. Normal mode may be confusing since one may not see the signal at first if the level control is not adjusted correctly. Auto mode causes the oscilloscope to sweep, even without a trigger. If no signal is present, a timer in the oscilloscope triggers the sweep. This ensures that the display will not disappear if the signal drops to small voltages. It is also the best mode to use if one is looking at many signals and does not wish to have to set the trigger each time. 4. Trigger source: This function allows one to select the source that must triger the scope. Several sources can trigger the sweep: • Any input channel (Chanel 1 or 2) • An external source, other than the signal applied to an input channel • The power source signal • A signal internally generated by the oscilloscope.
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Did you know? The graticule is a grid of squares that serve as reference marks for measuring the displayed trace.
5. Slope adjust: This allows the user to invert the waveform and, therefore, have the waveform displayed “upside-down.” 6. Mode select: If one has a dual trace oscilloscope, this function allows one to display one of the waveforms at a time, display two waveforms simultaneously and even to add the two waveforms. 7. Vertical position control: This is used to move the waveform vertically (up or down) across the screen. 8. AC/GND/DC select: This selector is used to connect an electrical signal from one circuit to another. The input coupling is the connection from the test circuit to the oscilloscope. The coupling can be set to DC, AC, or ground. DC coupling shows all of the input signals. AC coupling blocks the DC component of a signal so that one sees the waveform centred at zero volts. The ground setting disconnects the input signal from the vertical system, which enables one to see where zero volts is on the screen. 9. Volts/Div control: The volts per division setting varies the size of the waveform on the screen. The volts/div setting is a scale factor. For example, if the volts/div setting is 5 volts, then each of the eight vertical divisions represents 5 volts and the entire screen can show 40 volts from bottom to top. 10. Screen: The screen will display the waveforms measured. The display is usually a CRT or LCD panel which is laid out with both horizontal and vertical reference lines referred to as the graticule. 11. Focus control: This is used to adjust the sharpness of the waveform. Digital oscilloscopes may not have a focus control. 12. Intensity control: This is used to adjust the brightness of the waveform.
Principle of operation
Figure 2.8: Block diagram of an oscilloscope
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The oscilloscope can basically be divided into four sections: the display, the vertical controls, the horizontal controls and the trigger controls. The display is usually a CRT or LCD panel which is laid out with both horizontal and vertical reference lines referred to as the graticule. In addition to the screen, most display sections are equipped with three basic controls: a focus knob, an intensity knob and a beam finder button. The vertical section controls the amplitude of the displayed signal. The signal to be measured is fed via the scope probe to an attenuator and then to the vertical amplifier to either amplify or attenuate the input signal. From the vertical amplifier the signal is fed to the vertical deflection plates (y-plates) of the CRT. The vertical plates move the trace from top to bottom. This section of the scope contains the volts per division (Volts/Div) selector knob, the AC/DC/Ground selector switch and the vertical (primary) input for the instrument. Additionally, this section is typically equipped with the vertical beam position knob. The horizontal section controls the time base or “sweep” of the instrument. This is the part of the scope responsible for the deflection of the electron beam horizontally across the face of the oscilloscope. This is normally done with the aid of a sawtooth generator. The speed of the movement of the beam across the face of the scope (horizontally) is done by the time-base generator. Before the signal is fed to the x-plates (horizontal deflection plates), it is first amplified by the horizontal amplifier. The primary control is the time per division (T/Div) selector switch. Also included is a horizontal input for plotting dual X-Y axis signals. The horizontal beam position knob is generally located in this section. The trigger section controls the start event of the sweep. The trigger stage receives a signal from the vertical amplifier. The trigger can be set to restart automatically after each sweep or it can be set to respond to an internal or external signal. Triggering is necessary to provide for a stabilised signal display on the screen. The trigger section is responsible for synchronising the input signal and the time base signal. The main controls of this section are the source and coupling selector switches. An external trigger input (EXT Input) and level adjustment will also be included. In addition to the basic instrument, most oscilloscopes are supplied with a probe. The probe will connect to any input on the instrument and typically has a resistor of ten times the oscilloscope’s input impedance. This results in a X1 or X10 attenuation factor, but helps to isolate the capacitive load presented by the probe cable from the signal being measured.
Applications In general, oscilloscopes are used for the maintenance of electronic equipment and for laboratory work. Special purpose oscilloscopes may be used for such purposes as analysing an automotive ignition system, or displaying the waveform of the heartbeat of a person. One of the most common uses of scopes is troubleshooting electronic equipment. The advantage of using an oscilloscope is that one can literally see the signals at the measured points. Oscilloscopes can be used to • measure AC and DC voltages. • measure the frequency of waveforms. • analyse waveforms. • determine phase relationship between waveforms. • measure the generation period of waves.
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Care and maintenance The oscilloscope is a very sensitive and delicate piece of electronic equipment and must be handled with care at all times. Haphazard operation or improper setting of the controls can damage the electronic equipment. The following points are very important to remember when using an oscilloscope: • Always store in a dust-free area, because dust can be harmful to the instrument. • Follow correct operational instructions/procedures for specific instrument. • Always make sure the test leads are in good working order. • Make sure the BNC sockets on the oscilloscope are in good condition and rustfree.
Tools Crimping tool
Figure 2.9: Crimping tool with ferrules and lugs
1. Crimping jaw 2. Insulated handle 3. Lugs and ferrules Function: This is a tool used to crimp ferrules, lugs and plugs onto wires. It can also be used to strip the insulation off wires and to cut wire. Safe use: Crimping tools come in different shapes and sizes, so be sure to use the correct size for the ferrules and lugs. Ensure that your fingers are not caught in the crimping jaw. Do not apply too much pressure during crimping, because this might damage the crimping tool or even the ferrule or lug. Maintenance and care: The crimping tool must be kept clean, and the moving parts must be oiled regularly. Bending spring
Figure 2.10: Bending a conduit with a bending spring
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Function: A bending spring is used for the bending of PVC pipes (conduit). Bending springs are about 0.5 m long and come in two basic diameter sizes: 20 mm and 25 mm. Safe use: Ensure the correct size bending spring is used for the correct size PVC pipe thickness. The bending spring is placed inside the PVC pipe, which is then bent around the knee, until the correct angle is obtained. The spring prevents the walls of the PVC pipe from collapsing. Maintenance and care: Always keep the bending spring in a dry environment, because moisture can cause it to corrode.
Safe use of hand tools Electric drill 1 2
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Figure 2.11: Electric drill
1. Chuck 2. Handle 3. Power switch Function: The electric hand drill can be used for drilling holes through metal, plastic, wood or masonry. Some drills with a speed control can even be used as a screwdriver. Safe use: Always wear protective goggles when using an electric hand drill. All loose clothing and hair should be tucked away. Always maintain a secure footing and good balance. Make sure the bit is properly secured in the chuck. Always select the correct bit for the job. Never leave the chuck key in the chuck after the replacement of a bit. This can be very dangerous. Maintenance and care: Make sure the chuck is always secure and that the electrical cord of the drill is in good order. Keep the drill clean and store it in a safe place. Bench grinder 1 2
1. Safety shield 2. Grinding wheel 3. Power switch
Figure 2.12: Bench grinder
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Electrical Technology Function: Bench grinders are used to sharpen chisels, drill bits and other tools. They can also be used for general grinding applications (metal and plastic). Safe use: The disc grinder must be used with caution, because it is the cause of many injuries. When using a disc grinder, always wear protective gear over your clothes and eyes. Always use a vice-grip when grinding small objects and never use the side of the grinding wheel. Never try to touch the disk of a grinder that is spinning. Switch the grinder off when not in use. Maintenance and care: You must always ensure that the grinder is well secured and that the wheel and all the other guards, shields and safety switches are in good condition. Jigsaw 1
2 3 4 5 Figure 2.13: Jigsaw
1. 2. 3. 4. 5.
Handle Power switch Chip cover Base plate Blade
Function: A jigsaw is a tool used for cutting arbitrary (random) curves/shapes out of wood and perspex. The electric portable jigsaw’s blade has an up-and-down motion and can also be used for straight cutting. Safe use: Always ensure that the chip cover is in place to prevent sawdust and fragments from flying towards the user. Before use, make sure the blade is secured and sharp. Always wear protective glasses and an apron when using a jigsaw. Do not use on metal objects. Always cut away from the body and be sure the power lead is out of the way. Do not cut material that is too thick, because the blade gets very hot, and it also cannot be manoeuvred as well through thick material. Maintenance and care: All moving parts must be oiled regularly and the machine must be cleaned after use.
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Safe and correct use of tools In the electrical technology workshop one encounters many different tools and types of equipment. To prevent injuries and accidents from happening it is important to use the tools correctly and safely. Always remember that no matter how small or big or how quick a job may be, the unsafe use of tools can cause serious injury. The following general rules apply to all tools in the workshop: • Keep all tools in good condition through regular maintenance. • Use the right tool for the job. • Do not use tools that are damaged. • Follow the correct procedure for using each tool.
Intermediate soldering/desoldering skills (Using a solder wick) Soldering By now learners will have discovered that soldering is not as easy as it seems. It is an art that must be practised to perfection. In grade 10 learners started doing simple soldering tasks. In grade 11 it is time to continue working on the soldering skills in order to be able to make good, shiny, smooth solder joints. Remember, soldering is about practice, practice and more practice. Before progressing further, here is a recap of a few important rules to remember when soldering: • Always solder in a room that is well ventilated. • Never touch the tip of the soldering iron as it gets very hot (± 400˚C). • When a soldering iron is not in use, switch it off. • The tip of the soldering iron must be ‘tinned’(by melting solder onto the hot tip of the iron) for the best transfer of heat. • Always clean the tip of the soldering iron with a wet cloth or sponge. • Wash hands after soldering because solder contains lead which is a poisonous metal.
Warning Be careful! The tip of a soldering iron can easily exceed 400 degrees Celsius, and the tip of a cool soldering iron looks exactly like the tip of a hot one!
Simple soldering steps When soldering on vero or PC boards, make sure the copper tracks are clean and grease-free before following these steps: • Push the component leads or wire links through the board to protrude on the copper side of the board. • Use the soldering iron to heat up the joint to be made. • Ensure that the soldering iron is in touch with both the component lead and the copper track. • Apply the solder to the joint and not to the soldering iron. • Take care not to apply too much heat to the joint to be soldered. • Feed a little solder to the joint. It should flow smoothly onto the lead and the track to form a shiny volcano-shaped joint. • Remove first the solder and then the soldering iron. Allow the joint to cool off for a few seconds. • Inspect the joint to ensure that a good, shiny volcano-shaped joint has been formed. • If the joint is not up to standard, apply more heat and a little more solder. • Be careful not to apply too much solder as this may result in a ‘dry’ or gray joint.
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Electrical Technology Tip of soldering iron Solder wire
Circuit board
Copper pad on board
Lead from conponent
GOOD JOINT (volcano shape)
shiny solder
BAD JOINT (dry joint)
copper tracks
component lead
dull solder PCB or stripboard
component
Figure 2.14: Correct solder process
Figure 2.15: Soldering joints
Desoldering using a solder wick Soldering two electronic components together is an art form in itself. There often comes a time, however, when a soldered joint must be taken apart, or components must be replaced or removed from a PC or vero board. This requires the use of one of two tools – either a solder sucker or a solder wick. A solder wick is a long spool of braided, oxygen-free, copper wire. The use of the solder wick allows one to desolder a connection without damaging the connected components. As with the solder sucker, the use of the solder wick must be practiced for the best desoldering results.
Did you know? Capillary action is the tendency of a liquid to rise in narrow tubes or to be drawn into small openings such as those between grains of a rock. A familiar example of capillary action is the tendency of a dry paper towel to absorb a liquid by drawing it into the narrow openings between the fibers.
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Figure 2.16: Solder wick
The following steps can be followed to desolder a component with the aid of a solder wick. • Plug in the soldering iron and wait until it reaches operating temperature. • Press the solder wick against the joint to be de-soldered. • Press the soldering iron against the wick. As the wick heats, it will melt the solder in the joint and soak it up through capillary action, leaving the joint clean and solder-free. • Always remove the wick first, then the soldering iron. • Remember not to apply too much heat to the joint as this might also damage the fragile copper tracks. • Cut off the solder-soaked end of the wick and throw it away, leaving the wick clean for the next job.
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Printed circuit board manufacturing skills (design and make) Design a PCB Designing a PCB can be done simply by using a permanent marker to manually trace a circuit onto the PCB, or by using a PCB software package which will help to design the PCB. In most cases the more complex the circuit, the more difficult it will be to draw it manually. One can use the PCB software packages to draw the schematic diagram and then to create the PCB design. However, some software packages will even allow one to get the PCB design directly from the circuit diagram. In most cases the capability of each design package is directly linked to the cost. For the purpose of this book, reference is made to a PCB package that is available on the Internet free-of-charge, Express PCB. While this package is very user-friendly, the user does have to play around with it to understand all its capabilities. However, once the program has been downloaded, it is possible to design a PCB in a few simple steps, as set out below. Step 1: Determine size of PCB Once you have opened the program, you must determine the size of your work area (this is also the size of the PCB). This is important because the size of the PCB is determined by where the PCB will be fitted. If, for example, the PCB must slot into an enclosure of 80 mm × 40 mm, you determine your work area by simply dividing 80 and 40 by 2.54 to give you the number of dots horizontally and vertically across the work area, i.e. 80/2.54 = 31 (dots) horizontally and 40/2.54 = 16 (dots) vertically.
Figure 2.17: Determine the size of PCB
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Electrical Technology Step 2: Select the components Begin your layout by adding the components. Select the correct components from the Component Manager dialogue box.
Figure 2.18: Selection of components
Step 3: Position the components Drag each component to the desired position on your screen (working area).
Figure 2.19: Positioning of components
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Step 4: Add the traces Now add each trace by clicking on the pin of a component and dragging the trace to another pin. Make sure your trace is not too thin, because it will be etched away if etched too long.
Place a track Red tracks
Figure 2.20: Add traces
Step 5: Setting item properties You can set the properties of items in your layout by double-clicking on them. For example, double-click on a trace to change its layer or width.
Figure 2.21: Setting item properties
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Electrical Technology Step 6: Select tracks Select the tracks that you would like to move to the bottom copper layer of the PCB by simply clicking on the icon with the green line and the two arrows on top. Move to bottom copper layer icon
Green tracks
Figure 2.22: Selection of tracks
Step 7: Printing Once you have moved all tracks to the bottom copper layer, you are ready to print your design. This program allows you to print different options, e.g. • The top copper layer only • The bottom copper layer only • Silkscreen layer (component outlines), or • Silkscreen, pads and text on top layer.
Figure 2.23: Printing
Once you have printed your desired copper layer, you are now ready to transfer your design to the PCB. The transfer of your design to the PCB is described in the section on the making of a PCB.
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Making a PCB Most electronic hobbyists build their circuits on either veroboards or PC boards. Veroboards are ideally suited for simple circuits. However, a PCB is a better option for a more complex circuit. A PCB is a thin, synthetic plastic board covered with a thin layer of copper. Single-sided PCBs have only one copper layer, while doublesided PCBs have copper on both sides of the synthetic plastic board. Below are a few steps to make a simple PCB. • Cut the PCB to the correct size and file the edges of the board until smooth and free of burrs. • Using a scourer or some sort of abrasive material, clean the copper side of the board thoroughly. Do not touch the clean board with bare hands. Handle the PCB by holding the sides. • You are now ready to transfer your circuit design (this can be hand-drawn, computer-drawn or designed by a company) onto the PCB. This can be Figure 2.24: A clean PCB done using one of these methods. i) Using a “permanent” black marker and tracing your design onto the copper layer of the PCB. This method is very simple and relatively cheap. ii) Using “Press-’n-Peel” sheets. Your design is copied onto the non-glossy side of the “Press-’n-Peel” using a laser printer. The non-glossy side is then placed on the clean copper side of the PCB, and the design is ironed onto the copper. The process is relatively easy and the cost is not too high because an A4 sheet costs about R30. Remember that more than one design can fit onto an A4 sheet (depending on the size of the actual design). iii) Using a photolithographic method. The copper side of the PCB board must first be covered with a photosensitive material. You can use either a photo positive or negative method. A positive or negative of the circuit design can be copied with a laser printer on a clear transparency. The circuit design is then transferred to the photosensitive PCB, by making use of an ultra violet light. This method is very expensive because it Figure 2.25: Circuit transfered onto makes use of expensive material PCB and equipment. • You are now ready to remove the unwanted copper in order for only the copper tracks to remain. This process is called etching. The PCB, with the circuit design transferred onto the copper side is now placed into a plastic container (an unused ice-cream container will work well) filled with enough etchant to submerge/cover the board completely. A very popular etchant that is commonly used is ferric chloride; other etchants are also available, e.g. hydrochloric acid and ammonium persulfate. Ferric chloride is available in granular or powder form, as well as in a premixed liquid form. For more effective etching results, the ferric chloride liquid mix can be heated a little, and the PCB must be moved regularly. The etchant can be kept warm by putting it into a bigger container of boiling water. Once all the unwanted copper has been removed, the PCB can be taken out of the etching liquid. Only the masked copper tracks of the circuit design will be left on the PCB. • The PCB must now be rinsed thoroughly with clean water. It is advisable to use a ceramic sink in which to rinse the boards, because ferric chloride will react with any metal, including stainless steel.
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Figure 2.26: Etching the PCB
• All holes can now be drilled with the correct size drill bit (from 0.8 mm to 1 mm). Be very careful when drilling, because the drill bits break very easily and they are reasonably expensive to replace. Try to use a high-speed dremmel drill. Also use standard high-speed steel or cobalt steel drill bits. • Once all the holes have been drilled, the mask covering the copper tracks can be scrubbed off with fine steel wool under running water. The mask must only be removed when you are ready to solder, because the exposed copper tracks oxidise quickly, making soldering on them very difficult and causing the tracks to rust. • The PCB is now ready to be populated with the Figure 2.27: Etched, components. A clear vanish can be sprayed over the drilled and cleaned PCB populated board to make the copper tracks nice and shiny, and also to provide a bit of insulation against shorts. Did you know? For ferric chloride, I’ve heard that you should neutralise the acid by adding a base (sodium carbonate, sodium hydroxide, or calcium carbonate). This also solidifies the liquid, and after drying, it can be disposed of as solid waste.
Precautions to be taken when making a PCB • Always wear an apron when working with ferric chloride because it will stain your clothes on contact. • Protective glasses are essential, as any chemical that comes into contact with your eyes may possibly lead to blindness. Also wear protective glasses during the drilling process. • Use gloves when doing the etching. The chemical will stain the skin and can cause skin irritations. • Work in a well-ventilated room. • Store all used ferric chloride in a big plastic container, with a lid, that can be disposed of by a special waste removal company when full. • Never work in metal containers; rather use plastic or ceramic. Ferric chloride attacks most metals.
Cleaning and tidying of the workshop (Housekeeping) Good housekeeping in a workshop simply means the orderly arrangement of tools, equipment, operations, storage facilities and materials. Put it in simpler words, housekeeping can be defined as everything in its place and a place for everything. Every user of the workshop must accept responsibility for cleaning and tidying the workshop after each practical session. It is not the responsibility of the educator to tell the learners to clean and tidy the workshop every time. Learners must also note that marks are awarded for housekeeping when they do their PAT, so the responsibility rests on the learner to get into good housekeeping habits.
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Tools and measuring instruments
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There is not much one can do about the inherent dangers that accompany some types of tasks, but there are many things that can and must be done to ensure safety in the workplace. Always ensure that equipment and materials are kept in their proper places and are easily accessible to all. A neat and organised workplace is a safer workplace, and a safer working environment allows for better results and a happier workforce, and saves time. All users of the workshop can ensure that: • the workshop remains clean and neat; • the equipment and materials are stored in their proper places; • the first-aid kit is easily accessible and contains the necessary medical items; • fire extinguishers are maintained and in good working order; • warning signs are visible and easily understood; • areas containing machinery are demarcated and clean; • walking paths are clearly indicated and obstacle-free; • poisonous materials are safely stored and used; • sharp tools are used with caution; • games and jokes have no place in the workplace; • smoking and drinking are prohibited in the workplace; • any materials or liquids that have been spilled are immediately cleared; and • any damaged or broken tools or machinery are immediately reported.
Keeping the storeroom neat and tidy Besides keeping the workshop neat and tidy, everybody using the workshop must also help to ensure that the storerooms are in good order. A neat and tidy storeroom is always a joy, because it makes it easy to find tools and equipment. It is very helpful if there is a special labelling system in the storeroom for the quick location of tools and equipment. Educators must note that the storeroom is not open to all, and that only designated learners may enter the storeroom with permission from the educator.
Figure 2.28: Tidy storeroom
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Activity 1 1. 2. 3. 4. 5. 6. 7.
What is the main difference between a manual ranging multimeter and an auto ranging multimeter? Name the THREE main components of the digital voltmeter found in the digital multimeter. In your own words, explain how to measure current with the aid of a digital multimeter. Name at least FOUR applications of digital multimeters. Name FIVE important aspects to be considered regarding the care and maintenance of digital multimeters. Why would we use an insulation tester instead of a digital multimeter to test the insulation of wires on a construction site? With reference to the picture below, identify the labelled parts and give a short explanation of each part. 1 2 3
8. 9.
Give FOUR applications of an insulation tester. Using the simple block diagram below, briefly explain the operation of a simple function generator.
Waveform generator
Amplitude and frequency adjust
Output
Power supply
10. Show, with the aid of a simple sketch, how you would measure current in a DC circuit. 11. What is the difference between measuring AC voltage with an oscilloscope and with a digital multimeter? 12. Give the function of the following controls with reference to the oscilloscope: Horizontal position control; Volt/Div control and Time/Div control. 13. Name THREE uses of an oscilloscope. 14. Name THREE important safety rules when working with hand or power tools. 15. Why is it important to wear protective glasses when using a jigsaw? 16. Name TWO safety aspects to consider when working with a bench grinder. 17. Name FOUR rules that must be remembered when soldering. 18. Why is it important for the tip of the soldering iron to be ‘tinned’? 19. Why is it important to work in a ceramic sink with plastic fittings when handling ferric chloride? 20. Name at least FIVE precautions that must be taken when you make a PCB.
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Chapter 3 Single-phase AC generation
A
A
Difference between AC and DC
Instantaneous voltages and currents
Generating singlephase AC
Average and RMS voltages
B
B
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Electrical Technology
Introduction AC electricity is created by an AC electric generator, which determines the frequency. It is simply generated by moving a conductor through a magnetic field. What is special about AC electricity is that the voltage can be readily changed, thus making it more suitable for long-distance transmission than DC electricity. AC electricity can also employ capacitors and inductors in electronic circuitry, allowing for a wide range of applications.
Difference between AC and DC Alternating current (AC) electricity is the type of electricity commonly used in homes and businesses throughout the world. While direct current (DC) electricity flows in one direction through a wire, AC electricity alternates its direction in a back-and-forth motion. The direction alternates between 50 and 60 times per second, depending on the electrical system of the country. • Direct current (DC) flows in one direction only through the circuit. • Alternating current (AC) flows first in one direction, then in the opposite direction through the current. The same definitions apply to alternating voltage (AC voltage): • DC voltage has a fixed polarity (constant amplitude). • AC voltage switches polarity back and forth (continually changing amplitude). There are numerous sources of DC and AC current and voltage. However: • Sources of DC are commonly shown as a cell or battery: • Sources of AC are commonly shown as an AC generator:
Basic single-coil AC generator An AC generator uses the principal of Faraday’s electromagnetic induction to convert a mechanical energy, such as the rotation of a coil, into electrical energy, a sinusoidal waveform. A simple generator consists of a pair of permanent magnets producing a fixed magnetic field between a north and a south pole. Inside this magnetic field is a single rectangular loop of wire that can be rotated around a fixed axis, allowing it to cut the magnetic flux at various angles as shown in the diagram.
Take note A conductor moving at 90° to a magnetic field will have maximum current induced.
Figure 3.1: Generating an alternating EMF
40
Single-phase AC generation
3
As the coil rotates anticlockwise around the central axis, which is perpendicular to the magnetic field, the wire loop cuts the lines of force set up between the north and south poles at different angles. The amount of induced electro-motive force (EMF) in the loop at any instant in time is proportional to the angle of rotation of the wire loop. As the loop rotates, electrons in the wire loop flow in one direction around the loop. When the wire loop moves across the magnetic lines of force in the opposite direction, the electrons in the wire loop flow in the opposite direction. The direction of the electron movement determines the polarity of the induced voltage. Thus, when the loop or coil rotates one complete revolution, or 360o, one full sinusoidal waveform is produced, with one cycle of the waveform being produced for each revolution of the coil. As the coil rotates within the magnetic field, the electrical connections are made to the coil by means of carbon brushes and slip-rings which are used to transfer the electrical current induced in the coil to an electrical circuit.
Sinusoidal waveform construction By plotting values out onto graph paper, a sinusoidal waveform shape can be constructed. In order to keep things simple, the instantaneous values for the sinusoidal waveform will be plotted at every 45o and a maximum value of 100 V will be assumed. Plotting the instantaneous values at shorter intervals, for example at every 30o, would result in a more accurate waveform. Coil Angle ( θ )
0
45
90
135
180
225
270
315
360
e = Vmax.sinθ
0
70.71
100
70.71
0
-70.71
-100
-70.71
-0
Take note A conductor moving parallel to a magnetic field will have zero current induced.
Figure 3.2: Graphic representation of a sine wave
The points on the sinusoidal waveform are obtained by projecting across from the various positions of rotation between 0o and 360o to the ordinate of the waveform that corresponds to the angle θ, and when the wire loop or coil rotates one complete revolution, or 360o, one full waveform is produced. From plotting the sinusoidal waveform, it can be seen that when θ is equal to 0o, 180o or 360o, the generated EMF is zero, as the coil cuts the minimum amount of lines of flux. But when θ is equal to 90o and 270o, the generated EMF is at its maximum value, as the maximum amount of flux is cut. The sinusoidal waveform has a positive peak at 90o and a negative peak at 270o. Positions B, D, F and H generate a value of EMF corresponding to the formula: e = Emax.sinθ.
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Electrical Technology The waveform shape produced by a simple, single-loop generator is commonly referred to as a sine wave and is said to be sinusoidal in its shape. This type of waveform is called a sine wave because it is based on the trigonometric sine function used in mathematics, Y = Asinθ . When dealing with sine waves in the time domain, and especially with current-related sine waves, the unit of measurement used along the horizontal axis of the waveform can be time, degrees or radians. In electrical engineering it is more common to use the radian as the angular measurement of the angle along the horizontal axis, rather than degrees. For example, ω = 100 rad/s, or 500 rad/s.
Radians Take note π Radians = 180° Half rotation 2 π Radians = 360° Full rotation
The Radian (rad) is defined mathematically as a quadrant of a circle where the distance subtended on the circumference equals the radius (r) of the circle. Since the circumference of a circle is equal to 2π x radius, there must be 2π radians around a 360o circle, so 1 radian = 360o/2π = 57.3o. In electrical engineering the use of radians is very common so it is important to remember the following formula.
2π rads = 360˚ ∴1 rad = 57.3˚
Figure 3.3: Graphical representation of a radian
Using radians as the unit of measurement for a sinusoidal waveform would give 2π radians for one full cycle of 360o. Then half a sinusoidal waveform must be equal to 1π radians or just π (pi). Then knowing that π is equal to 3.142 or 22÷7, the relationship between degrees and radians for a sinusoidal waveform is given as is set out below.
Relationship between degrees and radians Applying these two equations to various points along the waveform gives us: Radians =
π × degrees 180˚
Degrees =
180˚ π
× degrees
30˚ → Radians =
π (30˚) = π rad 180˚ 6
90˚ → Radians =
π (90˚) = π rad 180˚ 2
5π rad → Degrees = 180˚ (5π) = 225˚ 4 π 4 3π rad → Degrees = 180˚ (3π) = 270˚ 2 π 2
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Single-phase AC generation
3
Hence:
Electric field strength (H) Electric field strength is a quantitative expression of the intensity of an electric field at a particular location. The standard unit is the volt per meter (V/m or Vm-1). A field strength of 1 V/m represents a potential difference of one volt between points separated by one meter. Any electrically charged object produces an electric field. This field has an effect on other charged objects in the vicinity. The field strength at a particular distance from an object is directly proportional to the electric charge, in coulombs, on that object. H = ampere/meter Example: A coil with non-magnetic core has 150 turns and draws a current of 1,25 ampere. Calculate the magneto-motive force (mmf) and magnetic field strength if the length of the core is 15 cm. Given: N = 150; I = 1,25 A; ℓ = 15 cm = 0,15 m (Always use standard values in calculations) mmf = N I = 150 × 1,25 = 187.5 ampere H = mmf/ℓ = 187, 5 0,15 = 1 250 ampere/m
Take note Coulomb is the quantity of electricity transported in a second by a current of 1 ampere.
Take note N – Number of turns I – Current ℓ – Length, in metres A –Area, in metres2
Magnetic flux (Φ) The magnetic flux through a surface refers to the number of magnetic field lines, or magnetic flux, which pass through a given cross-sectional area. It can be calculated using the formula: Φ = BA where: • Φ is the number of flux lines, measured in webers (Wb) • B is the magnetic field strength, measured in tesla (T) • A is the cross-sectional area, measured in m2
Flux density (B) An alternative expression for the intensity of an electric field is electric flux density. This refers to the number of lines of electric flux passing at right angles through a given
Take note Flux density Wb/m2 = Teslas
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Electrical Technology surface area, usually one metre squared (1 m2 ). Flux density can simply be defined as the flux per unit area and is measured in webers per square metre. The unit for flux density is the ‘tesla’. Electric flux density, like electric field strength, is directly proportional to the charge on the object. Flux density decreases as the distance from the source increases.
Remember A = metres2 A = 9 cm2 9 m2 A = ______ 10 000 = 900 × 10-6 m2
Example: A bar magnet with a cross-sectional area of 9 cm² has a flux density of 3 Wb/m². Calculate the flux at each pole. Given: A = 9 cm² = 900 × 10-6 m² ; B = 3 tesla Φ = BA = 3 × (900 × 10-6) = 2,7 mWb (milliweber)
The sinusoidal AC waveform
current or voltage
The most common AC waveform is a sine (or sinusoidal) waveform.
degrees period
Figure 3.4: Sine waveform
The vertical axis represents the amplitude of the AC current or voltage, in amperes or volts. The horizontal axis represents the angular displacement of the waveform. The units can be time, degrees or radians. The period (T) of the sinusoidal AC waveform is the time that it takes to complete one cycle in seconds. The frequency (f) of the sinusoidal AC waveform is the number of cycles completed in one second and it is measured in Hertz (Hz). The frequency or period of an AC waveform can therefore be calculated by using the following formulas: Frequency: f = 1/T (measured in Hz), and Period: T = 1/f (measured in seconds)
Instantaneous current Instantaneous values refer to the exact current induced at a specific angle of rotation in the conducting loop. If it was possible to “freeze” the rotation at a certain angle, the instantaneous value would be the current induced at that exact instant.
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current
Single-phase AC generation
3
degrees
Figure 3.5: Instantaneous current
i = Ipsin q OR i = Im Sinθ (Amperes) where i = instantaneous current in amperes Ip or Im = the maximum, or peak, current in amperes q = the angular displacement in degrees or radians
Instantaneous voltage Instantaneous values of voltage refer to the exact voltage (emf) at the end terminals of the rotating loop at a specific moment. Once again, if the rotation were “frozen” it would be the emf (voltage) at the terminals at an exact angle, and hence at the instant.
voltage
Vp or Vm
degrees
Figure 3.6: Instantaneous voltage
e = Vpsin q OR e = Vm Sinθ (Volts) where e = instantaneous voltage in volts Vp or Vm = the maximum, or peak, voltage in volts q = the angular displacement in degrees or radians
Peak vs peak-to-peak voltage Peak voltage is the voltage measured from the baseline of an AC waveform to its maximum, or peak, level. Unit: Volts peak (Vp) Symbol: Vp Peak-to-peak voltage is the voltage measured from the maximum positive level to the maximum negative level. Unit: Volts peak-to-peak (Vp-p) Symbol: Vp-p
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Electrical Technology Peak and peak-to-peak values are most often used when measuring the amplitude of AC waveforms directly from an oscilloscope display.
Figure 3.7: Peak vs peak-to-peak voltages
EMF induced in a conductor The amount of EMF induced into a single conductor cutting the magnetic lines of force is determined by the following three factors: • Speed – the speed at which the coil rotates inside the magnetic field (v). • Strength – the strength of the magnetic field (B). • Length – the length of the coil or conductor passing through the magnetic field (ℓ). Thus:
EMF = Bℓv sinθ
where Bℓv is the maximum (peak value) of the sine wave and θ is the rotational angle. To calculate the EMF induced into a single loop, the following formula is used: EMF = 2πBAn sinθ volt Where: A = the area of the loop (length × width) and n = the rotational speed in r/sec When there are more loops (coils), one needs to multiply EMF × N EMF = 2πBAnN sinθ volt, where N is the number of turns Example: A 30 cm long conductor moves perpendicularly through a magnetic field with a flux density of 0,08 T at a speed of 50 m/s. Calculate the EMF. Given : ℓ= 30 cm = 0,3 m; B = 0,08 T; V = 50 EMF = Bℓv sinθ = 0,08 × 0,3 × 50 × sin 90 = 1,2 volt Example: A coil with 200 turns has an area of 50 cm² and rotates at a speed of 1200 r/min in a magnetic field with a density of 0,5 Tesla. Calculate: (a) Frequency (b) EMF (c) Instantaneous value at an angle of 45 degrees
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Single-phase AC generation
3
Given: n = 1200 r/min; B = 0,5 T; N = 200; θ = 45˚ A = 50 cm2 a) f = revolutions/sec = 1200/60 = 20 rev/sec b) EMF = 2πBAnN sinθ = 2π × (0,5) × (5 × 10-3) × (20) × (200) × (sin 90) = 62,83 volt c) e = EMF sin 45 = 62,83 sin 45 = 44.43 volt
Root-mean-square (RMS) voltage RMS voltage is the amount of DC voltage that is required for producing the same amount of power as the AC waveform. Unit: Volts (V) Symbol: Vrms
Take note RMS refers to the heat generated in an AC circuit that would be exactly the same as the heat generated in an equivalent DC circuit.
The RMS voltage of a sinusoidal waveform is equal to 0.707 times its peak value. VRMS = 0.707 Vp
Figure 3.8: RMS voltage
AC levels are assumed to be expressed as RMS values unless clearly specified otherwise.
Average voltage Average voltage is the average value of all the values for one half-cycle of the waveform. Unit: Volts average (Vave) Symbol: Vave
Take note These values for RMS (0,707) and AVE (0,637) are only applicable to pure sine waves.
The average voltage of a sinusoidal waveform is equal to 0.637 times its peak value. Vave = 0.637 Vp
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Electrical Technology
Figure 3.9: Average voltage
Example An AC signal has a peak value of 75 V. Calculate the RMS and average value for this signal. Take note A 2 pole synchronous motor must turn at 3000 rpm to give 55 Hz. A 4 pole synchronous motor must turn at 1500 rpm to give 50 Hz.
VRMS = 0,707 Vp = 0.707 × 75 = 53.02 V Vave = 0,637 Vp = 0.637 × 75 = 47.78 V
Area of a coil When a current carrying conductor is formed into a loop or several loops to form a coil, a magnetic field develops around the coil. The magnetic field circling each loop of wire combines with the fields from the other loops to produce a concentrated field down the centre of the coil. The magnetic field is essentially uniform down the length of the coil when it is wound tighter. The strength of this coils’ magnetic field can be increased or decreased accordingly by increasing or decreasing the area of the coil. If we increase the area of the coil the magnetic field will intensify and if we decrease the area of the coil, the magnetic field will become weaker.
Pole pairs (P) and the number of windings (n) We know that the frequency of a supply is the number of times a cycle appears in one second and that frequency is measured in Hertz. f = hertz As one cycle of induced EMF is produced each full revolution of the coil through a magnetic field comprising of a north and south pole, as seen in figure 3.1, then if the coil rotates at a constant speed, a constant number of cycles will be produced per second, giving a constant frequency. So by increasing the speed of rotation of the coil, the frequency will also be increased. Therefore, frequency is proportional to the speed of rotation ( ƒ α n ), where n = rev/sec. Also, the simple, single-coil generator (figure 3.1) has only one north and one south pole, giving just one pair of poles. If more magnetic poles are adde to the generator in figure 3.1 so that it now has four poles in total, two north and two south, then
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Single-phase AC generation
3
for each revolution of the coil, two cycles will be produced for the same rotational speed. Therefore, frequency is proportional to the number of pairs of magnetic poles (ƒ ∞ p ) of the generator, where p = the number of “pairs of poles”. From these two facts it can be said that the frequency output from an AC generator is: f = n × p cycles/sec Frequency: f = n × p cycles/sec Where: n = the speed of rotation in rev/sec p = the number of “pairs of poles” 60 = the formula constant that converts rpm to to rps (cycles/sec, i.e. Hertz). Example What is the frequency of a four-pole generator if its rotor turns at a speed of 3600 rpm? f = pn/60 = 2 × 3 600/60 = 120 Hz
Lamination of core A magnetic core is a piece of magnetic material with a high permeability used to concentrate and guide magnetic fields in electrical, electromechanical and magnetic devices such as electromagnets, transformers, electric motors, inductors and magnetic assemblies. The induction of eddy currents within the core causes a resistive loss. Lamination of the core material can reduce eddy current loss, as can making the core from a magnetic, non-conductive material, such as ferrite.
Take note Laminations are thin, insulated metal strips put together to form a metal core.
A solid metal core will have a low resistance, and a big induced current. But induced arrest always opposes applied current, making the coil inefficient. By laminating the core, a current would be induced in each of the metal strips, but the sum of all these included “eddy currents” is only a fraction when compared to that current induced in a solid core. This makes the coil far more effective and efficient.
Activity 1 1. 2. 3. 4. 5. 6. 7.
What is the peak-to-peak value of a sinusoidal waveform that has a peak value of 12 V? What is the peak value of a sine wave that has a peak-to-peak value of 440 V? Determine the RMS value of a waveform that measures 15 Vp. Determine the peak value of 240 V. (Hint: Assume 240 V is in RMS.) Determine the average value of a waveform that measured 16 Vp. What is the peak value of a waveform that has an average value of 22.4 V? A coil with 300 turns around a wooden core has a circumference of 40 cm. The cross-sectional area of the ring is 5 cm². Calculate: 7.1 magnetic field strength at a current of 5 ampere. 7.2 flux, if flux density is 4,7 mT.
Take note The 240 V at our plugs in our homes is already an RMS value.
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Electrical Technology 8. 9. 10. 11. 12. 13.
50
A conductor with a length of 450 mm moves at a speed of 8 m/s through a magnetic field with a density of 1,5 Tesla. Calculate the EMF. What is the frequency of a four-pole generator if its rotor turns at a speed of 1 500 rpm? What determines the frequency of a generator? Convert the following degrees to radians: 300, 450, 900, 1 800. Convert the following radians to degrees: 1π/2, 3π/4, 5π/4. What is the main difference between a RMS voltage and an average voltage?
Chapter 4 Single-phase transformers
A
A
Magnetic induction
Types of transformers
Operation of transformers
Power calculations
B
B
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Electrical Technology
Single-phase transformers Introduction A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors – the transformer’s coils. A transformer is defined as an electrical component that increases or decreases AC voltage or current efficiently.
Magnetic induction
Remember A transformer steps voltage up or down, and current down or up.
Before one looks at transformers, it is necessary to revise magnetism, as the fundamental principles of transformers are based on magnetism. In electromagnetism, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in the current in a circuit. This property is also called self-inductance to distinguish it from mutual inductance, which describes the voltage induced in one electrical circuit by the rate of change of the electric current in another circuit. The quantitative definition of the self-inductance L of an electrical circuit in SI units (webers per ampere, known as henries) is e = -L di volts dt Where: e = the voltage in volts, and i = the current in amperes di = rate of change of current in amperes/sec. dt
Lenz’s law
Take note Lenz’s Law made simple… An induced current will always oppose the applied current.
Lenz’s law, in electromagnetism, states that an induced electric current flows in a direction such that the current opposes the change that induced it. This law was deduced in 1834 by the Russian physicist Heinrich Friedrich Emil Lenz (1804–65). Moving a pole of a permanent bar magnet through a coil of wire, for example, induces an electric current in the coil; the current in turn sets up a magnetic field around the coil, making it a magnet. Lenz’s law indicates the direction of the induced current. Because like magnetic poles repel each other, Lenz’s law states that when the north pole of the bar magnet is approaching the coil, the induced current flows in such a way as to make the side of the coil nearest the pole of the bar magnet itself a north pole to oppose the approaching bar magnet. Upon withdrawing the bar magnet from the coil, the induced current reverses itself, and the near side of the coil becomes a south pole to produce an attracting force on the receding bar magnet.
Magneto-motive force Magneto-motive force (mmf) (SI Unit: Ampere) is any physical driving (motive) force that produces magnetic flux. In this context, the expression “driving force” is used in a general sense of “work potential”. The magneto-motive force of wire is given by:
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in an inductor or electromagnet consisting of a coil
Single-phase transformers
4
Where: N = the number of turns of wire in the coil, and I = the current in the wire The henry (symbol H) is the SI unit of inductance. If the rate of change of current in a circuit is one ampere per second and the resulting electro-motive force is one volt, then the inductance of the circuit is one henry. H = IN l Where: IN = the magneto-motive force in amperes, and ℓ = the length of the core in metres.
Mutual inductance
Self-inductance is the current induced in the coil itself. Mutual inductance is the current that is induced in a second coil placed close by.
Electromagnetic induction is the production of an electric current in a conductor moving through a magnetic field. It underlies the operation of transformers. Michael Faraday states that the electro-motive force (EMF) produced around a closed path is proportional to the rate of change of the magnetic flux through any surface bounded by that path. In practice, this means that an electric current will be induced in any closed circuit when the magnetic flux through a surface bounded by the conductor changes. This applies whether the field itself changes in strength or the conductor is moved through it. A varying current in the first (or primary) winding creates a changing magnetic field in the transformer’s core and thus a varying magnetic field through the secondary winding. This varying magnetic field induces a varying electro-motive force (EMF), or “voltage”, in the secondary winding. This effect is called mutual induction.
Figure 4.1: Induction of a lower output voltage by means of mutual induction
Function and operation of transformers The main function of any transformer is to take a high voltage and convert it to a lower voltage value (step-down transformer) or to take a lower voltage and convert it into a higher voltage (step-up transformer). Depending on the application of the transformer, it can also be used to increase or decrease current. In some instances, a transformer can also be used as an isolation transformer, where the secondary is electrically isolated from the supply.
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Electrical Technology Take note. The stepping up or down of voltages and currents cannot happen independently of each other. The primary power and the secondary power of a transformer is the same, so as voltage increases, current will decrease accordingly. In other words, if the voltage is doubled the current will be halved. Basic transformer operation • A transformer consists of two coils, a primary and a secondary, and a core to support the two coils. • These two coils are not electrically connected. • The basic operation of the transformer is based on mutual induction. • An AC voltage is applied across the primary coil. • A magnetic field (flux) builds up and collapses in the primary coil. • This building up and collapsing of the magnetic flux in the primary coil cuts the windings of the secondary coil, inducing an alternating voltage in the secondary coil. • This induced secondary voltage can be more or it can be less than the supply voltage. Transformers come in a range of sizes, from a thumbnail-sized coupling transformer hidden inside a stage microphone to gigawatt units used to interconnect large portions of national power grids, all operating on the same basic principles and with many similarities in their parts.
Types of transformers Transformer classification Transformers are adapted to numerous engineering applications and may be classified in many ways: • by power level (from fraction of a watt to many megawatts), • by application (power supply, impedance matching, circuit isolation), • by frequency range (power, audio, RF), • by voltage class (a few volts to about 750 kilovolts), • by cooling type (air-cooled, oil-filled, fan-cooled, water-cooled, etc.), • by purpose (rectifier, arc furnace, amplifier output, etc.), and • by ratio of the number of turns in the coils. • Step-up The secondary has more turns than the primary.
AC Supply
Load
Figure 4.2: Step-up transformer
• Step-down The secondary has fewer turns than the primary.
AC Supply
Figure 4.3: Step-down transformer
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Load
Single-phase transformers
4
• Isolating Intended to transform from one voltage to the same voltage. The two coils have approximately equal numbers of turns, although often there is a slight difference in the number of turns, in order to compensate for losses (otherwise the output voltage would be a little less than, rather than the same as, the input voltage).
AC Input
AC Output
Figure 4.4: Isolating transformer
• Variable (Autotransformer) The secondary has an adjustable number of turns which can be selected without reconnecting the transformer. This transformer has a section of its winding common to both the primary and the secondary. The primary cannot be electrically isolated from the secondary.
Figure 4.5: Variable transformer
Losses Transformers are very efficient devices and the ideal transformer is said to be 100% efficient, i.e. there is no energy loss (output power = input power). Large power transformers (around 100 MVA and larger) may attain an efficiency as high as 99%. Small transformers, used to power small consumer electronics, may be less than 85% efficient. In general, transformer losses are produced by the electrical current flowing in the coils and the magnetic field alternating in the core. The losses associated with the coils are called the load losses, while the losses produced in the core are called noload losses.
Types of losses Copper or heat losses, or I2R losses, in the winding materials contribute the largest part of the load losses. They are created by the resistance of the conductor to the flow of current. The electron motion causes the conductor molecules to move and produce friction and heat.
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Electrical Technology Hysteresis losses (iron losses) come from the molecules in the core laminations resisting being magnetized and demagnetized by the alternating magnetic field. This resistance by the molecules causes friction that results in heat. The Greek word, hysteresis, means “to lag” and refers to the fact that the magnetic flux lags behind the magnetic force. Choice of size and type of core material reduces hysteresis losses. The biggest contributor to no-load losses is hysteresis losses. Eddy current losses (stray losses) occur when stray currents are created by induction in the iron or steel core of the transformer. These stray currents create small magnetic fields that oppose the magnetic field that induced the eddy currents in the first place. (They are creating a back EMF which opposes the original magnetic field.) It is for this reason that eddy current must be kept as small as possible. Eddy current losses can be reduced by electrically insulating a stack of plates in the core from each other, rather than using a solid block as a core. All transformers operating at low frequencies use laminated or similar cores. Thinner lamination of the core steel also reduces eddy current losses. Electric losses are the losses in the insulating material, which is a factor only in particular cases of very high voltage transformers.
Transformer construction and core types A transformer consists of a laminated core and two coils of windings. The core is laminated to limit eddy currents. Eddy currents are unwanted currents induced into the core as a result of alternating magnetic flux. Since the core forms a close loop, these currents can reach very high values, which result in a considerable amount of heat loss. Laminations are thin metal discs insulated from each other by enamel or varnish.
Figure 4.6: E and I laminating cores
Core shape Transformers used at power or audio frequencies have cores made of many thin laminations of silicon steel. By concentrating the magnetic flux, more of it is usefully linked by both primary and secondary windings. Since the steel core is conductive, it too has currents induced in it by the changing magnetic flux. Each layer is insulated from the adjacent layer to reduce the energy lost to eddy current heating of the core. A typical laminated core is made from E-shaped and I-shaped pieces, leading to the name “EI transformer”. Air core inductor The term air core coil describes an inductor that does not use a magnetic core made of a ferromagnetic material. The term refers to coils wound on plastic, ceramic, or other nonmagnetic forms, as well as those that actually have air inside the windings. Air core coils have lower inductance than ferromagnetic core coils, but are often used at high frequencies because they are free from the energy losses, called core losses, that occur in ferromagnetic cores, and which increase with frequency.
Figure 4.7: Air core
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Figure 4.8: Air core transformer
Single-phase transformers
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Solid cores In circuits that operate above mains frequencies – up to a few tens of kilohertz, such as switch-mode power supplies – powdered iron cores are used. These materials combine a high magnetic permeability with a high bulk material resistivity. At even higher frequencies (typically radio frequencies) other types of core made of nonconductive magnetic materials, such as various ceramic materials called ferrites, are common. Some transformers in radio-frequency circuits have adjustable cores which allow tuning of the coupling circuit. Toroidal cores Toroidal transformers are built around a ring-shaped core, which is made from a long strip of silicon steel or permalloy wound into a coil, or from ferrite, depending on frequency. The strip construction ensures that all the grain boundaries are pointing in the optimum direction, making the transformer more efficient by reducing the core’s reluctance. The ring shape eliminates the air gaps inherent in the construction of an EI core. The cross-section of the ring is usually square or rectangular, but more expensive cores with circular cross-sections are also available. The primary and secondary coils are wound concentrically to cover the entire surface of the core. This minimises the length of wire needed, and also provides screening to prevent the core’s magnetic field from generating electromagnetic interference.
Figure 4.9: Solid core transformer
Figure 4.10: Toroidal cores
Ferrite cores are used at frequencies up to a few tens of kilohertz to reduce losses, particularly in switch-mode power supplies. Toroidal transformers are more efficient (around 95%) than the cheaper laminated EI types. Other advantages, compared to EI types, include smaller size (about half), lower weight (about half), less mechanical hum (making them superior in audio amplifiers), lower exterior magnetic field (about one tenth), low off-load losses (making them more efficient in standby circuits), single-bolt mounting, and more choice of shapes. This last point means that, for a given power output, either a wide, flat toroid or a tall, narrow one with the same electrical properties can be chosen, depending on the space available. The main disadvantage is higher cost. A drawback of toroidal transformer construction is the higher cost of windings. As a consequence, toroidal transformers are uncommon above ratings of a few kVA. Small distribution transformers may achieve some of the benefits of a toroidal core by being split and forced open, and having a bobbin containing primary and secondary windings inserted. When fitting a toroidal transformer, it is important to avoid making an unintentional short-circuit through the core. This can happen if the steel mounting bolt in the middle of the core is allowed to touch metalwork at both ends, which could result in a dangerously large current flowing through the bolt.
Transformer applications Ideal transformer An ideal transformer is shown in the figure below. Current passing through the primary coil creates a magnetic field. The primary and secondary coils are wrapped around a core of very high magnetic permeability, such as iron, so that most of the magnetic flux passes through both the primary and secondary coils. An ideal transformer would have no losses, and would therefore be 100% efficient.
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Figure 4.11: Core type transformer
Take note Transformers alone cannot do the following: • Convert DC to AC or vice versa; • Change the voltage or current of DC; • Change the AC supply frequency.
Due to the high cost of distributing electricity at low voltage and high current levels, transformers fulfil a most important role in electrical distribution systems. Electricity suppliers (e.g. Eskom) distribute electricity over large areas using high voltages, commonly called transmission voltages. Transmission voltages are normally in the 35,000 volt to 50,000 volt range. Remember that volts times amps equals watts, and that wires are sized based upon their ability to carry amps. High voltage allows the electricity suppliers to use small sizes of wire to transmit high levels of power, or watts. Transmission lines can be recognized because they are supported by the very large steel towers that are seen around utility powerplants and substations. As this electricity gets closer to its point of use, it is converted, through the use of transformers, to a lower voltage, normally called distribution voltage. Distribution voltages range from 2,400 to 25,000 volts depending upon the electricity suppliers. Distribution lines are the ones that feed the polemount and padmount transformers located closest to your home or place of business. These transformers convert the distribution voltages to what we call utilization voltages. Utilization voltages are normally below 600 volts and are either single-phase or three-phase and are utilized for operating equipment, from the light bulbs and vacuum cleaners in our homes to the electric motors and elevators where we work. Autotransformers An autotransformer has only a single winding, which is tapped at some point along the winding. AC or pulsed voltage is applied across a portion of the winding, and a higher (or lower) voltage is produced across another portion of the same winding. For voltage ratios not exceeding about 3:1, an autotransformer is less costly, lighter, smaller and more efficient than a two-winding transformer of a similar rating.
Figure 4.12: Autotransformer
By exposing part of the winding coils and making the secondary connection through a sliding brush, an autotransformer with a variable turns ratio can be obtained, allowing for very small increments of voltage.
Figure 4.13: Autotransformer
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Centre-tapped transformer A centre-tap is a connection made to a point halfway along a winding of a transformer. Volts centre-tapped (VCT) describes the voltage output of a centretapped transformer. For example: a 24 VCT transformer will measure 24 VAC across the outer two taps (winding as a whole), and 12 VAC from each outer tap to the centre-tap (half-winding). These two 12 VAC supplies are 180 degrees out of phase with each other, thus making it easy to derive positive and negative 12 volt DC power supplies from them.
12V AC AC Input
24V AC 12V AC
Figure 4.14: Centre-tap transformer
In a rectifier, a centre-tapped transformer and two diodes can form a full-wave rectifier that allows both half-cycles of the AC waveform to contribute to the direct current, making it smoother than a half-wave rectifier.
Figure 4.15: A centre-tap transformer used in a rectifier circuit
Current transformer (CT) A current transformer (CT) is a measurement device designed to provide a current in its secondary coil proportional to the current flowing in its primary coil. Current transformers are commonly used in metering and protective relays in the electrical power industry where they allow safe measurement of large currents, often in the presence of high voltages. The current transformer safely isolates measurement and control circuitry from the high voltages typically present on the circuit being measured.
Take note 100:5 is a common CT ratio.
The CT is typically described by its current ratio from primary to secondary. For example, a 4000:5 CT would provide an output current of 5 amperes when the primary was passing 4000 amperes. Care must be taken not to disconnect the secondary winding from its load while current flows in the primary, as this will produce a dangerously high voltage across the open secondary and may permanently affect the accuracy of the transformer. An instrument that uses a CT is a clamp meter. In electrical and electronic engineering, a current clamp or current probe is an electrical device that has two jaws which open to allow clamping around an electrical conductor. This allows properties of the electric current in the conductor to be measured, without having to make physical contact with it, or having to disconnect it for insertion through the probe.
Figure 4.16: Clamp meter
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Figure 4.17: Connecting a current transformer (CT) to a circuit Take note Common PT ratios are: 10:1 20:1 40:1 80:1 100:1 120:1 And higher
Voltage transformers (VT) A voltage transformer (VT) or potential transformer (PT) is another type of instrument transformer used for metering and protection in high-voltage circuits. These transformers are designed to present negligible load to the supply being measured and to have a precise voltage ratio to accurately step down high voltages so that metering and protective relay equipment can be operated at a lower potential. Typically the secondary of a voltage transformer is rated for 69 V or 120 V at rated primary voltage, to match the input ratings of protective relays.
0 - 240 V AC voltmeter range
Figure 4.18: Connecting a potential (voltage) transformer (PT) to a circuit
Remember PTs and CTs allow us to measure high voltages and currents with lowrated instruments.
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Applications of transformers • Transformers are used for electric power transmission over long distances. • They are used in high-voltage, direct-current (HVDC) power transmission systems. • Large, specially constructed power transformers are used for the electric arc furnaces used in steelmaking.
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• Rotating transformers are designed so that one winding turns while the other remains stationary. A common use was the video-head system as used in VHS and Beta video-tape players. These can pass power or radio signals from a stationary mounting to a rotating mechanism, or radar antenna. • Sliding transformers can pass power or signals from a stationary mounting to a moving part, such as a machine tool head. An example is the linear variable differential transformer. • Some rotary transformers are precisely constructed in order to measure distances or angles. Usually they have a single primary and two or more secondary coils. Electronic circuits measure the different amplitudes of the currents in the secondary coils, such as in synchros and servos. • Small transformers are often used to isolate and link different parts of radio receivers and audio amplifiers, converting high current low voltage circuits to low current high voltage, or vice versa. • Balanced-to-unbalanced conversion: A special type of transformer called a balun is used in radio and audio circuits to convert between balanced circuits and unbalanced transmission lines such as antenna downleads. A balanced line is one in which the two conductors (signal and return) have the same impedance to ground: twisted pair and “balanced twin” are examples. Unbalanced lines include coaxial cables and strip-line traces on printed circuit boards. A similar use is for connecting the “single-ended” input stages of an amplifier to the highpowered “push-pull” output stage.
Transformer calculations (Ratio calculations) A simple transformer consists of two electrical conductors called the primary winding and the secondary winding.
Figure 4.19: Basic transformer information
If a load is connected to the secondary, an electric current will flow in the secondary winding and electrical energy will be transferred from the primary circuit through the transformer to the load. In an ideal transformer, the induced voltage in the secondary winding (Vs) is in proportion to the primary voltage (Vp), and is given by the ratio of the number of turns in the secondary (Ns) to the number of turns in the primary (Np) as follows: Is = __ Np V __p =__ Vs Ip Ns By appropriate selection of the ratio of turns, a transformer allows an alternating current (AC) voltage to be “stepped up” by making Ns greater than Np, or “stepped down” by making Ns less than Np.
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Electrical Technology This leads to the most common use of the transformer: to convert electrical energy at one voltage to a different voltage by means of windings with different numbers of turns. Not accounting for losses, for a given level of power transferred through a transformer, current in the secondary circuit is inversely proportional to the ratio of secondary voltage to primary voltage (or the secondary turns to primary turns). Example Suppose a transformer with a rating of 50 W and a windings ratio of 25:2 delivers a secondary voltage of 12 V. First we need to determine the current in the circuit. With the values given it is only possible to calculate the secondary current Is. Given: Np = 25, Ns = 2, Ps = 50 W, Vs = 12 V Ps
= Vs × Is
Is
= ____ Ps Vs
Is
= ____ 50 12
Is
= 4,17 ampere
Now that we have the secondary current, we can calculate the primary current. When calculating, write down the “wanted” first (Ip), followed by rest of formula: Ip ____ Is
= ____ Ns Np
Ip
= _________ Ns × Is Np
Ip
= 2 × 4,17 25
Ip
= 333,33 mA
In a practical transformer, the higher-voltage winding will have more turns of thinner wire than the lower-voltage windings.
Transformer rating and calculations VA Ratings Volt-ampere (VA) is a measurement of power in a direct current electrical circuit. The VA specification is also used in alternating current circuits, but is less precise in this application, because it represents apparent power, which often differs from true power. In a DC circuit, 1 VA is the equivalent of one watt (1 W). The power, P (in watts) in a DC circuit is equal to the product of the voltage V (in volts) and the current I (in amperes): P = VI
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In an AC circuit, power and VA mean the same thing only when there is no reactance. Reactance is introduced when a circuit contains an inductor or capacitor. Because most AC circuits contain reactance, the VA figure is greater than the actual dissipated or delivered power in watts. This can cause confusion in specifications for power supplies. For example, a supply might be rated at 600 VA. This does not mean it can deliver 600 watts, unless the equipment is reactance-free. In real life, the true wattage rating of a power supply is 1/2 to 2/3 of the VA rating. A transformer is not considered a load, therefore the power rating allocated to a transformer is called apparent power (Papp) and is measured in kVA (kilo-voltampere). The apparent power is the vector sum of real and reactive power. The apparent power is the magnitude of the complex power. Pact
Papp
Preac
Real power (Pact) Reactive power (Preac) Apparent power (Papp) Phase of Current (θ)
Pact = V × I (kVA) Apparent Papp = Ps × cos θ (kW) Active or true Preac = Ps × sin θ (kVAr) Reactive Figure 4.20: Power relationship in transformers
Summary on power • Power dissipated by a load is referred to as true power. True power (Pact ) is symbolised by the letter P and is measured in the unit of watts (W or kW). • Power merely absorbed and returned in load due to its reactive properties is referred to as reactive power. Reactive power (Preac ) is symbolised by the letter Q and is measured in the unit of Volt-Amps-Reactive (VAr or kVAr). • Total power in an AC circuit, both dissipated and absorbed/returned is referred to as apparent power. Apparent power (Papp) is symbolised by the letter S and is measured in the unit of Volt-Amps (VA or kVA). • These three types of power are trigonometrically related to one another. In a right triangle, P = adjacent length, Q = opposite length, and S = hypotenuse length. Power factor The ratio between real power and apparent power in a circuit is called the power factor. It is a practical measure of the efficiency of a power distribution system. For two systems transmitting the same amount of real power, the system with the lower power factor will have higher circulating currents due to energy that returns to the source from energy storage in the load. These higher currents produce higher losses and reduce overall transmission efficiency. A lower power factor circuit will have a higher apparent power and higher losses for the same amount of real power.
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Electrical Technology The power factor is normally a number between 0 and 1. This is just a dimensionless number. A high power factor is generally desirable in a transmission system to reduce transmission losses and improve voltage regulation at the load. It is often desirable to adjust the power factor of a system to near 1. The power factor is normally represented by the following formula: cos θ = Pact ____ Papp
Remember cos θ = 0,6 Never substitute cos 0,6 into the formula.
Example An inductive load works at a power factor of 0.6 lagging. The load draws a current of 12 amperes from a transformer with output voltage of 500 volt. Calculate: a) the rating of the transformer. b) the power consumed by the load. c) the reactive power. Given: cos θ = 0,6 ; Is = 12 A ; Vs = 500 V a)
Papp = V × I = 500 × 12 = 6 000 VA = 6 kVA
b)
Pact = V × I × cos θ = 500 × 12 × 0,6 = 3 600 Watt = 3,6 kW
c)
Preac
Preac = Papp sin θ OR Pr = √ Ps2 – Pa2 cos θ = 0,6 θ = 53,13 sin 53,13 = 0,8 Preac = 6 000 × 0,8 = 4 800 VAr = 4,8 kVAr Figure 4.21: Phasor diagram for components of power
Activity 1 1. 2.
3.
4. 5. 6.
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The turns ratio of a single-phase transformer is 75:3. Calculate the secondary voltage when the transformer is connected to 220 V AC supply. A single-phase step-down transformer is rated at 100 kVA and has a turn ratio of 10:1. Neglect losses and calculate: 2.1 secondary voltage if the primary voltage is 2 600 V. 2.2 secondary current is primary current is 30 A. A 11 kV /220 V single-phase step-down transformer has 3 000 primary turns. Neglect losses and calculate: 3.1 the transformer ratio. 3.2 number of secondary turns. 3.3 the primary current if the secondary of the transformer draws 1 500 amperes. How are eddy currents limited in transformers? Name 4 types of cores used in transformers. Draw a neatly labelled diagram of a single-phase transformer connected to 220 V AC supply. The load is a 1 K resistor. Label all voltages and currents.
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7. 8. 9. 10. 11. 12.
Define induction. Describe mutual induction with reference to transformers. Why are transformers not 100% efficient? Name four types of losses associated with transformers. Name three types of transformers and an application for each one. Calculate the voltage output by the secondary winding of a transformer if the primary voltage is 35 volts, the secondary winding has 4 500 turns, and the primary winding has 355 turns. Vsecondary = 13. Calculate the load current and load voltage in this transformer circuit:
Iload =
Vload =
14. Calculate the number of turns needed in the secondary winding of a transformer to transform a primary voltage of 300 volts down to a secondary voltage of 180 volts, if the primary winding has 1 150 turns of wire. Nsecondary = 15. Predict how all component voltages and currents in this circuit will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults): Fuse
V1
• • • •
T1 Load
Transformer T1 primary winding fails because of an open circuit. Transformer T1 primary winding fails because of a short circuit. Transformer T1 secondary winding fails because of an open circuit. Load fails shorted because of a short circuit.
For each of these conditions, explain why the resulting effects will occur. 16. Suppose 1 200 turns of copper wire are wrapped around one portion of an iron hoop, and 3 000 turns of wire are wrapped around another portion of that same hoop. If the 1 200-turn coil is energized with 15 volts AC (RMS), how much voltage will appear between the ends of the 3 000-turn coil? 17. Calculate the voltage output by the secondary winding of a transformer if the primary voltage is 230 volts, the secondary winding has 290 turns, and the primary winding has 1 120 turns. Vsecondary =
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18. Calculate the source current and load current in this transformer circuit:
Load 3,9 kΩ
Isource = Iload =
Practical Activity: 1 Wiring of single-phase transformer to mains supply Form of activity: Simulation Material and equipment: • Transformer with Prim 240 V/50 Hz and Sec 12-0-12. • Connecting wires • 2 Voltmeters (multimeter) Instructions: 1. Wire the circuit according to the diagram given.
2. Record all readings on the table provided. V1 = VPRIM = voltage of the supply V2 = VSEC = voltage of load (secondary)
RECORDING OF METER READINGS V1 (PRIM) V2 (SEC)
CONCLUSION: What do you observe and conclude from the readings?
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Practical Activity: 2 Measure primary and secondary voltage and current of transformer connected to load Form of activity: Simulation Material and equipment: • Transformer with Prim 240 V/50 Hz and Sec 12-0-12. • Connecting wires • 2 Voltmeters (multimeters) • 2 Ammeters (multimeters) • Fixed Resistor • Variable resistor Instructions: 1. Wire the circuit according to the diagram given.
2. Record all readings overleaf. V1 = VPRIM = voltage of the supply V2 = VSEC = voltage of load (secondary) A1 = IPRIM = current on primary side (drawn from the supply) A2 = ISEC = current on the secondary side (drawn by the load) 3. Set the variable resistor to minimum (position C at the bottom). Record all the readings on the table provided. 4. Set the variable resistor to medium (position B in the centre). Record all the readings on the table provided.
5. Set the variable resistor to maximum (position A at the top). Record all the readings on the table provided
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RECORDING OF METER READINGS VR set at position C
VR set at position B
VR set at position A
V1 V2 A1 A2
CONCLUSION: What do you observe and conclude from the readings as the load resistance changes?
Practical Activity: 3 Wiring of CT and VT (also called PT) to mains supply with instruments. How to measure high voltages and currents with low value instruments. Form of activity: Simulation Material and equipment: • Potential transformer with a ratio of 20:1 • Current transformer with a ratio of 1:5 • Connecting wires • 1 voltmeter (multimeter) with a maximum scale of 12 V (or close to it) • 1 ammeter (multimeter) with a maximum rating of 200 mA (or close to it) • 1 voltmeter (multimeter) set to 240 V or more • 1 ammeter (multimeter) set to 1 A or more • A load that will draw 1 A maximum from the supply NB: The supply voltage must be disconnected before the ammeter and volt meter can be removed out of the circuit. Instructions: 1. Wire the circuit according to the diagram given.
2. Record all readings on the table provided. V1 = VSUPPLY = High voltage V2 = VSEC = Low voltage on the 12 V meter A1 = ISUPPLY = Current drawn from the supply (high current) A2 = ISEC = Low current on the 200 mA ammeter
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3. RECORDING OF METER READINGS V1 (SUPPLY) V2 (SECONDARY) A1 (SUPPLY) A2 (SECONDARY)
4. Calculate the power on the supply side (V1 and A1). 5. Calculate the power on the low readings side (V2 and A2). 6. Calculate the constant of the VT and CT. CONCLUSION: 1. What do you observe and conclude from the readings? Are there any similarities between the readings of the meters and the VT and CT ratios? Explain your answer. 2. Is there any correlation between power on the primary, the power on the secondary and the constant?
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Chapter 5 Protective devices
A
B
Over-current and under-voltage protection
Contactors
The zero-volt coil
Testing and commissioning
A
B
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Introduction
Did you know? Current flow in a conductor always generates heat. The greater the current flow, the hotter the conductor. Excess heat is damaging to electrical components.
Take note The National Electrical Code defines over-current as any current that exceeds the rated current value of the equipment or the rating of a conductor. It may result from overload, short circuit, or ground fault.
Protective devices will be dealt with in this chapter – in other words, the safety mechanisms that can be put in place so that both the equipment and the user will be protected and safeguarded in case of excessive voltages and currents. The types of protection looked at include: over-current, under-voltage and overload protections, as well as the zero-volt coil. With reference to motor starters, the protective devices covered in this chapter will deal specifically with direct online motor starters.
Over-current and under-voltage protection When the first electric motors were connected to the supply, everything worked well, until the motor started drawing too much current due to the load conditions. The motor became very hot, the contactor’s terminals started to glow red and the insulation of the supply wires leading to the motor began melting, all as a result of the excessively high current. This needed to be corrected and the protective device was “born”. These protective devices were designed to keep the flow of current in a circuit at a safe level to prevent the circuit conductors from overheating. This is to protect the user as well as the equipment. It is also important to be able to connect the load back to the supply as soon as possible. If a production line in a factory comes to a standstill due to a fault, the company loses money. It is therefore vital that the protective device can be reset easily and without unnecessary time loss.
Figure 5.1: Sketch of over-current protection with the symbol used to represent it
Over-current protectors are most typically set between one and six times the normal current level. This is done to prevent the protector from tripping due to harmless temporary surge currents that occur when motors start up or transformers are energised. Harmful, sustained overloads can be caused by defective motors – such as worn motor bearings – overloaded equipment, or too many loads on one circuit.
Under-voltage protection Some manual motor starters offer low-voltage protection (LVP) as an option. Under -voltage occurs when a load is suddenly connected to a power supply. The load will start to draw current, and this causes the terminal voltage to drop temporarily. The LVP will automatically remove power from the motor when incoming power drops or is interrupted. An LVP starter must be manually reset when power is restored. This protects personnel from potential injury caused by machinery that would otherwise automatically restart when power is restored.
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Resettable over-current protection (motor protection) Bimetal strip: Overload protection can be accomplished with the use of a bimetal overload relay. A bimetal strip is used to convert a temperature change into mechanical displacement. It consists of two strips of different metals which expand at different rates as they are heated, usually steel and copper or, in some cases, brass. The strips are joined together throughout their length by riveting, brazing or welding. The different expansions force the flat strip to bend one way if heated, and in the opposite direction if cooled below its initial temperature.
Figure 5.2:
Figure 5.3:
Figure 5.2: At a certain temperature the two different metals are the same length. Figure 5.3: As they heat up, the metals will expand at different rates (shown in the top figure). But if they are riveted together the metal at the top expands faster and it will cause the unit to bend towards the slower-expanding metal.
Riveting is a method used to attach two pieces of metal together. The rivet is knocked flat on both ends, and this prevents the two pieces from moving apart.
Bimetal strips are used in miniature circuit breakers to protect circuits from excess current. A coil of wire is used to heat the bimetal strip, which bends and operates a linkage that unlatches a spring-operated contact. This interrupts the circuit and it can be reset when the bimetal strip has cooled down. Bimetal strips are also used in time-delay relays, lamp flashers and fluorescent lamp starters. In some devices, the current running directly through the bimetal strip is sufficient to heat it and operate contacts directly. This happens because, as current rises, heat also rises. The hotter the bimetal strip becomes, the more it bends. In an overload condition, the heat generated will cause the bimetal strip to bend until the mechanism is tripped, disconnecting the supply from the load.
Resettable overload protection Some overload relays equipped with a bimetal strip are designed to reset the circuit automatically when the bimetal strip has cooled and reshaped itself, restarting the motor. If the cause of the overload still exists, the relay will trip again and reset again at given intervals. Care must be exercised in the selection of this type of overload relay. In some cases, the trip current is set for that particular overload relay model, but in many cases the value of the trip current can be conveniently adjusted on the overload relay itself.
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Figure 5.4: An overload protector with resettable current ratings
There are other types of overload protection, of which the two most common types are: • electronic digital overload relay and • eutectic alloy relays.
Electronic digital overloads: resettable Electronic, digital overload relays containing a microprocessor may also be used, especially for high-value motors. These devices model the heating of the motor windings by monitoring the motor current. They can also include metering and communication functions.
Figure 5.5: An overload relay that makes use of a microprocessor
Eutectic alloy overload relays The eutectic alloy is like solder and it is used to retain a spring-loaded contact. When too much current passes through the heating element for too long a time, the alloy melts and the spring releases the contact, opening the control circuit and shutting down the motor. Since eutectic alloy elements are not adjustable, they are resistant to casual tampering. However, the heater coil element must be changed to match the motor rated current.
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Figure 5.6: Eutectic alloy overload relay
Zero-volt coil/no-volt coil (operator protection) Starters using magnetic contactors usually derive their power supply for the contactor coil from the same source as the motor supply. An auxiliary contact from the main contactor is used to keep the coil energised after the start button has been released. If a momentary loss of supply voltage occurs, the contactor will open and not close again until it is manually restarted. This prevents the restarting of the motor after a power failure. Imagine that a factory closes at 14:00 due to a power failure and everyone goes home. At 23:00 that night, power is restored, and the motors continue their operation with no one in sight – with disastrous consequences! The zero-volt coil prevents this from happening. This connection also provides a small degree of protection against low power supply voltage and loss of a phase. However, since contactor coils will hold the circuit closed with as little as 80% of normal voltage applied to the coil, this is not a primary means of protecting motors from low voltage operation. The zero-volt coil is simply a set of auxiliary switches on the contactor and is always a normally open switch. It is usually numbered as 53 and 54 on some contactors, or 13 and 14 as shown below.
Figure 5.7: Auxiliary contacts 13 and 14 used for zero-volt coil (or holding in)
Direct online starter/contactor This section will deal systematically with all the parts/components of a direct online starter and explain the purpose of each part, how it works and how to test each individual part. The first component is the contactor, followed by the start and stop buttons.
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The contactor A contactor is basically a big relay, and when the terminals labelled A1 and A2 are connected to 240 V, it is activated (current flows through it). A1
A2 Figure 5.8: Symbol for a main contactor
Figure 5.9: A main contactor with built-in overload relay is shown in the photo above. Note the symbol for such a system.
When 240 V is connected, current flows through the relay and this produces a magnetic field which attracts the moving core of the contactor. This in turn causes a number of switches to close or open at the same time, as shown in the picture below.
Did you know? Devices switching more than 15 amperes or in circuits rated more than a few kilowatts are usually called contactors. Figure 5.10: A main contactor, as used in some of our schools, is shown above
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Although contactors used in the school’s workshop look like the one shown in Figure 5.10, they are not found like this in the industry. This system is used in training to reduce the time it takes to connect the circuit up, so that more students can practice their wiring skills. In reality you would have to connect the wires to the actual contactor, as shown in the sketch below.
Metal plate (up)
Open
Open contacts Switch terminals
Figure 5.11: Main contactor with open contacts
Metal plate (down)
Closed Closed contacts
Switch terminals
Figure 5.12: Main contactor with closed contacts. Note the springs that return the contacts to their normal position once power is disconnected
When the contactor coil is de-energised, a spring returns the electromagnet core to its initial position and opens the contacts. A contactor is used in a starting circuit for electric motors (or other loads) so that the current drawn by the motor does not flow through the coil itself, but rather through the switches (contacts), which are heavy-duty, metal strips that make contact and can handle the high current through them.
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Electrical Technology How to test the main contactor This is what one would do to test the main contactor:
Take note Please make sure that the supply is disconnected before testing.
Take a multimeter and set it to the ohm scale. Take the leads of the meter and connect them across the terminals labelled A1 and A2 (these are the terminals of the coil inside the contactor). Depending on the make of contactor, it should give a reading of around 500 Ω. If this is correct, test all the normally open and closed switches belonging to the contactor to see if they are functioning properly. (Use the same procedure as for the start and stop buttons, which is discussed next.)
Did you know? Most motor control contactors at low voltages (600 volts and less) are air break contactors. This means that the air surrounding the contacts extinguishes the arc when interrupting the circuit. Modern medium-voltage motor controllers use vacuum contactors. High voltage contactors (greater than 1000 volts) may use vacuum or an inert gas around the contacts to contain the arc that occurs when the contacts make or break.
Figure 5.13: Contactor information such as voltage and current ratings
Before using a contactor it is always important to check its voltage rating. This means the recommended voltage for the contactor to operate properly. Contactors come in 120 V, 240 V and 380 V packages. The information is always given on the side of the contactor.
Start button To start the motor one uses a push button. This is a button that is spring loaded, which means it returns to its original position (state) once the pressure is removed by taking one’s finger off the button. It is a normally open switch (N/O). This means that without pressure there is no contact between the two terminals, but when it is pushed, the terminals close. The colour of a start button is usually green (like in a traffic light, where green means go).
1
Ω
Figure 5.14: Start button
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Figure 5.15: Testing for continuity when start button is pressed
Protective devices How to test the start button Quite often when a motor does not want to start, one has to find the fault in the circuit. One starts by systematically checking whether all the parts work correctly. To do this one must know how to test the various parts. Take a multimeter and set it to the ohm scale. Connect the leads of the meter across the terminals of the start button (without pushing it). It should read “infinity”. When the button is pressed, the contacts close and there should be a short-circuit reading (usually 0,1 to 0,6 ohm). This indicates that the start button is working perfectly.
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Take note All testing must be done with the supply disconnected.
Stop button To stop the motor we make use of a similar spring-loaded push button. The only difference is that this is a normally closed switch (N/C). This means that without pressure there is contact between the two terminals, but when you push it the terminals open, disconnecting the supply from the load. The colour of a stop button is usually red (like in a traffic light, where red means stop).
0,1
Ω
Figure 5.16: Stop button
Figure 5.17: Testing continuity for a stop button
How to test the stop button Take a multimeter and set it to the ohm scale. Connect the leads of the meter across the terminals of the stop button (without pushing it). It should read “continuity” (usually 0,1 to 0,6 ohm). When the button is pressed, the contacts open and it should read “infinity”. This indicates that the stop button is working perfectly.
Overload protection This has already been discussed at the start of the chapter, but just to revise: Overload protection is there to prevent the current drawn by the load from exceeding a certain value. This is done to protect the load as well as the operator. A variety of overload protection devices is available on the market today. The type of protection depends entirely on the following: • The load • The current rating at which the supply must be disconnected • The supply voltage • How fast the supply must be disconnected • Whether the overload should be resettable, manually restarted or automatically restarted
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Setting over-current protection Only certain types of overload protection units allow one to adjust the current rating at which the device must trip. This rating would depend entirely on the load, and on changing load conditions.
Figure 5.18: Adjustable setting on an overload can be very convenient
Sometimes motors run freely, but any sudden increase in load demand causes more current to be drawn from the supply. Examples of this are: • A drill – Once started, the drill turns freely, but as the drill bit starts biting into the metal or wood, the motor works so much harder, and will draw more current. • A vacuum cleaner – Once it is operating, any obstruction to the inlet pipe will cause the motor to start to labour. All these factors would have to be considered before the value of the current rating is set on the device. Once the circuit is operational, it is not wise to adjust trip levels, as it is considered unsafe.
Wiring diagram of a DOL starter Before starting with the explanation of the direct-on-line starter for an electric motor one needs to look at the entire circuit diagram, which will then be broken down into manageable sections that will include: • Enabling activity • Design tips for a control circuit • Design tips for a main circuit • Tests that can be carried out • Commissioning of a DOL starter.
Stop MC1
O/L MC1 (N/O) Holding in
Start
MC1
Figure 5.19: The full design circuit for a direct-on-line starter for an electric motor
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Before we start designing motor control circuits we are going carry out a specific activity. The purpose of this activity is to establish the idea that if a contactor closes, it will activate a switch belonging to it elsewhere in the circuit. The focus is on the labelling and identifying of which switches belong to which contactors. Once you can do this, designing motor control circuits becomes easier. Look carefully at the circuit below and make sure that you know which switch belongs to which contactor. Then complete the table for this circuit.
Activity 1 1. What belongs where in a circuit containing relays (contactors)?
Figure 5.20: A circuit containing contactors, lights and manual switches.
2. Complete the table below: Switch 1 (Left position) and Switch 2 open
Switch 1 (Left position) and Switch 2 closed
L1
L1
L2
L2
MC1
MC1
MC2
MC2
Switch 1 (Right position) and Switch 2 open
Switch 1 (Right position) and Switch 2 closed
L1
L1
L2
L2
MC1
MC1
MC2
MC2
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Motor starters A direct-on-line (DOL) or across-the-line starter applies the full line voltage to the motor terminals. This is the simplest type of motor starter. A DOL motor starter also contains protection devices and, in some cases, condition monitoring. A motor starter is usually designed in TWO sections, namely the control circuit and the main circuit.
Practical wiring of a DOL starter The control circuit: The control circuit is the one that contains all the start, stop, main contactors and timers. The advantage of building this first is that one can check that the circuit operates in the correct sequence and that it meets the design criteria without connecting any load (motor or other) to the supply. This prevents unnecessary damage to equipment. Always make sure that the following criteria are adhered to, as it will save a lot of time in the end: • The live wire must be at the top of the circuit. • The neutral wire must be at the bottom of the circuit. • ALL switches, from starts (N/O), stops (N/C) and switches from the main contactor itself, are always drawn in their normal state (without power connected or being pushed). • The stop is ALWAYS as close to the Live as possible. • Nothing can be connected between the bottom of a main contactor and Neutral. • When using more than one main contactor, make sure they are always connected in parallel – ALWAYS. • Labelling is IMPORTANT. Every part must be clearly labelled. When you do the wiring, make sure to wire EXACTLY according to the diagram, step-bystep, wire-by-wire. One can even highlight on the circuit the wire that has been connected. This will help in the beginning, but this skill will soon be mastered and then it will be easy.
STOP
START
MC1 (N/O) Holding in
MC1
Control circuit
Figure 5.21: Wiring diagram of a control circuit for DOL starter
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The main circuit: The main circuit is the easy one. This only contains the switches of the main contactor, overload protection and the actual load. Its main job is to connect the supply to the load. This means there will only be the Live, the contacts from the main contactor, the overload, and the motor (load) in this part of the circuit.
MC1
Main circuit
Figure 5.22: Wiring diagram of the main circuit for a DOL starter
When the two circuits are put together, it will look as follows:
STOP MC1
START
MC1 (N/O) Holding IN
MC1
Control circuit
Main circuit
Figure 5.23: The full control and main circuit for a fully functional DOL starter for a single-phase motor
This circuit has three protection parts: • The stop button – is to ensure that the supply can be isolated at any time during the operational process • Overload protection – to disconnect the supply from the load when the current exceeds a preset value • Zero-volt coil – to ensure that the motor must be started manually after a power failure has occurred.
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Electrical Technology Testing and commissioning There are some tests that can be performed before the supply is connected.
Take note The supply MUST be off. This is usually done by means of a keyoperated switch on the main panel. This is to prevent accidental shock when wiring the circuit.
Figure 5.24: A key in the panel disconnects the supply while the circuit is being wired
Take note We usually make use of stackable leads when we wire these circuits. Ensure that the ends of the terminals are covered, as exposed terminals can be live when you press buttons, and you may get a nasty surprise.
Take note Even with the stop switch pressed, there is still 240 V on one terminal of the stop button. Be careful. Only change wires if the isolator key has been turned off.
The following test can be carried out to ensure correct functioning before the supply is connected. • Switch OFF the control key on the main panel (or turn off the circuit breaker to the circuit). • Connect a multimeter to the live and neutral from the supply. • Set it to the ohm scale (usually the lowest setting which is 200 Ω). • It should read “infinity” (open circuit). • When the start button is pressed, the multimeter should display the reading of the coil of the main contactor (about 500 Ω). • While still holding in the start button, press the STOP button at the same time. The reading on the meter should return to infinity. This indicates that the start button, the stop button, and the main contactor are correct. • Please disconnect the multimeter at this point before proceeding. • The key can now be turned and the circuit can be tested with the full supply connected to it. What should happen when supply is connected? When the start button is pressed the contactor should activate and stay in, even if pressure is removed from the start button again. When the stop button is pressed, the main contactor will de-energise and return to its normal state. It is important to be able to follow logically what will happen in a circuit, from start to finish. In other words, can you predict the sequence in which the contactors and timers will come in, and which switches will come into action at which stage?
Practical: connecting the DOL starter to a load The following would be typical instructions for a practical on a DOL motor starter circuit. This falls under applied theory, as learners would first have to acquire the theoretical knowledge regarding all the parts before they can go on to the designing and building stage.
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Activity 2 DOL motor starter 1. Purpose To connect a single-phase AC motor by means of a direct-on-line starting connection. (The motor must be a capacitor-start induction motor.) All interlocks, overloads and safety mechanisms must be shown. If the start button is pressed, the motor must run, and continue to run even after the start button has been released. If the stop button is pressed, the motor must stop. If a power failure occurs, the motor should be started manually. 2. Equipment 1 × start button 1 × stop button 1 × main contactor with auxiliary contacts 1 × overload 1 × capacitor-start induction motor connecting wires 3. Control circuit diagram Draw a neat control circuit diagram. All connecting points must be clearly shown.
(10)
4. Main circuit diagram Draw a neat main circuit diagram to show how the main wiring should be connected. All connecting points must be clearly shown.
(10)
5. Connect the control circuit according to your diagram, and call the educator when you are sure your circuit is correct. correct 1st time 10 correct 2nd time 5 thereafter 2
(10)
6. Connect the main circuit diagram according to your diagram, and call the educator when you are sure your circuit is correct. correct 1st time 10 correct 2nd time 5 thereafter 2 7. Make use of a megger and measure the resistance value of the: Main winding: Start winding:
(10)
(2) (2) [44]
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Activity 3 Sequence starting 1. Purpose To design a circuit with the given equipment so that when the first start button is pressed, a warning light will be switched on. If the second start button is now pressed, the motor must be started. In other words, if the warning light is not switched on, it must not be possible to start the motor either, even if start button 2 is pressed. Your circuit must have two start buttons and two stop buttons. If either stop button is pressed, then both the warning light and the motor must switch off immediately. All interlocks, overloads and safety mechanisms must be shown. 2. Equipment 2 × start buttons 2 × stop buttons 2 × main contactors with auxiliary contacts 1 × overload 1 × light station 1 × single-phase motor connecting wires 3. Control circuit diagram Draw a neat control circuit diagram. All connecting points must be clearly shown.
(20)
4. Main circuit diagram Draw a neat main circuit diagram to show how the main wiring should be connected. All connecting points must be clearly shown. (10) 5. Connect the control circuit according to your diagram, and call the educator when you are sure your circuit is correct. correct 1st time 10 correct 2nd time 5 thereafter 2
(10)
6. Connect the main circuit diagram according to your diagram, and call the educator when you are sure your circuit is correct. correct 1st time 10 correct 2nd time 5 thereafter 2
(10) [50]
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Activity 4 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
What is the purpose of overload protection? What is the definition of over-current as laid down by the National Electrical Code? What damage may result from an overload in motor circuits? Why are overload protectors typically set to one to six times higher than normal current? Explain how the bimetal strip overload relay works. Name two other types of overload protection used in motor control circuits. What is meant by low voltage protection? What is a zero-volt coil? Explain the term N/O with reference to a spring-loaded push button. What is the usual colour of the start and stop buttons? What is an easy way to remember this? How can a stop button be tested with a multimeter to see if it is correct or not? What is a main contactor? What are the most important things to check before selecting a contactor? How would you test the coil of the main contactor to determine if it is functional? What is the purpose of drawing and building a control circuit before you build a main circuit? What is one of the most important safety aspects to keep in mind when building any motor control circuit? Name three types of overload protection used in motor starters. Draw a neat control circuit for a DOL starter system of a single-phase motor. Draw a neat main circuit for the DOL starter system of a single-phase motor. What would happen if we connect a 380 V contactor to a 240 V supply?
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Chapter 6 Single-phase motors
A
A
B
Single-phase induction motor
Motor testing
Capacitor start motor
Capacitor start Capacitor run motor
B
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Introduction Electrical motors are electromechanical devices that convert electrical energy into mechanical energy. The operating principle of most motors is based on the interaction of magnetic fields and current carrying conductors. Electrical motors are used in a variety of applications, ranging from industrial to household, and from power tools to even electronic applications. Depending on the application of the electric motor, it may vary in size from very big to very small. This chapter will deal with: • the different types of single-phase induction motors, • their applications, • basic operating principles, and • testing of these motors.
Operation of single-phase induction motors There are probably more single-phase AC induction motors in use today than the total of all the other types put together. It is logical that the least expensive, lowest maintenance type motor should be used most often. The single-phase AC induction motor best fits this description. 1 2 3 4 5 6 7 8 9 10 Figure 6.1: Single-phase induction motor
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Cooling fan cover Cooling fan Back end shield Starting capacitor Stator Rotor Front bearing Front-end shield Foot mount Wire terminal box
As the name suggests, this type of motor has only one stator winding (main winding) and operates with a single-phase power supply. In all single-phase induction motors, the rotor is the squirrel-cage type. The single-phase induction motor is not self-starting. When the motor is connected to a single-phase power supply, the main winding carries an alternating current. This current produces a pulsating magnetic field. Due to induction, the rotor is energised. As the main magnetic field is pulsating, it will not generate the torque necessary for the motor
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Single-phase motors
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rotation. It will cause the rotor to vibrate, but not to rotate. Hence, the single-phase induction motor needs to have a starting mechanism that can provide the starting kick for the motor to rotate. Depending on the various start techniques, singlephase AC induction motors are further classified and described in the following sections.
Figure 6.2: Rotor
Figure 6.3: Stator
Universal motor A motor which may be operated or which can run on either a direct supply or a single-phase AC supply is known as a universal motor. Why is it called a universal motor? It is because of its ability to run on both AC and DC supply with similar characteristics. A universal motor has a high starting torque and variable speed characteristics. Such a motor runs at dangerously high speeds during no load periods. Types A universal motor can be manufactured in two different ways: • Non-compensated type with concentrated poles • Compensated type with distributed field. The compensated type is preferred for high power rating appliances and the noncompensated type for low power rated appliances. Both the compensated and noncompensated motors have a construction similar to that of a DC series motor. Both the types of motor develop unidirectional torque regardless of the supply by which they are run. The supply may be AC or DC but the direction of torque is the same. Can the direction of rotation be reversed for these types of motors? Yes, the direction of rotation can be changed. For the non-compensated motor with a salient pole, the direction of rotation can be reversed by changing the direction of flow of current through the armature or field winding. This can also be done by interchanging the leads on the brush holders. In the case of the compensated type motor, change either the armature leads or the field leads. This will reverse the rotation. Speed/load characteristics Very similar to that of a DC series motor, the universal motor also has varying speed characteristics. The speed is low at full loads. The speed is very high and dangerous at no-loads. During no-loads, the speed is limited only by its own frictional and windage load. Speed control The speed control of a universal motor is very important and the following methods are employed:
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Electrical Technology Resistance method: In this method of speed control, a variable resistance is connected in series with the motor. The amount of resistance in the circuit can be changed. A foot pedal is used for this purpose. Usually this method is employed for motors used in sewing machines. Centrifugal mechanism: This method is used whenever the application involves a number of speeds. The best example is a home food and fruit mixer. Here a centrifugal device is attached to the motor. If the motor rises above the specified speed set by the lever, the centrifugal device opens the contact which brings a resistor into the circuit. This causes the motor speed to decrease below the set speed. When the motor runs more slowly than the speed set by the lever, the contact is established and the resistance is short circuited. This causes the speed to increase. The variations in speed are not noticeable as the process is repeated in a rapid manner. Applications Universal motors are mostly employed in • Vacuum cleaners • Portable drills • Drink mixers • Sewing machines
Other single-phase motors (split-phase) How to obtain a rotating magnetic field in single-phase motors Single-phase motors have one big disadvantage: they are not self-starting! This means that it requires the addition of extra components to produce a rotating magnetic field. The single-phase coil of a single-phase induction motor does not produce a rotating magnetic field, but a pulsating field. The result of this is that no torque is developed to get the rotor to start turning. To overcome this problem of no rotating field in a single-phase motor, a two-phase motor powered from single-phase was designed that would produce a phase shift of 90° between the two windings. The phase shift can be created by making the one winding more inductive or capacitive than the other. The one winding is commonly referred to as the start winding and the other as the run winding. When the voltage applied over the two fields leads or lags by 90°, then both the current and the magnetic field will have a 900 phase shift. These two fields combine to form a rotating magnetic field. This leads to the development of a permanent split-phase motor. The name of the motor normally describes its starting mechanism: • Split-phase • Capacitor-run • Capacitor-start • Capacitor-start-and-run • Shaded pole
Split-phase motor The split-phase motor is also known as an induction-start/induction-run motor. It has two windings: a start and a main winding. The start winding is made with smaller gauge wire and fewer turns relative to the main winding to create more resistance, thus putting the start winding’s field at a different angle to that of the main winding, which causes the motor to start rotating. The main winding, which is of a heavier wire, keeps the motor running the rest of the time.
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Good applications for split-phase motors include small grinders, small fans and blowers and other low-starting torque applications. Avoid using this type of motor in any applications requiring high on/off cycle rates or high torque.
Figure 6.4: Split-phase motor
Capacitor-start motor (CSM) Function of components The starting mechanism of the single-phase capacitor-start motor is mainly an additional stator winding (start/auxiliary winding). The start winding has a series capacitor and/or a centrifugal switch. When the supply voltage is applied, current in the main winding lags the supply voltage due to the main winding impedance. At the same time, current in the start winding leads the supply voltage. Interaction between the magnetic fields generated by the main winding and the starting mechanism generates a resultant magnetic field rotating in one direction. The rotor starts rotating in the direction of the resultant rotating magnetic field. Once the motor reaches about 75% of its rated speed, a centrifugal switch opens and disconnects the start winding. From this point on, the single-phase motor can maintain sufficient torque to operate on its own. Since the capacitor is in series with the start circuit, it creates more starting torque, typically 200% to 400% of the rated torque. The electrolytic start capacitor helps motors achieve the most beneficial phase angles between the magnetic fields of the start and main windings. The start winding is disconnected when the motor reaches about 75% of full-load speed. The start capacitor is designed for short-time duty. Extended application of voltage to the capacitor will cause premature failure, if not immediate destruction. Typical ratings for motor start capacitors range from 100 to 1,000 μF and 250 volts AC. These are physically large capacitors. Capacitance is a measure of how much charge a capacitor can store relative to the voltage applied.
Figure 6.5: Capacitor-start motor
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Remember When changing direction of rotation, swop start winding with respect to the main winding but never both.
Application and uses CSMs are used for a wide range of belt-drive applications, such as small conveyors, bench grinders, large blowers and pumps, as well as many direct-drive or geared applications. These are the “workhorses” of general-purpose, single-phase, industrial motors. Reversal of direction of rotation The direction of rotation of an AC motor depends on the magnetic polarity of the start winding. Reversing the polarity of the start winding, in relationship to the run winding, reverses the direction of rotation of all single-phase alternating current (AC) motors.
Figure 6.6: Reversal of the direction of rotation of a capacitor-start motor
Testing a capacitor-start motor To ensure that the motor is in good condition, there are two basic inspections (tests) that must be done: the one is a visual inspection (mechanical test) and the other is an electrical inspection (test). Visual inspection is done by looking at the motor and inspecting its overall condition, whereas an electrical inspection involves the use of an insulation tester (megger) to perform some electrical tests. • Visual inspection test The first and very important test is the visual inspection. There are two types of visual inspection tests that can be done: firstly, the electrical inspection and secondly, the mechanical inspection. Visual electrical inspection: – Check if electrical cables are isolated and the cover plates holding the terminals are sealed. – Check the motor terminal box for loose wires or broken terminals. – Check for burn marks. – Check that capacitor is in good condition. Visual mechanical inspection: – Check the mounting of the motor. Make sure all bolts are tight and there is no play in belts or pulleys. – Check condition of the rotor and shaft: key way, front bearing and back bearing. – Check condition of motor frame and condition of the terminal box. – Check front/back-end shield, stator/field housing, condition of cooling fan and fan cover and cooling fins
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Once the motor has been disconnected and removed from its position, the following three electrical tests can be done: continuity test, insulation test and the earth continuity test. • The continuity test This test is performed using an insulation tester or continuity tester. It determines the continuity of the conductors as well as the condition of the capacitor. The value of the reading should be low. The number of windings and the size of the motor will influence the value of the reading. • Insulation test This test has TWO components. One must first determine the value of insulation between the conductors. One then determines the insulation between the conductors and earth. This test is performed using an insulation tester. This value should be high to infinity (1 MΩ or higher). • Earth continuity test This test is performed using an insulation tester or continuity tester. It determines the continuity of the earth wire to the distribution board or earth spike. This value should be high to infinity (1 MΩ or higher).
Capacitor-start-and-run-motor (CSR motor) The capacitor-start, capacitor-run motor (or CSR motor) produces a high starting torque and increases the running efficiency. It is actually a capacitor-start motor with a running capacitor added permanently to the starting winding. The starting winding is energised all the time while the motor is running. This produces one of the best all-around motors used in the industry. This motor is costly due to the start and run capacitors and the centrifugal switch. It is able to handle applications too demanding for any other kind of single-phase motor. These include woodworking machinery, air compressors, high-pressure water pumps, vacuum pumps and other high torque applications. Function of components The CSR motor is basically the same as the CSM motor with the addition of a running capacitor. The CSR motor begins operation on a phase displacement between the starting and running windings, which allows rotation to begin. The running capacitor lends a small amount of assistance to the starting of the motor, but its main function is to increase the running efficiency of the motor.
Figure 6.7: Capacitor-start-and-run motor connections
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Electrical Technology Applications and uses CSR motors are used in woodworking machinery, air compressors, high-pressure water pumps, vacuum pumps and other applications requiring a high torque of between 1 and 10 hp. Reversal of direction of rotation The direction of rotation of an AC motor depends on the magnetic polarity of the start winding. Reversing the polarity of the start winding, in relationship to the run winding, reverses the direction of rotation of all single-phase alternating current (AC) motors.
Figure 6.8: Reversal of direction of rotation of a capacitor start and run motor
Testing a capacitor-start-and-run motor The capacitor-start-and-run motor is sometimes difficult to troubleshoot because of the number of components that must be added to a regular motor to produce it. The windings, bearings, potential relays, starting capacitor and running capacitor must all be checked. The windings of a CSR motor can be checked easily using an insulation tester (megger) to determine if the windings are shorted, open, or grounded. In most cases, the windings will be enclosed in a casing and the terminals will be on the outside of the casing. However, the type of motor makes little difference in checking the winding, as long as the technician uses the correct terminals. To ensure that the motor is in good condition, there are two basic inspections (tests) that must be done. The one is a visual inspection (mechanical test) and the other is an electrical inspection (test). The visual inspection is done by looking at the motor and inspecting its overall condition, whereas an electrical inspection involves the use of an insulation tester (megger) to do some electrical tests. • Visual inspection test The first and very important test is the visual inspection. There are two types of visual inspection tests that can be done: firstly, the electrical inspection and secondly, the mechanical inspection. Visual electrical inspection: – Check if electrical cables are isolated and the cover plates holding the terminals are sealed. – Check the motor starter for loose wires or broken terminals. – Check for burn marks. – Check that capacitor is in good condition.
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Visual mechanical inspection: – Check the mounting of the motor. Make sure all bolts are tight and there is no play in belts or pulleys. – Check condition of the rotor and shaft: key way, front bearing and back bearing. – Check condition of motor frame and condition of the terminal box. – Check front/back-end shield, stator/field housing, condition of cooling fan and fan cover and cooling fins Once the motor has been disconnected and removed from its position, the following three electrical tests can be done: continuity test, insulation test and the earth continuity test. • The continuity test This test is performed using an insulation tester or continuity tester. It determines the continuity of the conductors as well as the condition of the capacitors. The value of the test should be low. The number of windings and the size of the motor will influence the value of the reading. • Insulation test This test has TWO components. One must first determine the value of insulation between the conductors. One then determines the insulation between the conductors and the capacitors. This test is performed using an insulation tester. The values should be high to infinity (1 MΩ or higher). • Earth continuity test This test is performed using an insulation tester or continuity tester. It determines the continuity of the earth wire to the distribution board or earth spike. This value should be high to infinity (1 MΩ or higher). It also tests if there are any leakages/shorts between the windings and earth.
Take note These three electrical tests must be done in the correct order as given in the text.
Activity 1 1. 2.
Name 4 types of single-phase induction motors. Name 4 methods used to generate a rotational magnetic field in a singlephase motor. 3. Describe the principle of operation of a CSM motor. 4. Name 4 tests to be performed on a single-phase motor. 5. Give an application for a split-phase motor. 6. Draw a neatly labelled diagram of a CSR motor. 7. Describe how you will go about faultfinding on a single-phase induction motor. 8. Explain in your own words how you will change the direction of rotation of a capacitor-start induction motor. 9. Why is it important to do the electrical testing of a motor only after it has been disconnected ? 10. What is the importance of the earth insulation test?
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Practical 1 Testing of a capacitor-start motor Form of activity: Testing Material and Equipment: • Insulation tester/megger • Capacitor-start motor • Single-phase supply Instructions: 1. Teacher will provide learner with the single-phase motor to be tested. 2. Learners to ensure they select the correct settings on the insulation tester (megger). 3. Learners to use the insulation tester to take the necessary readings and record these in the table provided. A1 – A2
A2 – B2
B1 – Cb
A1 – B1
A2 – Ca
B2 – Ca
A1 – Ca
A2 – Cb
B2 – Cb
Ar – Cb
B1 – B2
Ca – Cb
A2 – B2
B1 – Ca
Continuity readings (take A as main winding and B as start winding) Component
Reading
Conclusion
A1 – A2 B1 – B2 Cap a – Cap b Insulation readings between components Component
Reading
Conclusion
A1 – B1 A1 – Cap a B1 – Cap a Insulation readings to earth Component A1 – Earth B1 – Earth Cap a – Earth
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Mechanical/Visual inspection of motor Condition of rotor and shaft Component
Report on condition
Key way Front bearing Back bearing Condition of motor frame Condition of terminal box Flange/foot mount Front/back-end shield Stator/field housing Mounting bolts and nuts/screws Condition of cooling fan Fan cover and cooling fins 4. Describe how the rotational direction of this motor can be changed.
Practical 2 Wire a direct-on–line motor control circuit Form of activity: Simulation Material and equipment: • 1 × motor control board • Connecting wires • 1 × contactors with auxiliary contacts and overloads (or separate overloads) • 1 × stop button • 1 × emergency stop button (press type) • 1 × start button • 1 × single-phase motor Instructions: Wiring of circuits Wire the equipment according to the given diagrams. Do NOT switch on the power supply before your TEACHER has checked the circuits. First build the control circuit and then ask your teacher to check and assess. Only when the control circuit is correct, may you start with the main circuit. Control circuit: • Correct the first try, 10 marks • Correct the second try, 5 marks • Correct the third try, 2 marks
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Main circuit: • Correct the first try, 10 marks • Correct the second try, 5 marks • Correct the third try, 2 marks Live Stop button NO MC 1
Start button
Main contactor MC 1 Overload Neutral
Control circuit for DOL motor L
N
MC 2 Overload
Single-phase Single phase motor motor
Main (power) circuit for DOL motor
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Chapter 7 RCL
A
B Series RLC circuit
A
Capacitive reactance
Phasor diagrams
B Resonance 101
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Introduction Up to now the focus has been on resistors connected in series, parallel and combination networks. Ohm’s law was investigated and it was proven that the current is always directly proportional to voltage, but inversely proportional to resistance. And although that is completely true for pure resistive circuits, it is not always true for circuits containing coils (inductors) and capacitors. The focus now shifts to the effect that these components will have on a circuit when connected to an AC supply. The components that will be dealt with are the resistor, the coil and the capacitor.
Pure resistors (R) The first component that will be investigated is the resistor. A straight length of a conductor or a carbon resistor can be regarded as a pure resistor. The effect that the resistor has on the voltage and the current is shown in a phasor (vector) diagram. If an alternating voltage of V volts is applied to a resistance of R ohms, a current I amps will flow. This can be calculated by using Ohm’s law. Switch
Figure 7.1: A pure resistive circuit
The above is valid for any instant, so that if the voltage is zero, the current is zero and when the voltage is a maximum, then the current is a maximum, and it is said that the current and voltage are in phase.
Figure 7.2: Phasor diagram of a pure resistive AC circuit
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If the current and voltage for a very simple AC circuit consisting of a suppy and a resistor were plotted, the graph would look something like this:
Figure 7.3: Oscillograms for a pure resistive circuit, with voltage and current in phase
The voltage and the current are always in phase with each other.
Pure inductance (L) A coil of many turns of insulated, heavy-gauge copper neatly and closely wound may be taken to have negligible resistance. Such a component is said to be purely inductive. A circuit is inductive if it possesses inductance. When a pure inductive coil is connected to an AC supply, the current lags behind the applied voltage by an angle of 90°. This effect is shown in the phasor diagram.
Switch
Figure 7.4: Simple inductive circuit
Figure 7.5: Phasor diagram of a pure inductive AC circuit
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Figure 7.6: The current lags behind the applied voltage by an angle of 90°
The voltage always leads the current by 90° (or the current lags the voltage by 90°).
Pure capacitance (C) A capacitor (condenser) is an electrical apparatus that possesses the capacity to store a certain quantity of electricity. This characteristic is called capacitance. The most common type of capacitor consists simply of two strips of metal foil separated from each other by a thin dielectric (insulation). Waxed paper is often used as a dielectric. When AC voltage is applied to a capacitor, the resulting current leads the voltage by an angle of 90°. This effect is shown in the following phasor diagram.
Figure 7.7: Simple capacitive circuit
Figure 7.8: Phasor diagram of pure capacitive AC circuit
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Figure 7.9: The current leads the applied voltage by an angle of 90°
The current always leads the voltage by 90° (or the voltage lags the current).
In pure resistive circuits When two resistors in series are connected to an ac supply, one would like to know what effect the change in frequency will have on the current and the voltage in that circuit. To investigate and prove this effect an oscilloscope and a signal generator can be used. The following section of the work could serve as an investigation in the workshop to prove that the theory matches the practical. A series RR circuit is shown below. In addition, it also shows the connections for an oscilloscope measuring the voltage across the supply and the 1 kΩ resistor.
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Take note A mechanical quantity, like speed, can be represented by a vector. A vector is a line with an arrow on the end that will represent the actual speed (size), as well as the direction. In electrical terminology, certain voltage or current values can have a certain size (magnitude), but the direction that current flows becomes problematic. One can, however, represent the phase relationship between current and voltage. This is called a phasor diagram. A phasor represents magnitude as well as the phase relationship between voltage and current. This will become apparent as the effects of these components are investigated in AC circuits.
Take note An oscilloscope can measure many things, but in this activity it will be used to measure the voltage values in a circuit, as well as the phase relationship between the these voltages. Figure 7.10: Connecting an oscilloscope to a pure resistive circuit
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Electrical Technology The voltages measured across the supply and the 1 kΩ resistor will appear on the oscilloscope as shown below. They will be perfectly in phase with each other. That means they both start at the same time and they both reach their peak at the same time.
Figure 7.11: Oscilloscope screen image
Remember The value 0,707 refers to the RMS value of an AC wave.
With the Time per division set to T/div = 50μs and the voltage per division set to V/div = 0,5 V, the following calculations can be made: Take note: V
=
(V/div)(No. blocks)(0,707)
Vt
=
(0,5)(3)(0,707) = 1,06 V
Vr
=
(0,5)(1,5)(0,707) = 0,530 V
f
=
1 T
=
1 ((50μs)(10))
= 2 kHz
Phase angle = 0° (VS and VT in phase with each other). VR 0,53 The supply current = ___ = ____ = 530 μA R 1000 All this information can also be represented on a phasor diagram.
Figure 7.12: Phasor representations of the voltage and current values
The big question is what will happen if the frequency is changed. This is what will happen.
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Figure 7.13: Oscilloscope screen image
T/div = 12,5μs V/div = 0,5 V Vt =
(0,5)(3)(0,707) = 1,06 V
Vr =
(0,5)(1,5)(0,707) = 0,530 V
f =
1 T
=
1 ((0,5μs)(6))
= 8 kHz
Phase angle = 0° (VS and VT in phase with each other). VR 0,53 The supply current = ___ = ____ = 530 μA R 1000 The phasor diagram for the given information at the new frequency will look as follows.
Figure 7.14: Phasor representations of the voltage and current values.
At this stage one must ask what the point of this whole exercise was, as no noticeable changes at the different frequencies were noted. And that was the whole point: the fact that frequency has absolutely no effect on the phase relationship between Vr and Vt . This means that frequency has no effect on the magnitude or the phase relationship between voltage drops in a series circuit. As it is a series circuit (and according to Kirchoff ), the current flowing in a series circuit is the same through all the components, which means that the current (I) is used as the reference in all the phasor diagrams. In a nut shell then. A resistor causes no phase shift between voltage and current at any frequency. The relationship is always constant and they are always in phase with each other. This fact will be referred to in all the other activities.
Remember Remember that the current is being used as the reference, and the reference is always drawn to the right, and the other values are filled in with respect to that.
Take note When drawing a phasor diagram the following steps are followed: • What is the reference? (In other words, what stays constant in the circuit: current or voltage?) • Draw in VR as it will always be in phase with current. (This was proved above.) • Draw in VT with respect to VR (using the phase angle).
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Power Power is measured in Watts or kilo-Watts (kW) and is the product of voltage and current. But only the voltage and current that are in phase with each other. From the activity it was proved that current and voltage are always in phase with each other, and therefore in a pure resistive circuit P = IV (measured in watts).
Inductive reactance (XL) The symbol for inductance is the letter “L”. When an AC supply is connected to an inductive circuit, the current is limited by the coil/inductor. But Ohm’s law uses I = V and the value of the coil is measured in henries. R A method is required whereby the henries can be converted to an equivalent ohms value. That is achieved by using a formula where XL= 2πfL ohms
Take note A circuit or coil possesses an inductance of 1 henry if a rate of change of current of 1 amp per second results in a back EMF of 1 volt.
where, • 2π refers to one cycle, or one revolution in radians • f is the supply frequency in Hz • L is the inductance of the coil in henry (H) The current flowing in the circuit can now be calculated as: I = V amps XL
In a circuit containing a resistor and a coil Different units can never just be added together. Ohms and henries can never be added. But that is not all: one needs to know the effect that changes in frequency have on the voltage and current in a coil before the ohm values can be added. The circuit in Figure 7.15 shows a series circuit joining a coil of 36 mH and a resistance of 2 kΩ connected to a 9 V/5 kHz supply. This is commonly referred to as an RL circuit.
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VT
Figure 7.15: An RL series circuit
At this frequency a number of calculations can be done, for example: XL = 2πfL = 2π(5000)(36 × 10-3) = 1,13 kΩ It is also noted in the phasor diagram shown below that VT leads VR by approximately 30°. This means that we have the following voltage phasor diagram.
Figure 7.16: Phasor diagram indicating voltage values
Since the current is the same everywhere in a series circuit, each of the voltage values can be divided by it. This results in the following, and these values are transferred to a similar phasor diagram: VT = Total Resistance __ I VR = R __ I V __L = XL I The transferred phasor diagram appears as shown below.
Figure 7.17: Phasor diagram showing ohm values
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Impedance Impedance (Z) is a measure of the total opposition to current flow in an alternating current circuit, made up of two components, ohmic resistance (R) and reactance (XL), expressed in ohms. As we can see from the diagram it is not possible to just add the ohms value of the resistor and the coil together, as they are now out of phase with each other. The only way we can manage this is to make use of Pythagoras, and this can be done because XL and R are at right angles to each other. To make this a little easier we make use of an impedance triangle, as it makes the link to mathematics just that little bit easier. An impedance triangle shows all the ohms values in the circuit, including the phase relationship between them.
Figure 7.18: Impedance triangle for an RL circuit
Impedance, power, power factor and phase angle of an RL circuit One can now calculate (mathematically) the value of the total resistance (now called impedance) of the circuit. Z = √ (R2 + XL2) = √ (2 000)2 + (1 130)2 Take note Keep in mind that Z is always larger than R in any RL, RC or RCL circuit.
= 2,3 kΩ Therefore: I = Vs Z 9 = 2300 = 3,91 mA It was mentioned that the angle between the two values was about 30°, but this can be accurately calculated using our knowledge of trigonometry. In the impedance triangle, the resistance (R) is the adjacent, and the impedance (Z) is the hypotenuse. One can therefore use the cos function, as cos θ = Hypotenuse . Adjacent Calculating the phase angle is simply: Cos θ = R Z = 2 000 2 300 = 0,869
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This cos θ is called the power factor. To get the angle in degrees, one must solve for θ by doing the following: θ = cos-1 (0,869) = 29,59° lagging (because IT laggs VT) In calculating the power in the circuit, one has to be a little more careful. Only the product (multiplication) of the current and the voltage values in phase with each other will give us the power in watts (W). This component of power is called the true power (P). However, the horizontal value of the supply voltage, in all these calculations, will always be VR, but in future calculations this may not be given. Fortunately trigonometry comes to the rescue again. To calculate the horizontal value:
Take note Although there other components of power as well, they will be dealt with the motor and transformer sections.
Figure 7.19: Phasor diagram showing voltage values
To calculate the horizontal value: V = Cos θ hor ___ VT VHOR
= VT cos θ
This enables us to calculate the power in the circuit, as P
= I × VHOR = I × VT × cos θ (Watts) = (3,91 mA)(9)(cos 29,59) = 30,61 mW
Take note Do not confuse cos θ and θ. Cos θ = 0,869, so the calculation could look like this. P = I × VHOR × cos θ = (3,91 mA)(9)(0,869) = 30,61 mW and will still be 100% correct.
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Electrical Technology The information for the RL circuit gained thus far has been recorded in the table below in the 5 kHz row. The calculations have been repeated at different frequencies and the new values added to the table as well. Now the effect that a change in frequency has on the values in the circuit can be clearly seen.
Take note The current is only constant if the frequency remains constant. The moment frequency changes, everything changes.
XL
Z
Cos θ
θ
Current (I) V Z
5 kHz
1 130 Ω
2 300 Ω
0,869 lagging
29,59°
3,91 mA
9 kHz
2 040 Ω
2 850 Ω
0,702 lagging
45,43°
3,16 mA
11 kHz
2 490 Ω
3 190 Ω
0,627 lagging
51,17°
2,82 mA
This information gives us clear and very definite facts to consider. One can clearly see that as frequency increases: • Inductive reactance (XL) increases • Impedance (Z) increases • Cos θ decreases • The phase angle increases • Current decreases (even though it is a series circuit, but the change in frequency caused this). The effect that the increase in the phase angle will have on the voltages from the supply and the voltage across the resistor and the coil will now be explored. Both the wave representation and the phasor representation are given to try to put this relationship in perspective.
Phasor and wave representations The wave and phasor diagram at 5 kHz: VT VR
V
t
29,59°
29,59°
Figure 7.20: The waves (oscillograms) for the RL circuit and the equivalent phasor representation of the waves
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The wave and phasor diagram at 9 kHz.
Figure 7.21: The waves (oscillograms) for the RL circuit and the equivalent phasor representation of the waves
The wave and phasor diagram at 11 kHz:
Figure 7.22: The waves (oscillograms) for the RL circuit and the equivalent phasor representation of the waves
From the sketches one can see that the waves move more and more apart (out of phase) as the frequency increases. Why is this happening? When an AC supply is connected to a coil, self-induction takes place. This is when the changing magnetic field cuts the conductors of the coil itself, and induces a current in it. This induced current in the coil always opposes the applied current (Lenz’s law). So the applied current and the induced current move in opposite directions, and the remaining current flowing in the circuit is the difference between them. However, when the frequency increases, the rate at which the changing magnetic field cuts the coils is increased, and so is the induced current. Once again, the induced current opposes the applied current, with the result that the remaining current flowing in the circuit at a higher frequency is less.
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IAPPLIED IINDUCED
LOW f
IACTUAL
IAPPLIED IINDUCED
HIGH f
IACTUAL
Figure 7.23: Phasors indicating applied, induced and remaining current in a coil
Capacitive reactance (Xc) The symbol for capacitance is the letter C, and the unit is the farad (F), which is a very large unit, so that the microfarad (μF), nanofarad (nF) and picofarad (pF) are more often used. When AC supply is connected to a capacitor, the current is limited to the value: I = V amps Xc Once again, there is a method of converting capacitance into an equivalent ohms value, and this equivalent ohm value is called capacitive reactance (Xc). Xc =
1 ohms 2πfC
where, • 2π refers to one cycle, or one revolution in rad • f is the supply frequency in Hz, and • C is the capacitance in farad (F) The current flowing in the circuit can now be calculated as: I= V amps XC In a circuit containing a resistor and a capacitor As for the RL circuit different units cannot be added together. In this case ohms and Farads are different, and the frequency will once again play a role. One needs to know what effect changes in frequency will have on the voltage and current in a capacitor before the respective ohm values can be added. The circuit in Figure 7.24 shows a series circuit joining a capacitor of 9 nF and a resistance of 2 kΩ connected to a 9 V, 5 kHz supply. This is commonly referred to as an RC circuit.
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VT
Figure 7.24: An RC series circuit
At this frequency of 5 kHz a number of calculations can be done, for example: XC = =
1 2πfC 1 2π(5000)(9 nF)
= 3,54 kΩ It is also noted that VR leads VT by approximately 60°. This means that we have the following voltage phasor diagram:
I
Figure 7.25: Phasor diagram showing voltage values
Just as in the RL circuit, each of the voltage values can be divided by the current. These values are transferred to a phasor diagram that represents resistance (R) and reactance (XC). VT ___ = Z I VR ___ = R I VC ___ = XC I
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Electrical Technology The transferred phasor diagram appears as shown below:
Figure 7.26: Phasor diagram showing ohm values
Impedance Impedance is the combined resistance of the capacitor and the resistor.
The impedance triangle for the RC circuit look as follows:
Figure 7.27: Impedance triangle for an RC circuit
Impedance, power, power factor and phase angle of an RC circuit How to calculate (mathematically) the value of the impedance in the circuit was explained earlier in this chapter: Take note Keep in mind that Z is always larger than R in any RL, RC and RCL circuit.
Z = √ (R2 + Xc2) = √ (2 000)2 + (3 540)2 = 4,06 kΩ Therefore: I = Vs Z 9 = 4060 = 2,22 mA
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Likewise, the power factor (Cos θ) and phase angle (θ): Cos θ = R Z = 2 000 4 060 = 0,493 (This cos θ is called the power factor) θ = cos-1 (0,493) = 60,49° leading (because IT leads VT) The true power is calculated as P
= I × VHOR = I × VT × cos θ (Watts) = (2,22 mA)(9)(cos 60,49) = 30,61 mW
This information has been recorded in the table below in the 5 kHz row. The calculations have been repeated at different frequencies and the new values added to the table as well. Now the effect that a change in frequency has on the values in the circuit can be clearly seen: XC
Z
Cos θ
θ
Current (I)
5 kHz
3 540 Ω
4 060 Ω
0,493 lagging
60,49°
2,22 mA
9 kHz
1 960 Ω
2 800 Ω
0,714 lagging
44,42°
3,21 mA
11 kHz
1 610 Ω
2 570 Ω
0,778 lagging
38,9°
3,50 mA
This information gives us clear and very definite facts to consider. One can clearly see that as frequency increases: • Capacitive reactance (XC) decreases • Impedance (Z) decreases • Cos θ increases • The phase angle decreases • Current increases. The effect that the decrease in phase angle will have on the voltages from the supply and the voltage across the resistor will now be explored. Both the wave representation and the phasor representation are given to try to put this relationship in perspective.
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Electrical Technology From the sketches one can see that the waves move closer (more in phase) as the frequency increases. The wave and phasor diagram at 5 kHz:
Figure 7.28: The waves (oscillograms) for the RC circuit and the equivalent phasor representation of the waves
The wave and phasor diagram at 9 kHz
44,42º
44,42º
Figure 7.29: The waves (oscillograms) for the RC circuit and the equivalent phasor representation of the waves
The wave and phasor diagram at 11 kHz:
Figure 7.30: The waves (oscillograms) for the RC circuit and the equivalent phasor representation of the waves
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Why is this happening? A capacitor connected to a supply at a low frequency has sufficient time to charge up. If given enough time, it will charge completely and block the flow of current through the circuit. The more time it has to charge, the more it causes the voltage and the current to move out of phase. The higher the frequency the less time it has to charge up because the polarity of the supply changes so rapidly that the capacitor does not have time to complete its charge. The less time it has to charge, the more current can flow in the circuit, and this seems to cause less of a phase angle between voltage and current.
In a circuit containing a resistor and a capacitor and a coil The RCL circuit really gets interesting, as now three different values, namely ohms, henries and farads, need to be combined into a single value, which is still called impedance (Z). The circuit in Figure 7.31 shows a series circuit joining a capacitor of 9 nF, a coil of 36 mH and a resistance of 2 kΩ connected to a 9 V/5 kHz supply. This is commonly referred to as a RCL circuit.
VT
Figure 7.31: An RCL series circuit
At this frequency of 5 kHz a lot of calculations can be done. One can calculate: Capacitive reactance:
XC = =
1 2πfC 1 2π(5 kHz)(9 nF)
= 3,54 kΩ Inductive reactance:
XL = 2πfL = 2π(5000)(36 × 10-3) = 1,13 kΩ
Impedance:
Z = √ R2 + (XL–XC)2 = √ (2 000)2 + (1 130 – 3 540)2 = 3,13 kΩ
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Cos θ = R Z = 2 000 3 130 = 0,639 leading (because XC is larger than XL which results in IT leading VT)
Phase angle:
θ = cos-1 (0,639) = 50,28°
This means that the voltage phasor diagram looks as follows.
Figure 7.32: A phasor diagram showing voltage values for an RCL circuit
Just as in the RL and RC circuits, each of the voltage values can be divided by the current. These values are transferred to a phasor diagram that represents resistance (R), and the reactances XC and XL. The transferred phasor diagram appears as shown below.
Figure 7.33: Phasor diagram showing ohm values for an RCL circuit
Impedance This is the combined resistance of the capacitor, the coil and the resistor. Keeping in mind that the components of XL and XC are 180° apart (or out of phase with each other) they can be seen as two tug-of-war teams. They pull in direct opposition to each other, and can simply be subtracted. However, their resultant (what is left) must still be added to the resistance of the resistor. From there the formula: Z = √(R2 + (XL – Xc)2
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The impedance triangle for the RCL circuit will depend on the values of XL and XC. Basically one will look at the impedance phasor, as that determines how the triangle is drawn.
If Z is above R
then the triangle is above
And if Z is below R
then the triangle is below
Impedance, power, power factor and phase angle of an RCL circuit The information obtained above has been recorded in the table below, with the calculations will be repeated at different frequencies and the new values added to the table. XL
XC
Z
Cos θ
θ
Current (I)
5 kHz
1 130 Ω
3 540 Ω
3 130 Ω
0,639 lagging
50,28°
2,88 mA
7 kHz
1 580 Ω
2 530 Ω
2 210 Ω
0,905 lagging
25,18°
4,07 mA
9 kHz
2 040 Ω
1 960 Ω
2 002 Ω
0,999 lagging
2,56°
4,50 mA
11 kHz
2 490 Ω
1 610 Ω
2 190 Ω
0,913 lagging
25,04°
4,11 mA
This information gives us clear and very definite facts to consider, and is very different to what was observed in the previous two cases. One can clearly see that as frequency increases: • Capacitive reactance (XC) decreases • Inductive reactance (XL) increases • Impedance (Z) first decreases and then increases • Cos θ increases and then decreases • The phase angle decreases and then increases • Current increases and then decreases. The true power (at 5 kHz) is calculated as: P = I × VHOR = I × VT × cos θ (Watts) = (2,88 mA)(9)(cos 50,28) = 16,56 mW
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Electrical Technology The effect that changing the frequency has on the voltages from the supply and the voltage across the resistor is demonstrated below. Both the wave representation and the phasor representation are given to try to put this relationship in perspective. Phasor and wave representations: The wave and phasor diagram at 5 kHz:
50,28º
50,28º leading
Figure 7.34: The waves (oscillograms) for the RCL circuit and the equivalent phasor representation of the waves
The wave and phasor diagram at 7 kHz:
25,18º
25,18º leading
Figure 7.35: The waves (oscillograms) for the RCL circuit and the equivalent phasor representation of the waves
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The wave and phasor diagram at 9 kHz:
2,56º
2,56º lagging
Figure 7.36: The waves (oscillograms) for the RCL circuit and the equivalent phasor representation of the waves
The wave and phasor diagram at 11 kHz:
25,04º
25,04º lagging
Figure 7.37: The waves (oscillograms) for the RCL circuit and the equivalent phasor representation of the waves
From the sketches one can see that the waves first move closer (more in phase) as the frequency increases, and after a certain point they move apart again; also that the angle turns from leading to lagging. Why is this happening? It is a combination of the coil and the capacitor’s actions, and the changing reactance values of the capacitor and the coil respectively. It is purely dependent on the frequency, and which one of the coil or the capacitor has the larger reactance at that specific frequency.
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Resonance (fr) In a series RLC circuit, a frequency point is reached where the inductive reactance of the inductor becomes equal in value to the capacitive reactance of the capacitor. The point at which this occurs is called the resonant frequency (ƒr). The phasor representation at this resonant frequency will be used to highlight a few important facts.
I
Figure 7.38: Phasor diagram representing the ohm values, and a phasor diagram representing the voltage values at resonance
From the phasor diagrams, one can conclude the following about the characteristics of an RCL circuit at resonance: • • • • • • • •
XL =XC R=Z VL =VC Cos θ = 1 θ = 0° I is max Z is min VR =VS
The value of the frequency at resonance can be calculated by the formula: fr =
1 2π √ LC
This is can be deduced from the following: At resonant frequency: XL = XC Therefore: 2πfL = f2 = f =
124
1 2πfC 1 4π2 LC 1 4π2LC
RCL fr =
7
1 2π √LC
Series resonance circuits are among the most important circuits used in electronics. They can be found in various forms in main AC filters, and in radio and television sets, producing a very selective tuning circuit for the receiving of different channels. In radio circuits they can be used to do the following: • Accept low frequencies and reject high frequencies (low pass filter) • Accept high frequencies and reject low frequencies (high pass filter) • Accept only a certain range of frequencies • Reject only a certain range of frequencies
The following graphs show how reactance changes with frequency for both RL and RC circuits, and how that culminates in the series RCL circuit and where resonance can be seen on them. Inductive reactance against frequency If either the frequency or the inductance is increased, the overall inductive reactance value of the inductor will also increase. The graph of inductive reactance against frequency is a straight linear line. The inductive reactance value of an inductor increases linearly as the frequency across it increases. Therefore, inductive reactance is positive and is directly proportional to frequency (XL∝ƒ).
Figure 7.39: A graph showing the relationship between frequency and inductive reactance
Capacitive Reactance against frequency If either the frequency or the capacitance is increased, the overall capacitive reactance would decrease. The graph of capacitive reactance against frequency is a hyperbolic curve. The reactance value of a capacitor has a very high value at low frequencies but quickly decreases as the frequency across it increases. Therefore, capacitive reactance is negative and is inversely proportional to frequency. (XC∝ 1ƒ )
Figure 7.40: A graph showing the relationship between frequency and capacitive reactance
One can see that the values of these resistances depend upon the frequency of the supply. At a higher frequency XL is high and at a low frequency XC is high. Then there must be a frequency point where the value of XL is the same as the value of XC. If the curve for inductive reactance is placed on top of the curve for capacitive reactance, so that both curves are on the same axes, the point of intersection will indicate the series resonance frequency point.
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r
Figure 7.41: A graph showing the relationship between frequency, capacitive reactance and inductive reactance, and a simplified graph showing impedance versus frequency.
Electrical resonance occurs in an AC circuit when the two reactances, which are opposite and equal, cancel each other out as XL = XC. The point on the graph at which this happens is where the two reactance curves cross each other. In a series resonance circuit, the resonant frequency is where Z is a minimum. In fact, Z is equal to R. Z = = = Z =
√ R2 + (XL – XC)2 √ R2 + 0 √ R2 R
Calculations Example 1
Figure 7.42: A series RL circuit
If the voltage across the resistor is 4 V, and the supply voltage is 5 V, calculate the voltage across the coil. Answer: Because the voltages are out of phase with each other, we cannot simply subtract them. We have to use Pythagoras. VL = √ VT2 – VR2 = √ 52 – 42 = 3 V Example 2 A circuit has a resistance of 3 ohm and an inductive reactance of 4 ohm. If the current flowing through the coil is 2 amps, what will be the value of the supply voltage if its frequency is 50 Hz?
Figure 7.43: A series circuit for a RL circuit
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Answer: The first thing that needs to be done is that the impedance must be found. Inductive reactance has already been given, therefore impedance can be determined immediately. Z = R2 + XL2
=
32 + 42 = 5 Ω
Then Ohm’s law is applied, because the supply voltage is the product of the total current flowing in the circuit and the total resistance (Z). VT = I × Z = (2)(5) = 10 V Example 3: Resistance and capacitance in series When a resistance is added in series with a capacitor, one needs to calculate the total resistance of the circuit, which is called the impedance. It is very similar to the above example. A resistance of 5 ohm and a capacitive reactance of 12 ohm are connected in series. If the current flowing through the circuit is 4 milli-amps, what will be the value of the supply voltage if its frequency is 50 Hz?
Figure 7.44 A series RC circuit
Answer:
Z = R2 + Xc2
=
52 + 122 = 13 Ω
Now the value of the supply voltage can be calculated: V = It × Z = 4 mA × 13 = 52 mV
Resistance, inductance and capacitance in series Example 4: An AC circuit contains a resistance of 8 ohm, a capacitance reactance of 6 ohm and inductive reactance of 9 ohm, all connected in series. If the current is 2 amp, calculate: • The supply voltage • The power factor
Figure 7.45 A circuit for a series RCL circuit
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Electrical Technology Answers: To calculate impedance: Z = =
R2 + (XL – XC)2 82 + (9 – 6)2
= 8,54 ohm Supply voltage:
V = It × Z = 2 × 8,54 = 17,08 volt
Power factor: cos θ
=
R Z
=
8 8,54 = 0,936 lagging (XL > XC)
Example 5 A series circuit consists of a resistance of 40 ohm, inductance of 140 mH and a capacitor of 49 μF. If the circuit is fed by a 220 volt 50 Hz supply, calculate: a) the capacitive reactance b) the inductive reactance c) the impedance of the circuit d) the current in the circuit e) phase angle f) voltage across the coil g) voltage across the capacitor h) voltage across the resistance Draw a voltage phasor diagram and show all values. Given: • C = 49 μF • L = 140 mH • R = 40 ohm • V = 220 volt • f = 50 Hz
Figure 7.46: An RCL circuit
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Answers: a)
XC
=
1 2πfC
XC
=
1 2π × 50 × 49 × 10−6
= 64,96 ohm b)
XL
= 2πfL
XL
= 2π × 50 × 140 × 10−6 = 44 ohm
c)
Z
=
R2 + (XC – XL)2
=
402 + (64,96 – 44)2
XC > XL (capacitive circuit)
= 45,16 ohm d)
It
=
Vt Z
=
220 45,16
amps amps
= 4,872 A e)
Cos θ
θ
=
R Z
= cos-1
40 45,16
= 27,608° f)
VL
= It × XL = 4,872 × 44 = 214,368 volt
g)
VC
= It × XC = 4,872 ×64,96 = 316,485 volt
h)
VR
= It × R = 4,872 × 40 = 194,88 volt
Test your answers! Vt
=
VR2 + (VC – VL)2
= 194,882 + (316,485 – 214,368)2 = 220 volt
(if no rounding was done)
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Electrical Technology The voltage phasor diagram is shown below. Phasor and wave representation VL = 214 V
VR = 194 V = 27,6º VC – VL = 102 V VT = 220 V
VC = 316 V
Figure 7.47 This phasor diagram shows the current leading the supply voltage.
Example 6 Figure 7.48 depicts the reactance of an inductor and a capacitor, and the resistance of a resistor versus frequency. Interpret the information and answer the questions that follow.
Figure 7.48 Reactances and resistance versus frequency
a) Draw TWO approximate impedance phasor diagrams of an RLC series circuit next to each other, with the frequency at point A; and C respectively. b) The circuit represented by the above graph consists of a 3 kΩ resistor, a 50 μF capacitor and a 0,1 H coil. Calculate the frequency at point B.
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RCL
7
Answers: a)
I
⍜
⍜
I
Figure 7.49: Phasor diagram showing resistance, reactance and impedance
b)
ƒr
=
1 2π LC
ƒr
=
ƒr
= 71,18 Hz
2π
1 0,1 × 50 × 10−6
Example 7 A series circuit with a 250 μF capacitor, a 120 mH coil and a resistor of 15 Ω is connected across a 240 V/ 50 Hz supply. a) b) c) d) e)
Calculate the total impedance in the circuit. Calculate the voltage drop across the coil. Calculate the phase angle. Is the circuit more inductive or capacitive? Motivate your answer. Must the frequency increase or decrease for the circuit to resonate? Motivate your answer.
(9) (6) (3) (2) (3)
Answers: a)
XL =
2πfL = 2π × 50 × 120 × 10−3 = 37,70 Ω
XC =
1 2πfC
XC =
(3)
1 2π (50)(250 × 10−6)
XC = 12,73 Ω
(3)
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7
Electrical Technology
b)
Z
= R2 + (XL – XC)2
Z
=
Z
= 29,13 Ω
I
=
V Z
I
=
240 29,13
I
= 8,24 A
152 + (37,70 – 12,73)2 (3)
(3)
VL = I × XL VL = 8,24 × 37,70 VL = 310,65 V c)
cosθ =
(3)
R Z
θ
= cos-1 15 29,13
(3)
θ
= 59,01˚
(2)
d) Inductive. XL>XC
(2)
e) Decrease. Because XC needs to increase for the circuit to be more capacitive
(3)
Example 8 1.2
IT = 2 mA
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RCL
7
Use the phasor diagram to answer the following questions: a) b) c) d) e) f) g)
Draw a neat circuit diagram that will represent the phasor diagram above. Is the circuit more inductive or more capacitive? Motivate your answer. Calculate the supply voltage. Is the power factor leading or lagging? Explain your answer. Calculate the reactive values of the coil and the capacitor. Calculate the actual values of the components in the circuit Draw a neat impedance triangle.
(3) (3) (3) (3) (6) (9) (3) [27]
Answers: a)
b) Capacitive because VL 3 is TRUE, and the value for “An apple is not a fruit.” is FALSE. The system allows one to represent electronic logic switching circuits (gates) with a series of algebraic expressions.
Logic words O
1
Low
High
Off
On
0V
5V
Open
Closed
Boolean expressions can only represent three basic operations: • Logical addition: This is also called the OR function and is normally represented with a plus sign (+). • Logical multiplication: This is also called the AND function and is represented with a dot (.). • Logical inversion: This is also called the NOT___ or INVERTER function and is represented with a line above the function ( ) or an accent sign next to the function or variable ( ´ ), i.e. (A.B) = (A.B)´. Boolean algebra is, therefore, a system of mathematics based on logic that has its own set of rules or laws which are used to define and reduce Boolean expressions. The variables used in Boolean algebra have only one of two possible values, logic “0” and logic “1”, but an expression can have an infinite number of variables, all labelled individually to represent inputs to the expression, for example, variables A, B, C, giving us a logical expression of A + B = C, but each variable can ONLY be a 0 or a 1.
Take note A voltage signal with zero (0) corresponds to 0 volts and one (1) corresponds to five or three volts.
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Electrical Technology
SUM of PRODUCT (SOP) notation The SOP notation is where the Boolean expression is made up of a number of product terms (AND terms), separated by a sum sign (OR sign). Boolean expressions can be written in either the SUM of PRODUCT (SOP) notation – also referred to as Minterms – or in the PRODUCT of SUM (POS) notation, also referred to as Maxterms. Of the two notations, the SOP is the more popular one. E.g. Sum sign (OR Function)
Q = (A.B) + (A.C) + (B.C)
} SUM of PRODUCTS Notation (SOP)
Product terms (AND Function) How the SOP expression is derived from a truth table is demonstrated in the example below. Example With reference to the truth table below, derive the output Boolean expression in the SUM of PRODUCTS (SOP) notation. It is important to remember that when any variable is represented by logic ‘0’ in the truth table, that variable is represented as an inverted variable, i.e. A. If such a variable is represented by logic ‘1’, that variable is represented as a non-inverted variable, i.e. A. So if inputs A, B and C have the following logic values in a truth table: A = 0, B = 1 and C = 0, then the product term representing these three inputs can be written as A.B.C Inputs
Remember Remember for SOP: • Identify all the ‘1’ outputs. • Write that number of input combinations. • Complement all 0s on the input combinations.
Output
A
B
C
Q
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
Product term 1 = A.B.C
Product term 2 = A.B.C
Product term 3 = A.B.C
Figure 11.2: Truth table with product terms
The SOP output expression is derived from the truth table by identifying all the outputs where there is logic 1 at the output. These product terms are then all ORed together.
228
From the truth table above Q = A.B.C + A.B.C + A.B.C (This expression may not be in it simplest form, it may be simplified further by using Boolean algebra.) More about equation simplification later.
Logic
11
PRODUCT of SUM (POS) notation The POS notation is where the Boolean expression is made up of a number of sum terms (OR terms), separated by a product sign (AND sign). The PRODUCT of SUM (POS) notation, which is also sometimes referred to as Maxterms, is used less frequently but is also relatively easy to understand. E.g. Product sign (AND function)
Q = (A+B). (A+C). (B+C)
} PRODUCT of SUMS notation (POS)
Sum terms (OR function) How the POS expression is derived from a truth table is demonstrated in the example below. Example With reference to the truth table below, derive the output Boolean expression in the PRODUCT of SUMS (POS) notation. Remember that when any variable is represented by logic ‘0’ in the truth table, that variable is represented as a noninverted variable ie. A. If such a variable is represented by logic ‘1’, that variable is represented as an inverted variable, i.e. A. Inputs
Output
A
B
C
Q
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
SUM term 1 = A+B+C
SUM term 2 = A+B+C
SUM term 3 = A+B+C
Figure 11.3: Truth table with sum terms
Remember Remember for POS: • Identify all the ‘0’ outputs. • Write that number of input combinations. • Complement all the 1s on the input combinations.
The POS output expression is derived from the truth table by identifying all the outputs where there is a logic 0 at the output. All these sum terms are then ANDed to form the final logic expression in POS notation. From the truth table above Q = (A+B+C). (A+B+C). (A+B+C) (This may not be in its simplest form and may be simplified further by using Boolean algebra).
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Electrical Technology
NOT Gate (Inverter) A NOT gate can only have one input and one output. The output of the NOT gate will always be the inverse of the input, i.e. Q = not A (A). If the input is logic 1, then the output will be logic 0 and vice versa. Switching circuit
Figure 11.4 (a): NOT gate switching circuit
Logic symbols
Figure 11.4 (b): NOT gate logic symbols
Truth Table Input A
Output Q
0
1
1
0
Figure 11.4 (c): NOT gate truth table
The Boolean expression for this gate can be written as: Q = A or A´; The line over the A means the output is inverted and is pronounced not A. The accent sign next to A also means that A is inverted.
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AND Gate The AND gate is a simple gate that can have two or more inputs. In Grade 11, learners are introduced to the three-input AND gate. The output (Q) will be logic 1 only when all the three inputs are logic 1s. In other words, inputs A, B and C must all be 1s for the output to be logic 1. If any one of the inputs is logic 0, the output to the gate will be logic 0. Below is the switching circuit, logic symbol, Boolean expressions and truth table for the three-input AND Gate. Switching circuit
Figure 11.5 (a): AND gate switching circuit
Logic symbols
&
Figure 11.5 (b): AND gate logic symbols
Truth Table Input A
Input B
Input C
Output Q
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
Figure 11.5 (c): AND gate truth table
The Boolean expression for this gate can be written as: Q = A.B.C or Q = B.C.A or Q = C.A.B. In other words, the inputs can be written in any order as long as all three are present as part of the inputs. This is commonly referred to as the commutative law.
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11
Electrical Technology
NAND Gate The NAND gate is a combination of an AND gate and a NOT gate. All it does is indicate that the output of the AND gate is inverted. For a three-input NAND gate, the output will be logic 1 when any one of the three inputs is logic 0. With all the inputs on logic 1, the output will be logic 0. This gate is very versatile and can be used to create various other logic gates. The NAND gate is commonly referred to as a universal gate. Below is the switching circuit, logic symbol, Boolean expressions and truth table for the three-input NAND gate. Switching circuit
Figure 11.6 (a): NAND gate switching circuit
Logic symbols
&
Figure 11.6 (b): NAND gate logic symbols
Truth Table Input A
Input B
Input C
Output Q
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
Figure 11.6 (c): NAND gate truth table
The Boolean expression for this gate can be written as: Q = A.B.C and can be said as: A AND B AND C, all inverted.
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OR Gate The OR gate is a simple gate that can have two or more inputs. In the three-input OR gate, the output (Q) will be logic 1, with any one of the three inputs being logic 1. The output will be logic 0 only when all the inputs are logic 0s. Below is the switching circuit, logic symbol, Boolean expressions and truth table for the three input OR Gate. Switching circuit 3 Input OR Gate
Figure 11.7 (a): OR gate switching circuit
Logic symbols
Figure 11.7 (b): OR gate logic symbols
Truth Table Input A
Input B
Input C
Output Q
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
Figure 11.7 (c): OR gate truth table
The Boolean expression for this gate can be written as: Q = A+B+C or Q = B+C+A or Q = C+A+B. In other words, the inputs can be written in any order as long as all three are present as part of the inputs. This is commonly referred to as the commutative law.
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11
Electrical Technology
NOR Gate The NOR gate is a combination of the OR gate and a NOT gate. All it does is indicate that the output of the OR gate is inverted. For a three-input NOR gate, the output will be logic 1 only when all three inputs are logic 0s. With any input on a logic 1, the output will be logic 0. As with the NAND gate, this gate is also very versatile and can be used to create various other logic gates. Below are the switching circuit, logic symbol, Boolean expressions and truth table for the threeinput NOR gate. Switching circuit 3 Input NOR Gate
Figure 11.8 (a): NOR gate switching circuit
Logic symbols ≥1
Figure 11.8 (b): NOR gate logic symbols
Truth Table Input A
Input B
Input C
Output Q
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
Figure 11.8 (c): NOR gate truth table
The Boolean expression for this gate can be written as: Q = A+B+C and can be said as A OR B OR C, all inverted.
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Logic
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XOR Gate (Exclusive-OR gate) The XOR gate is a specialized gate with only two inputs. The output of this gate will be logic 0 only when both inputs are logic 1s or when both inputs are logic 0s. For any other input combinations, the output will be logic 1. Below are the switching circuit, logic symbol, Boolean expressions and truth table for the two input XOR gate. Switching circuit 2 Input Exclusive-OR Gate (XOR Gate)
Remember It reminds us of the 2 – way switching done in grade 10. Figure 11.9(a): XOR gate switching circuit
Logic symbols
Figure 11.9 (b): XOR gate logic symbols
Truth Table Input A
Input B
Output Q
0
0
0
0
1
1
1
0
1
1
1
0
Figure 11.9 (c): XOR gate truth table
The Boolean expression for this gate can be written as: Q = A.B+A.B or Q = A ⊕ B . The last expression is more commonly used to represent the output of the Exclusive-OR gate.
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11
Electrical Technology
XNOR Gate (Exclusive-NOR gate) The XNOR gate is also a specialized gate with only two inputs. This gate is the inverse of the XOR gate, with the output of this gate being logic 1 only when both inputs are logic 1s or when both inputs are logic 0s. For any other input combinations, the output will be logic 0. Below are the switching circuit, logic symbol, Boolean expressions and truth table for the two input XNOR gate. Switching circuit 2 Input Exclusive-NOR Gate (X NOR Gate)
Figure 11.10 (a): XNOR gate switching circuit
Logic symbols
Figure 11.10 (b): XNOR gate logic symbols
Truth Table Input A
Input B
Output Q
0
0
1
0
1
0
1
0
0
1
1
1
Figure 11.10 (c): XNOR gate truth table
The Boolean expression for this gate can be written as: Q = A.B+A.B or Q = A ⊕ B The last expression is more commonly used to represent the output of the Exclusive-NOR gate.
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Logic
11
The NAND Gate as universal gate As mentioned earlier, the NAND gate is referred to as a universal logic gate, because it can be used to represent various other logic gates. As a logic designer working from home, one may find oneself with only NAND gates to do a certain logic circuit. Using the NAND gate as a universal gate will make it so much easier to design and construct the circuit.
Take note The NAND gates can be used to obtain all the other logic functions.
Creating an INVERTER using a NAND gate
Figure 11.11 (a): NAND gate as INVERTER
Creating an AND gate using NAND gates
Figure 11.11 (b): NAND gate as an AND gate
Creating an OR gate using NAND gates
Figure 11.11 (c): NAND gate as an OR gate
Creating a NOR gate using NAND gates
Figure 11.11(d): NAND gate as a NOR gate
How to convert a basic gate combination to NAND gate only The following simple steps can be followed to convert any simple Boolean expression to NAND gates only: • Take the original Boolean expression and double invert the equation – the double inversion (double negate) of the equation will not change the equation in any way, it will only help to get to the NAND equivalent. How does this double inversion work? If logic 1 is inverted once, it becomes logic 0, and if this 0 is now inverted again, it becomes logic 1 again. (In other words, the logic 1 one started with did not actually change, i.e. A = A • Apply De Morgan’s theorem where needed. Refer to the table of Boolean laws (break the line and change the sign). • The equation should now be in NAND gate format.
Remember Always break the line from the bottom.
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11
Electrical Technology This concept is demonstrated with the aid of an example. Example 1 Convert the following Boolean expression to NAND gates only; also draw the NAND gate logic circuit for this expression.
Take note Using De Morgan to redesign a logic function that uses NAND gates only does not make the circuit simpler. But it does allow us to build any circuit using only one type of logic gate. This is quite often cheaper to build.
Q = A.B+C = (A.B)+C
Double invert the original equation – by double inverting, the equation actually remains the same.
= (A.B).C
Apply De Morgan’s law (refer to the table of Boolean laws).
= (A.B).C
Boolean law 9 – double invert C (refer to the table of Boolean laws)
Figure 11.12: NAND gates only
Example 2 Q = A.B+C.D+A.C = A.B+C.D+A.C
Double invert the original equation – by double inverting, the equation actually remains the same
= (A.B). (C.D). (A.C) Apply De Morgan’s law (refer to the table of Boolean laws)
Figure 11.13: NAND gates only
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The NOR Gate as universal gate As mentioned earlier, the NOR gate is also very versatile and can be used to represent various other logic gates. This is very useful if one finds one only has NOR gates to do a specific circuit design. The NOR gate as INVERTER
Figure 11.14 (a): NOR gate as INVERTER
The NOR gate as an AND gate
Figure 11.14 (b): NOR gate as AND gate
The NOR gate as an OR gate
Figure 11.14 (c): NOR gate as OR gate
The NOR gate as a NAND gate
Figure 11.14 (d): NOR gate as NAND gate
Combinational/complex circuits So far this chapter has only dealt with individual/single logic gates. It is, however, possible to combine these logic gates to form more complex circuits and to perform various logical functions. To be able to work with these more complex circuits require a good understanding of the operation of the individual logic gates. Combinational logic circuits can be very simple or very complicated. As combinational logic circuits are made up of individual logic gates only, they can also be considered as “decision-making circuits”. Combinational logic is about combining logic gates to process two or more signals in order to produce at least one output signal according to the logical function of each logic gate. Common combinational circuits made up from individual logic gates that carry out a desired function include multiplexers, demultiplexers, encoders, decoders and full and half adders. The following section of the work will focus on working from a given complex circuit and then writing down the Boolean expression and completing the truth table for the circuit.
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11
Electrical Technology The following steps can be followed when determining the Boolean expression and truth table for a complex/combination circuit. Example 1 With reference to the circuit below, write down the Boolean expression for the output Q and also compile a truth table for this circuit. 1=(A.B) Q = (A.B)+C
Figure 11.15 (a): Combination circuit
The Boolean expression is written as follows: • Write down the individual Boolean expression output for each logic gate, starting with gate 1. Output of gate 1 = A.B, • The final Boolean expression (Q) is written by combining the individual Boolean expressions for the gates in the proper form. Final output = Output of gate 1 OR Input C Final Boolean expression for above circuit is: Q = (A.B)+C The truth table is compiled as follows: • First determine the number of inputs there are in the circuit (1,2,3, etc.). This will allow one to set up the initial truth table with all the possible input combinations, e.g. 2 inputs will have 22 = 4 input combinations, whereas 3 inputs will have 23 = 8 input combinations. For this example there will be 3 inputs, therefore, there will be 8 possible input combinations. A
B
C
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
Figure 11.15 (b): Truth table
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Logic
11
• Now add to the initial table an output for each logic gate output in the complex circuit. Label the outputs accordingly. A
B
C
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1 = A.B
Q = A.B+C
Figure 11.15 (c): Truth table
• Work through each logic gate in the complex circuit and complete the truth table up to the final output. A
B
C
1 = A.B
Q = A.B+C
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
Figure 11.15 (d): Truth table
Example 2 Determine the Boolean expression as well as the truth table for the logic circuit below. 1=(A.B) Q = (A.B)+(A.C) 2=(A.C)
Figure 11.16 (a): Combination circuit
STEP 1 • Write down the individual Boolean expression output for each logic gate, starting with gate 1. Output of gate 1 = A.B Output for gate 2 = A.C • The final Boolean expression is written by combining the individual Boolean expressions for the gates. Final output (Q) = Output of gate 1 (OR) Output of gate 2 Final Boolean expression for above circuit is: Q = (A.B)+(A.C)
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11
Electrical Technology The truth table is compiled as follows: • First determine the number of inputs there are in the circuit. This will allow one to set up the initial truth table with all the possible input combinations. For this example there are again 3 inputs, therefore, 8 possible input combinations. A
B
C
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
Figure 11.16 (b): Truth table
• Now add to the initial table an output for each logic gate output in the complex circuit. Label the inputs accordingly. A
B
C
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1 = A.B
2 = A.C
Q = A.B +A.C
Figure 11.16 (c): Truth table
• Work through each logic gate in the complex circuit and complete the truth table up to the final output. A
B
C
1 = A.B
2 = A.C
Q =A.B + A.C
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
Figure 11.15 (d): Truth table
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Example 3 Determine the Boolean expression as well as the truth table for the logic circuit below.
Figure 11.17 (a): Combination circuit
STEPS • Write down the individual Boolean expression output for each logic gate, starting with gate 1. Output for gate 1 = A.B Output for gate 2 = A+B • The final Boolean expression is written by combining the individual Boolean expressions. Final output (Q) = Output of gate 1 (AND) Output of gate 2 (AND) input C Final Boolean expression for above circuit is: Q = (A.B).(A+B).C The truth table is compiled as follows: • First determine the number of inputs there are in the circuit. This will allow one to set up the initial truth table with all the possible input combinations. For this example there are again 3 inputs, therefore, 8 possible input combinations. A
B
C
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
Figure 11.17 (b): Truth table
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Electrical Technology • Now add to the initial table an output for each logic gate output in the complex circuit. Label the inputs accordingly. A
B
C
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1 = A.B
2 = A+B
Q = (A.B).(A+B).C
Figure 11.17 (c): Truth table
• Work your way through each logic gate in the complex circuit and complete the truth table up to the final output. A
B
C
1 = A.B
2 = A+B
Q =(A.B).(A+B).C
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
Figure 11.17 (d): Truth table
It is also possible to draw the logic circuit from a given Boolean expression. Here is an example to demonstrate how this is done. Example 1 Draw a logic circuit for the following Boolean expression. Q = A.B.C+D Steps • Inputs A, B and C are first fed through an AND gate
Figure 11.18 (a):
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• Input D and the output of the AND gate are now fed through an OR gate to give the final gate combination.
Figure 11.18 (b):
Example 2 Draw a logic circuit for the following Boolean expression. Q = A.B + C.D Steps • First invert input A and feed it through an AND gate with input B.
Figure 11.19 (a):
• Now invert input D and feed it through an AND gate with input C.
Figure 11.19(b):
• The outputs of the two AND gates must now be fed through an OR gate to give the final gate combination.
Figure 11.19 (c):
Example 3 Draw a logic circuit for the following Boolean expression. Q = A.B+C Steps • Inputs A and B must first go through an AND gate.
Figure 11.20 (a):
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Electrical Technology • Input C and the output of the AND gate are now fed through a NOR gate to give the final gate combination.
Figure 11.20 (b)
Half adder As mentioned earlier, logic gate combinations can perform various mathematical functions one of which is the addition of two binary bits. The logic function used to add up two binary bits is referred to as a half adder. As with the decimal number system, where one normally generates a sum bit as well as a carry bit, the binary addition works on exactly the same principle. Here is a quick revision of the binary addition rules that were covered in grade 10. Addition rules 0+0→ 0 Carry bit Sum bit 0+1→ 1 1+0→ 1 1 + 1 → 0, carry 1, and the carry is to the next MSB (or 102, which is the binary equivalent for 2 ). This section will look at the operation of the half adder in more detail. When two binary bits are added, there will be 22 = 4 possible input combinations in the truth table as shown below. Also included in the truth table as outputs will be the sum and carry outputs. The truth table is completed by simply adding bit A to bit B (use the addition rules) and writing down the sum and carry bits in the truth table. Truth Table A
B
Sum
Carry
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
Figure 11.21 (a): Half adder truth table
Once the truth table is complete, write down the output equation for both the sum and the carry outputs in SOP notation. i.e.
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Sum = A.B+A.B or alternatively A ⊕ B and Carry = A.B
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On closer examination of both the sum and carry outputs it is seen that they actually represent TWO standard logic gates. The sum output can be represented by an exclusive-OR gate and the carry can be represented by an AND gate. A
B
Sum
Carry
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
Output of XOR
Output of AND
Figure 11.21 (b): Half adder truth table
If one looks at the sum and carry output, one can clearly see that the outputs represent the binary equivalent of the decimal numbers of the addition process.
Sum
Carry
0
0
1
0
1
0
0
1
LSB
(012) = 0 in decimal (012) = 1 in decimal (012) = 1 in decimal (012) = 2 in decimal
MSB
Figure 11.21 (c): Sum and carry outputs
From the information in the truth table one can now draw the logic circuit that will be able to perform this function (adding of two binary bits). One starts by first drawing the circuit for the sum as indicated below: Sum = A.B+A.B or alternatively A ⊕ B
Figure 11.22 (a): Sum bit for half adder
OR if S = A ⊕ B
Figure 11.22 (b): Sum bit for half adder
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Figure 11.22 (c): Carry bit for half adder
The two circuits are now combined to give the half adder (H/A)
Figure 11.22 (d): Complete circuit for half adder
Simple alarm circuit design The owner of a spaza shop in your area asks you to design a simple alarm for his shop. The shop has one window and one door. You must design an alarm that will sound if either the window or the door is opened. Steps Remember Door open 1 Door closed 0 Window open 1 Window closed 0
• The window and the door will represent two inputs and the siren will represent the output. Logic 1 represents an open input and logic 0 represents a closed input. • Now compile the truth table for the two inputs. With two inputs we will have 22 = 4 combinations for the input of the truth table. Window A
Door B
Siren Q
0
0
0
0
1
1
1
0
1
1
1
1
Output to be considered
Figure 11.23 (a): Truth table for simple alarm
Take note AB + AB + AB = B(A+A)+ A(B+B) = B.1 + A.1 = B+A =A+B
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• Identify all the places in the truth table where the output is logic 1 and write down the Boolean expression in the SOP notation. i.e. Q = A.B+A.B+A.B Remember this equation is not in its simplest form and can be simplified by making use of Boolean laws or by using Karnaugh maps. More about simplification once we have learned more about Boolean laws. The simplified expression for the equation above is: Q=A+B • From the simplified expression, we can now build the logic function represented by the simplified expression: Input A and input B must go through an OR gate to give us our final simplified logic circuit.
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Figure 11.23(b): Final circuit for simple alarm
Boolean laws So far Boolean expressions have been mentioned frequently, but they have not yet been explained. These expressions are expressions that mathematically link the output of a logic function with its input. In some instances, they can be very short and simple, but in other instances, these Boolean expressions can be very long and complicated. When these expressions are so long, it is important to simplify the expression before a logic circuit is built. The simplification of these expressions helps to reduce the number of logic gates needed in a specific design and makes the circuit simpler. The reduction in the number of gates used has a direct impact on the cost of the project. Boolean laws are logic laws that will help one to simplify long and complex Boolean expressions mathematically and enable one to make simpler designs. Rules
Explanation of rule
Rule 1
A . 0 = 0 } A variable ANDed with 0 is always equal to 0.
Rule 2
A . 1 = A } A variable ANDed with 1 is always equal to the variable.
Rule3
A . A = A } A variable ORed with 1 is always equal to 1.
Rule 4
A . A = 0 } A variable ANDed with its complement is always equal to 0.
Rule 5
A + 0 = A } A variable ORed with 0 is always equal to 1.
Rule 6
A + 1 = 1 } A variable ORed with 1 is always equal to 1.
Rule 7
A + A = A } A variable ORed with itself is always equal to the variable.
Rule 8
A + A = 1 } A variable ORed with its complement is always equal to 1.
Rule 9
A = A } A double inverted function = the function
Rule 10 Commutative Law
A + B = B + A } The order in which two variables are ORed makes no difference.
Take note Boolean laws are used to simplify complicated Boolean expressions.
A.B = B.A } The order in which two variables are ANDed makes no difference. Rule 11 Associative Law
A + (B + C) = (A + B) +C } Free association (grouping) of any two terms A (B.C) = (A.B) C } Free association (grouping) of any two terms
Rule 12 Distributive Law
A (B + C) = A.B + A.C } Simplification by the removal of the brackets
Rule 13 De Morgan’s Law
1 A + B = A . B } The complement of the sum equals the product of the complements. Or, when you break the line you change the sign. 2 A . B = A + B } The complement of the product equals the sum of the compliments. Or, when you break the line you change the sign.
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A + A.B = A } Deduced from rules 2 & 6 Or A + A.B = A = A ( 1 + B ) A is taken out as common factor (Distributive Rule 12) = A (1) Rule 6 = A Rule 2
Rule 15 (deduced)
A + A.B = A + B } Deduced from laws 1,2,4,12,&14 OR A + A.B = A + B = (A + A.B) + A.B
(Rule 14)
= (A.A + A.B) + A.B
(Rule 1)
= (A.A + A.B ) + 0 + A.B
(Just add a zero)
= (A.A + A.B ) + A.A + A.B (Rule 4) = A (A + B) + A (A + B)
(Distributive Rule 12)
= (A + B ) . (A + A) Distributive Rule 12
(A + B) is taken out as common factor.
= (A + B) .(1)
Rule 8
=A+B
Rule 2
Figure 11.24: Boolean laws
Use of truth tables to prove De Morgan’s laws Please note that all the rules above can be proved with the aid of a truth table. Because De Morgan is a very popular law, the two De Morgan’s laws will be used as examples. A + B = A . B } The complement of the sum equals the product of the compliments. (Or: When you break the line, you change the sign.) A
B
A
B
A+B
A.B
A+B
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
Figure 11.25 (a): De Morgan’s law (1) truth table
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A . B = A + B } The complement of the product equals the sum of the complements. (Or: When you break the line, you change the sign.) A
B
A
B
A.B
A+B
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
Figure 11.25 (b): De Morgan’s law (2) truth table
Simplification of Boolean expressions The simplification of Boolean equations can be a very challenging task. When simplifying an equation, the most difficult part is identifying the rules to be used to help with the simplification. It is important to remember that Boolean equations can be simplified in a number of ways, as long as the correct rules are used. One’s ability to solve and simplify Boolean expressions will be developed only by completing as many examples as possible. Examples Make use of Boolean rules to simplify the following Boolean expressions. 1.
2.
3.
4. 5.
6. 7.
F = ( A + A ) +A = ( A + A) =A F = ( K + K) + 1 = K+1 =1
Rule 7 Rule 7
Rule 7 Rule 6
F = (B . B) + 1 = (0) + 1 = 1 F = 1 .(YZ) = YZ
Rule 2
F = (Z + Z) . (P + P) = (1) . (P+P) = 1 .P = P
Rules 8 Rule 7 Rule 2
F = A.B . C.D = (A + B) . (C + D)
De Morgan’s Law
Rule 4 Rule 6
F = (A + B) + (A + C) = A.A + A.C + A.B + B.C = A + A.C + A.B + B.C = A (1 + C) + A.B + B.C = A (1) + A.B + B.C = A (1 + B) + B.C = A(1) + B.C = A + B.C
Rule 12 Rule 3 A is taken out as common factor (Distributive Rule 12) Rule 6 A is taken out as common factor (Distributive Rule 12) Rule 6
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F = X.Y + X.Y + XYZ = X.Y (1 + Z) + X.Y = X.Y (1) + X.Y = X.Y + X.Y = X ( Y + Y) = X.(1) =X
XY is taken out as common factor (Distributive Rule 12) Rule 6 Rule 2 X is taken out as common factor (Distributive Rule 12) Rule 8
9.
F = K.L.M + K.L.M + K.L.M + K.L.M = K.L (M + M) + K.M (L + L) K.L and K.M are taken out as common factor (Distributive Rule 12) = K.L (1) + K.M (1) Rule 8 = K.L + K.M Rule 2
10.
F = C + B.C = C + (B + C) = (C + C) + B =1+B =1
11.
F = (A + C)(A.D + AD) + A.C + C = (A + C)A(D + D) + A.C + C = (A + C)A + A.C + C = A((A + C) + C) + C = A(A + C) + C = AA + AC + C = A(A + C) + C = A + (A + 1)C =A+C
12.
De Morgan Associative Rule 11 Rule 8 Rule 6
A is taken out as common factor (Distributive Rule 12) Rule 8 A is taken out as common factor (Distributive Rule 12) Rule 7 Distributive Rule 12 A is taken out as common factor (Distributive Rule 12) C is taken out as common factor (Distributive Rule 12) and Rule 3 Rule 6 and 2
Prove that: A.B + A.B = A.B + A.B Work with the left-hand side of the equation (LHS) LHS = A.B + A.B = A.B. A.B De Morgan = (A + B ) . (A + B) De Morgan twice = (A + B ) . (A + B) Rule 9 twice (term A and B) = A.A + A.B + A.B + B.B Distributive Rule 12 = 0 + A.B + A.B + 0 Rule 4 twice = A.B + A.B therefore the LHS = RHS
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Prove that: A.B.C + A.B.C + A.B.C = A.B + A.C Work with the left-hand side of the equation (LHS) LHS = A.B.C + A.B.C + A.B.C = A.B (C + C) + A.B.C A.B is taken out as common factor (Distributive Rule 12) = A.B + A.B.C Rule 8 = A (B + B.C) A is taken out as common factor (Distributive Rule 12) = A ( B + C) Rule 15 = A.B + A.C therefore the LHS=RHS
Activity 1 1. 2. 3.
4. 5. 6. 7.
How many possible input combinations can we get if we have a four variable logic gate? What is the difference between the Sum of Product and Product of Sum notation? Give an example of each. Draw the logic symbol, Boolean expression and truth table for the following logic gates: • Three-input AND Gate • Two-input NOR Gate • Three-input NAND Gate • Two-input Exclusive-OR Gate The NAND gate is commonly referred to as universal logic gate. Why is this so? Draw the NAND gate equivalent of an OR gate and a NOT gate. Draw the NOR gate equivalent of an AND gate and a OR gate. For each of the following logic circuits, write down the Boolean expression for the output Q, and then develop a truth table for each circuit:
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8.
9.
Draw the logic circuit for each of the following Boolean expressions: Q = A.B + A.C Q = (A + B) +C Q = A.B.C + A.B.C Q = B ( A + C) Complete the truth table below for a half adder. A
B
0
0
0
1
1
0
1
1
Sum
Carry
10. Two binary signals A and B must be compared and as soon as A is not equal to B, a light emitting diode must switch on. Design a minimum circuit to execute this function. Give the truth table, Boolean expression and circuit for this design. 11. Convert the following Boolean expressions to NAND gates only; also draw the NAND gate logic circuit for each expression: Q = A.B + C.D Q = A.B +C Q = A.B + BC + C.D 12. Simplify the following simple Boolean expressions: Q = (A + A) +A Q = (D . 1)+ 1 Q = (C + C)+1 Q=A+B+C+D+1 Q=J.K.L.M.0 13. Give THREE reasons why we need to simplify Boolean expressions.
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14. By making use of Boolean laws or De Morgan’s theorem, simplify the following Boolean expressions: Q = A.B.C + A.B + C Q = (A + B) (A + C) Q = A.B + A.B + A.B.C Q = (J + K) + (L + M) Q = M.N.O + M.N.O Q = X.Y + Y.Z + Y.Z Q = X.Y.Z + X.Y.Z + X.Y.Z + X.Y Q = M.N + M + N + M.N.O 15. Prove the following statements: A.B.C + A.B.C + A.B.C = A.B + A.C A.B + A + B = 0 A.B (C+C ) + A.B (C + C) = A 16. In the control room of a factory, three motors are monitored. If two or more of the motors develop a fault, an indicator lamp must go off in the control room, notifying the person in the control room. Design a logic circuit that will be able to perform this function. 17. An exclusive-OR gate can be built by making use of only four NAND gates. Show how this is possible by making use of a truth table, Boolean algebra and a circuit diagram.
Practical activity 1 To verify the outputs of a 2 input NAND gate using logic ICs as well as a multiple input NAND gate. Form of activity: Simulation Material and equipment: • Digital trainer or equivalent trainer • 7400 logic IC • Single strand hook-up wire • Logic IC datasheet Note: • Before starting with this activity, first familiarise yourself with the pin connections of the ICs you are about to use. • The pins are numbered anti-clockwise around the IC (chip), starting near the notch or dot. • The 74XX TTL IC series is so designed that inputs not connected will be interpreted as a HIGH. This is also referred to as a ‘floating’ HIGH. • Below is some information to help you with your activity.
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Instructions: Part 1: • Insert the 7400 logic IC into the breadboard of the logic trainer. Consult the educator for the correct insertion of the IC. • Connect the supply and the ground connections to the respective inputs. • With the information given to you above, connect any one of the four logic gates and complete the truth table below. (10) • Do not connect the power unless the educator has checked your connections. Input A
Input B
0
0
0
1
1
0
1
1
Output
• Why is the above gate also known as a universal gate? • Draw a logic circuit of an AND gate consisting of NAND gates only. Part 2: • Now that you have completed the above activity, use the same logic IC (7400) and construct the circuit below on your breadboard. • Remember to verify the pin connections from the above information. • Do not connect the power unless the educator has checked your connections.
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(2) (3)
(5)
Logic
• Now draw up and complete the truth table that will represent the above circuit. (Tip: this will be a three input-truth table.) • Draw a logic circuit for the following Boolean expression: A + BC + D.
11
(8) (5) Total = 33
Practical activity 2 Using logic gate combinations to form a half adder Form of activity: Simulation Material and equipment: • Digital trainer or equivalent trainer • 7432 logic IC • 7404 logic IC • 7408 logic IC • 7400 logic IC • Single strand hook-up wire • Logic IC data sheet Note: • Before starting with this activity, first familiarise yourself with the pin connections of the ICs you are about to use. • The pins are numbered anti-clockwise around the IC (chip), starting near the notch or dot. • The 74XX TTL IC series is so designed that inputs not connected will be interpreted as a HIGH. This is also referred to as a ‘floating’ HIGH. • Below is some information to help you with your activity.
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Instructions: Part 1: • With reference to the logic circuit given below, identify all the logic gates in the circuit. • Use the logic gates provided to construct the logic circuit for the full adder. • Remember to verify the pin connections from the above information and datasheet. • Do not connect the power unless the educator has checked your connections. • If your circuit is correct, switch on the supply and complete the truth table below.
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Input A
Input B
0
0
0
1
1
0
1
1
Sum
Carry
(3) (10)
(8)
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Part 2: • Now that you have completed the above activity, use the logic ICs to construct the above half-adder circuit by making use of NAND gates ONLY. (15) • Remember to verify the pin connections from the above information and datasheet. • Do not connect the power unless the educator has checked your connections. • If your circuit is correct, switch on the supply and complete the truth table below to verify that it corresponds to that of a half-adder. (8) Input A
Input B
0
0
0
1
1
0
1
1
Sum
Carry
Total = 44
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Chapter 12 Communication
A
A
Repeater systems
Modulation / demodulation
Omni-directional antennas
B
B FM transmitter
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Introduction The aim of this chapter on communications is to describe basic communication concepts. The focus will mainly be on radio communication systems, e.g. point-to-point transmission, repeater systems and cellular systems. It will also deal with the basic theory of antennas, as well as the RF wave shapes (polar diagrams) of basic antennas. It will briefly touch on the function of the carrier wave, how modulation is obtained, FM/M radio transmitters and AM/FM receivers.
Radio communication systems Point-to-point transmission Point-to-point transmission is the communication or sending of information/ data between two designated communication stations only. Point-to-point communication is used over many different types of networks, e.g. serial cable, phone line, cellular telephone, radio links and fibre optics. Directional antennas are usually the best to use for point-to-point transmission. The signal is basically focused into a narrow beam instead being allowed to radiate in all directions, as the isotropic antenna found in a base station does. The higher the gain of the antenna, the narrower the focus of that beam. The high directional gain of a Yagi antenna makes it ideal for point-to-point fixed frequency communication.
Repeater systems A repeater system is an automatic radio-relay station, usually located on a mountain top, tall building or radio tower, that enables communication between mobiles/ portables that cannot communicate with each other directly due to distance or obstructions. The introduction of a repeater will ensure better reception on both the transmitter and receiver sides, and extend coverage to communicate over greater distances. A repeater is a combination of radios connected in order to pass on or “repeat” incoming signals. A single repeater system requires two separate frequencies for the receiver and transmitter and is used wherever greater coverage in a local area is required. The single repeater (shown below in Figure 12.2), which is usually located on a mountain top or tower, retransmits any signal received, allowing for greater range over ground or between mobile radios that cannot communicate directly due to obstructions. A repeater is a combination of a radio receiver and a radio transmitter that receives a weak or low-level signal and retransmits it at a higher level or higher power, so that the signal can cover longer distances without losing its strength. All stations using the repeater transmit on the repeater’s input frequency and receive on its output frequency. A repeater is a full-duplex radio which receives signals on one frequency and at the same time re-transmits them on another frequency. These transmitting signals are normally transmitted with greater power. Repeater systems greatly extend the operating range and coverage of amateur mobile and handheld transceivers. In order to listen and receive at the same time, repeaters use two different frequencies. The one frequency is used for transmitting and the other one for receiving. In the 2 meter band, these two frequencies are 600 kHz apart. For other bands, the difference in frequency is even more, e.g. for the 6 meter band the two frequencies
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are separated by 1 MHz. This difference in frequency is known as offset. The repeater input (receive) frequency can be either higher or lower than the repeater output (transmit) frequency. Because the transmitter and receiver are on at the same time, isolation is important to prevent the repeater’s own transmitter from degrading the repeater receiver. If the repeater transmitter and receiver are not isolated well, the repeater’s own transmitter will make the repeater receiver less sensitive. Isolating is made easier between repeater receiver and transmitter by maximizing, as much as possible, the separation between input and output frequencies. Block diagram of a simple repeater
Figure 12.1: Simple repeater
Antenna: The antenna is used to transmit signals that are going in and out of the repeater. Most antennas are high performance, high gain and heavy duty, and are located on a hill or high building. Feed line: This is a special type of feed line called a hard line connecting the antenna to the duplexer. A hard line is used because signal loss is much less than with a coax cable, so more power gets to the antenna and weaker signals can also be received. Duplexer: The duplexer separates and isolates the incoming signals from the outgoing signals. It is designed to pass a very narrow range of frequencies and reject the others. Receiver: This receives the input signals. The receiver is very sensitive and selective. Weaker signals can therefore also be heard by the repeater. Transmitter: The transmitter is made up of an exciter and a power amplifier. The exciter is responsible for the modulating of the audio coming from the receiver. The power amplifier simply amplifies the level of the signal to allow it to be transmitted further. Controller: The controller is the most important part of the repeater that handles repeater station ID using voice or morse code. It activates the transmitter at the appropriate times and sometimes performs other functions, depending on how sophisticated it is. The controller is a small computer that is programmed to control the repeater. A multiple-link repeater system provides radio coverage over long distances. In applications where the distance has become too long or the coverage provided is too restricted for a single repeater, more repeaters are needed to enable radio users to communicate over the greater distance.
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Electrical Technology Repeater systems are commonly used by: • Forestry agencies – National parks and forest fire fighting crews require communication over large areas between field crews and dispatch centres. Repeaters on hilltops enable these extended area communications. • Ambulance services – Repeaters will ensure constant, high-quality communication between ambulances and their base. • Utilities – Utilities (hydro, oil and gas) use repeaters to provide coverage over a large facility such as a dam or refinery, as well as along a transmission line or pipeline. • Police – Police agencies have a repeater network on building rooftops to ensure constant communications between wherever an officer may be and the dispatch centre or fellow officers.
Figure 12.2: Multiple repeater system
Figure 12.3: Simple repeater system
Cellular systems The heart of the cellular system is made up of individual radio coverage areas called “cells.” Each cell is a self-contained calling area. Each of these cells has its own fixed-location transceiver (transmitter and receiver in one) known as a cell site or base station. Because the cellular system is a radio system, no exact boundary can be drawn on a map. In most cases, calls can be placed and received throughout the service area, except for certain enclosed areas such as underground parking garages. The “No Service” indicator will light up on the cellular phone when one is in one of those areas or outside of the service area. The cell site’s transmitter is low powered and does not reach much further than the boundaries of the cell. It is, therefore, possible to reuse channels (frequencies) – a given channel can be used at the same time in different cells, as long as the cells do not border one another, without causing signal interference. This is particularly valuable in urban areas where lots of cellular phones are in use at the same time.
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Every cellular system, digital or analog, comprises four parts: 1. Cells and cell sites (base stations) 2. Switching station (mobile telephone switching office or MTSO) 3. System operator and its local office 4. Cellular telephones. All cell sites are connected to the mobile telephone switching office (MTSO), which provides connection into the public switched telephone network (PSTN) – the local telephone company (Telkom). The MTSO also provides other central functions, including call processing, traffic management and transferring calls as a phone moves between cell sites. Cellular systems offer a number of advantages over alternative solutions: • increased capacity • reduced power use • larger coverage area • reduced interference from other signals.
Antennas In a radio system, electromagnetic waves travel from the transmitter to the receiver through space, and the antennas are used to connect the transmitters and the receivers to the radio signals. Transmitting and receiving antennas share many important characteristics, and the same antenna is very often used for both transmitting and receiving. The antenna of a radio receiver or transmitter is crucial for good quality reception or transmission. Antennas can vary in shape and size – from a simple homemade antenna, a whip antenna for cars, a simple folded dipole, to an outside roof-mounted yagi antenna for a ham radio. As a receiver, the antenna intercepts the electromagnetically transmitted radio waves which, in turn, induce a small voltage in the antenna that can be amplified by the receiver.
Relation between frequency and wavelength
Figure 12.4: Electromagnetic spectrum
When looking at the electromagnetic spectrum, one will see that it covers a whole range of frequencies, starting from very low to very high. The range that is generally used for electromagnetic communication ranges from 30 Hz to 300 GHz. What is interesting about these frequencies of radio waves is that the wavelength of the waveform is determined by its frequency. The relationship between a radio signal’s frequency and its wavelength can be found by using the following formula: Wavelength = 300 / frequency in MHz
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Electrical Technology According to this formula, a frequency of 9680 kHz would be equivalent to a wavelength of 30.99 metres, which would round off to 31 metres, and a frequency of 94 MHz would be equivalent to a wavelength of 3.191 metres. It is thus evident that the higher the frequency, the shorter the wavelength. This is important because the length or height of various types of antennas must often be a fraction (usually one-quarter or one-half) of the wavelength of the signal to be transmitted or received. This means that most antennas designed for frequencies near 4000 kHz will be physically much larger than antennas designed for frequencies near 30 MHz. Radio stations transmitting or receiving on the AM band will, therefore, have much longer antennas than those radio stations transmitting on the FM band. The very high frequency range (30 MHz to 300 MHz) is predominantly used for line-of-sight communication. Its primary use is for FM broadcast, TV broadcast (channels 2-13), air traffic control, ship control close to shore and space telemetry. The frequency range from 300 MHz to 3 000 MHz, is the ultra-high frequency range commonly used for TV broadcast (UHF channels), radar, cell phones, public safety and satellite communication. Many other consumer products that utilise communication links are found in this band of frequencies. This includes cordless phones, wireless intercom, baby monitors, and even remote-control vehicles. The upper range of the electromagnetic spectrum between 300 GHz and 430 THz is where one will find infra-red signals. Infra-red signals are normally measured in microns instead of frequency. It is used for detecting heat sources in environmental, military, space and manufacturing applications. The highest band in the electromagnetic spectrum include the x-ray and Gamma rays and its uses include medical and military applications and flaw detection.
Radio waves Electromagnetic radio waves are produced when electrons are being accelerated in an aerial or antenna. Electromagnetic radio waves are energy carriers, which are associated with a changing magnetic field of the same frequency and phase. The fields are at right angles to each other and to the direction of travel of the wave. Radio waves commonly travel at about 300 000 km per second. Radio waves have the longest wavelengths in the electromagnetic spectrum. These waves can be longer than a football field or as short as a football. The radio waves radiated into space by the transmitting antenna are a very complex form of energy containing both electric and magnetic fields. Radio waves do more than just bring music to your radio, they also carry signals for your television and cell phones.
Radio wave propagation Radio propagation is a term used to explain how radio waves behave when they are transmitted, or travel from one point on the Earth to another. Like light waves, radio waves are affected by the phenomena of reflection, refraction, diffraction, absorption and scattering. Once energy is released from an aerial, it will travel through space, until it is picked up by an aerial or until it strikes an object and is reflected. When a radiated wave leaves the aerial, some of the energy travels along the Earth, following the curvature of the Earth, which is called a ground wave (surface wave). Other waves are transmitted from one point to another in a line–of-sight manner or transmitted
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to a satellite and back to Earth and are referred to as space waves. Waves that are travelling skywards, because they are below a certain critical frequency (about 30 MHz), are returned (reflected) back to Earth by the ionosphere, and are referred to as sky waves. There are basically three types of RF (radio frequency) propagation: • Ground-wave propagation – AM radio • Sky-wave (ionospheric) propagation – amateur radios operate in this range • Line-of-sight (LOS) propagation – FM radio, microwave and satellite. Ground-wave radio signal propagation is ideal for relatively short-distance propagation on these frequencies during the daytime. Sky-wave (ionospheric) propagation is not possible during the day because of the attenuation of the signals on these frequencies caused by the D-region in the ionosphere (the lowest region of the ionosphere). Because sky-wave propagation depends on the Earth’s ionosphere, it changes with the weather and time of day. In view of this, radio communication stations need to rely on ground-wave propagation to achieve their coverage. A ground-wave radio signal is made up of a number of components. If the antenna are in the line of sight, then there will be a direct wave as well as a reflected signal. As the names suggest, the direct signal is one that travels directly between the two antenna and is not affected by the locality. There will also be a reflected signal as the transmission will be reflected by a number of objects, including the Earth’s surface and any hills or large buildings that may be present. In addition to this, there is surface-wave. This tends to follow the curvature of the Earth and enables coverage to be achieved beyond the horizon. It is the sum of all these components that is known as the ground-wave. Beyond the horizon, the direct and reflected waves are blocked by the curvature of the Earth, and the signal is purely made up from the diffracted surface wave. It is for this reason that surface-wave is commonly called ground-wave propagation. Ionosphere (D-zone)
e Line of sight wav y k S ve Space wa Surface wave
Figure 12.5: Radio wave propagation
Antenna polarisation How the antenna is orientated, physically, determines its polarisation. An antenna erected vertically is said to be “vertically polarised” while an antenna erected horizontally is said to be “horizontally polarised”. Other specialised antennas exist with “cross polarisation”, having both vertical and horizontal components and one can also have “circular polarisation”.
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Electrical Technology Note that when a signal is transmitted at one polarisation but received at a different polarisation, a mismatch will exist, resulting in a loss in gain (decibels). It is, therefore, important that both the transmitter and the receiver are polarised in the same direction (both horizontal or both vertical). This is quite significant and is often taken into account when TV channels and other services are allocated.
Figure 12.6(a): Vertically mounted antenna
Figure 12.6(b): Horizontally mounted antenna
Omni-directional antennas (car antenna)
Figure 12.7: Omnidirectional car antenna
The omni-directional antenna radiates or receives equally well in all directions. It is also called the “non-directional” antenna because it does not favor any particular direction. Figure 12.8 shows the pattern for an omni-directional antenna with the radiation patterns. This type of pattern is commonly associated with verticals, ground planes and other antenna types in which the radiator element is vertical with respect to the Earth’s surface. The important thing to note is that for receivers, all four signals (or signals from any direction, for that matter) are received equally well. For transmitters, the radiated signal has the same strength in all directions. This pattern is useful for broadcasting a signal to all points of the compass, or when listening for signals from all points. Omni-directional antennas are widely used for radio broadcasting antennas, and in mobile devices that use radio, such as cell phones, FM radios, walkie-talkies, cordless phones and GPS, as well as in base stations that communicate with mobile phones, such as the police, taxi dispatcher and aircraft communication centres. Examples of omni-directional antenna are: car antennas, ‘rubber duckie’ as used on walkie-talkies, the mast radiator (a radio tower in which the whole structure itself functions as an antenna) and vertically-oriented dipole (bunny ears for TV reception). This type of antenna design can deliver very long communication distances, but has one drawback, which is poor coverage below the antenna.
Omni-directional antenna polar diagram The polar diagram of an omni-directional antenna shows that the direction of maximum sensitivity or radiation is equal all around the axis of the RF antenna. -
Did you know? Dipole antennas were invented by German physicist Heinrich Hertz around 1886.
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Figure 12.8: Radiation pattern of an Omni-directional antenna
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Half-wave dipole antennas The half-wave dipole antenna is one of the most popular and simple RF antennas currently in use and it is also incorporated into many other RF antenna designs, where it forms the radiating or driven element for the antenna. The half-wave dipole antenna is widely used because it is easy to build and the cost is relatively low. It must, however, be noted that the drawbacks of the half-wave dipole antenna are that it has little directionality and the gain is low. As the name suggests, the dipole antenna consists of two terminals or “poles” into which radio frequency current flows. These two poles can be either metal conductors or simply wires which are placed in line with each other, as seen in the diagram below. The total length of the two poles is about ½ of the wavelength of the operating frequency. Therefore, the length of each pole is about ¼ of the wavelength, with their centres connected to a transmitter lead. The RF current is applied to the centre between the two poles. The dipole is naturally a balanced antenna, because it is bilaterally symmetrical. Although most half-wave dipoles are mounted horizontally, some are mounted vertically and then behave like an omnidirectional antenna. The most common application of the dipole is as television antennas (bunny ears).
Figure 12.9(a): Half-wave dipole antenna
Figure 12.9(b): Half-wave dipole antenna
Dipole polar diagram The polar diagram of a half-wave dipole antenna shows that the direction of maximum sensitivity or radiation is at right angles to the axis of the RF antenna. The radiation falls to zero along the axis of the RF antenna. That’s why a TV antenna (bunny ears) has to be properly mounted and facing the correct way in order to obtain a clear picture.
Figure 12.10: Radiation pattern of a half-wave dipole
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Quarter-wave antennas
Take note Guglielmo Marconi was an Italian inventor, known as the father of long distance radio transmission and for his development of the radio telegraph system.
A quarter-wave antenna is a grounded antenna that is a ¼ wavelength of the transmitted or received frequency. The quarter-wave antenna is also commonly referred to as a “Marconi antenna.” It consists of only a quarter–wavelength, vertical radiator. The two components making up the total radiation from this antenna are: the radiated signal that leaves the antenna directly and a ground reflection that appears to come from an underground image of the real antenna. This image is sometimes called the mirror image and is considered to be as far below the ground as the real antenna is above it. The mirror image is, therefore, providing the other quarter-wavelength, making it the equivalent of a vertically mounted dipole. Because of this arrangement the quarter-wave antenna is also an omni-directional antenna. The antenna does not always need to be placed at the Earth’s surface to produce an image. Another method of achieving reflected images is through the use of ground planes, such as a large, reflecting, metallic surface used as a substitute for the ground or earth. The rooftops of cars, trucks and airplanes are all good ground planes for these quarter-wave antennas. This method is frequently used for VHF/ UHF antennas.
Figure 12.11(b): Quarter wave antenna on car roof
Figure 12.11(a): A quarter-wave antenna with its reflective wave
Quarter-wave antenna polar diagram The polar diagram of a quarter-wave dipole antenna shows that the direction of maximum sensitivity or radiation is the same as the dipole antenna, except that one half of the radiation pattern appears below the ground surface and, in fact, does not exist. The figure below shows the radiation in the vertical plane. The horizontal plane is a circle.
Figure 12.12: Radiation pattern of a quarter-wave antenna
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Directional antennas As the name indicates, directional antennas radiate or receive signals best in one or more directions, allowing for better performance and less interference. While there is a multitude of directional antenna designs in use today, the Yagi is the most popular, well-known and most seen. The most common Yagi antennas are the YagiUda and the log-periodic antenna, which are most commonly sold as TV antennas. Some people call these “beam” antennas because of their high gain. The Yagi-Uda consists of: • a simple dipole as its driven element, • a reflector that is 5% longer than the dipole, placed at 0.2 the wave length behind the dipole, and • a director that is 5% shorter than dipole placed at 0.2 the wavelength in front of the dipole. A Yagi can have more than one director placed in front of the dipole, the one relatively shorter than the other. All of these components are supported on a single crossbar known as a boom. The roles of the reflector and the directors are to effectively increase the gain and to make the antenna more focused (directional). Yagi-Uda antennas are directional along the axis perpendicular to the dipole in the plane of the elements, from the reflector toward the driven element and the director(s).
Take note The main difference between the Yagi and the Log periodic antenna is that the Log periodic antenna has electrical connections to each element, whereas the Yagi-Uda design operates on the basis of electromagnetic interaction between the “parasitic” elements and the one driven (dipole) element.
Did you know? The word “Yagi” is the name of one of the Japanese inventors of these directional antennas. The other inventor’s name was Uda, so in technical circles these are YagiUda antennas in honour of the inventor team. The invention dates back to the early 1900s.
Feed (Co-axial)
Figure 12.13(a): Yagi-Uda antenna
Figure 12.13(b): Directional antenna
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Directional antenna polar diagram The polar diagram of a directional Yagi antenna shows that the direction of maximum sensitivity or radiation is in the direction of the element axis. The main lobe is lying in the forward direction along the axis of the elements, with a few very small lobes in other directions.
Figure 12.14: Polar diagram of directional antenna
Directional principle of operation for different types of modulation (how modulation is obtained) Communication by radio is made possible by electrical energy that travels from the transmitter to the receiver in the form of electromagnetic waves. For the successful transmission of these waves (signals), they must be modulated. Modulation is obtained when a radio frequency (RF) signal is changed in order to transmit/carry intelligence. To modulate means to regulate, change or adjust some parameters of a high frequency carrier wave by means of a lower frequency audio (information) signal. It is where a low frequency audio (AF) wave signal is mixed with a high frequency carrier (RF) wave.
Purpose of carrier wave Carrier waves are used in telecommunications, to convey either video or audio signals. In simpler terms it can be said that the carrier wave is there to carry the intelligence/information (video or audio). The high-frequency carrier wave (RF) signal is “modulated” (changed) by a lowfrequency audio wave (AF) signal in order to encode the information that is to be broadcast. There are many types of modulation, but the simplest are used in radio broadcasting. Two basic modulation types are AM (amplitude modulation) and FM (frequency modulation). In either case, the resulting signal is decoded by the radio receiver to produce an audible waveform.
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Modulation and demodulation Modulation Modulation is the process whereby a radio frequency or light wave’s amplitude, frequency or phase is changed in order to transmit intelligence. The characteristics of the carrier wave are instantaneously varied by another “modulating” waveform. Modulation is the modifying of a signal to carry intelligent data (audio or video) over the communication channels. Communication by radio is made possible by electrical energy that travels from the transmitter to the receiver in the form of electromagnetic waves. While transmitting information, an antenna must be fed with radio frequency (RF) power. However, speech and music are audio frequency (AF) voltages and currents. The transmission of sound by radio, therefore, involves modulating the RF, so that it ‘carries’ the (AF) information. During modulation some of the characteristics of the radio wave, either the amplitude or the frequency, are made to vary in sympathy (harmony) with the intelligence to be transmitted. Several types of modulation are available, depending on the system requirements and equipment. The most frequently used types of modulation are amplitude modulation, frequency modulation and phase modulation.
Demodulation Demodulation is the act of returning modulated data signals to their original form, i.e. unscrambling the received signal. Once the modulated signal has been picked up by the receiving antenna, it cannot simply be fed directly to a speaker. The intelligence or low frequency audio signal (AF) must be separated (extracted) from the high frequency radio signal (RF) in order for it to make sense again. The audio frequency (AF) is separated from the modulated radio frequency (RF) by the detector or demodulator.
Amplitude modulation (AM) Amplitude modulation (AM) is a process of changing the carrier waves’ amplitude in accordance (harmony) with the audio signal. The frequency of the carrier wave remains the same.
c) Carrier modulated with audio signal: (AM)
Figure 12.15: Amplitude modulation
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Electrical Technology Advantages of AM • Its unsophisticated signal can be detected (turned into sound) with simple equipment. • If a signal is strong enough, not even a power source is needed. • It uses a narrower bandwidth than FM. Disadvantages of AM • The signal is subject to interference from electrical storms (lightning). • AM transmissions cannot be ionospherically propagated during the day. • Twice the bandwidth is used to convey the same information and only 25% of the power is used in each sideband. The remaining 50% of power is expended in the carrier.
Frequency modulation (FM) Frequency modulation (FM) is a process of changing the carrier waves’ frequency in accordance (harmony) with the audio signal. The amplitude of the carrier wave remains the same. FM is transmitted on very high frequency (VHF) airwaves in the frequency range of 88 to 108 MHz.
Did you know? FM radio was invented by Edwin H Armstrong in the 1930s for the specific purpose of overcoming the interference (static) problem of AM radio, to which it is relatively immune.
c) Carrier modulated with audio signal: (FM)
Figure 12.16: Frequency modulation
Advantages of FM • FM overcomes the interference of static (compared to AM). • FM transmission can take place any time of the day or night.
Single-sideband suppressed carrier modulation (SSBSCM) Single-sideband suppressed carrier modulation (SSBSCM modulation) is basically a form of amplitude modulation, AM. By removing some of the components of the ordinary AM signal, it is possible to improve the efficiency of the modulated signal significantly. As the name implies, single-sideband suppressed carrier modulation (SSBSM) uses only one sideband for a given audio path to provide the final signal. To understand this concept better, one must look at an AM modulated signal. The AM signal generally consists of a carrier wave, an upper sideband and a lower sideband. Each sideband is a mirror image of the other, as can be seen in the diagram below. With SSBSCM, both the carrier wave and one of the sidebands have been removed (suppressed), leaving only the upper or only the lower sideband as shown in Figure 12.17.
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The main reason why SSBSCM is so widely used is because: • as the carrier is not transmitted, this enables a 50% reduction in transmitter power level for the same level of information carrying signal. (Note for an AM transmission using 100% modulation, half of the power is used in the carrier and a total of half the power in the two sideband – each sideband has a quarter of the power.) • as only one sideband is transmitted, there is a further reduction in transmitter power. • as only one sideband is transmitted, the receiver bandwidth can be reduced by half. This improves the signal to noise ratio by a factor of two, i.e. 3 dB, because the narrower bandwidth used will allow through less noise and interference. As with any system, there are also some disadvantages to this system: • Having no carrier, there is a need to reinsert the carrier at the receiver side. • Any slight differences in carrier reinsertion frequency will give rise to changes in the pitch of the audio.
Figure 12.17: Single-sideband suppressed carrier modulation
Single-sideband modulation is widely used in the HF portion, or short-wave portion of the radio spectrum for two-way radio communication. Many users requiring two-way radio communication will use single sideband. These range from marine applications (generally HF point-to-point transmissions) and military to radio amateurs or radio hams.
The transmitter When radio signals are to be transmitted from one point to another, one needs a transmitter circuit for the transmission of the signal, and a receiver for the reception of the transmitted signal. For the purposes of this book, block diagrams of both the AM and FM transmitter will be looked at, as well as the AM and FM receivers. With reference to the two transmitters mentioned, the main difference between the two circuits is that the AM transmitter uses an AM modulator, whereas the FM transmitter uses a FM modulator. Looking at the receivers, the AM receiver makes use of an AM detector and the FM receiver uses a discriminator. Detectors and discriminators are just two forms of demodulators.
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AM transmitter Below is an example of a simple AM transmitter with its functional blocks.
AM Modulator
Figure 12.18: AM Transmitter
Microphone: Converts sound pressure waves to electrical signals Audio amplifier: The low-power, audio signals produced by the microphone are amplified by the audio amplifier before they are fed to the frequency modulator. RF oscillator: The RF carrier wave is generated by the RF oscillator. Amplitude modulator: This is where the RF carrier waves’ amplitude is changed in accordance (harmony) with the audio signal to provide the AM signal. (Amplitude modulation takes place here.) RF power amplifier: The low-powered AM signal is amplified by the RF power amplifier, ready to be transmitted. Antenna: The antenna is driven by the high power RF amplifier and changes the RF signals into electromagnetic waves that are transmitted into the atmosphere.
FM transmitter Below is an example of a simple FM transmitter with its functional blocks.
Figure 12.19: FM transmitter
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Microphone: Converts sound pressure waves to electrical signals Audio amplifier: The low-power, audio signals are amplified by the audio amplifier before being fed to the frequency modulated oscillator. RF oscillator: The RF carrier wave is generated by the RF oscillator. Frequency modulator: This is where the RF carrier waves’ frequency is changed in accordance (harmony) with the audio signal to provide the FM signal. (Frequency modulation takes place here.) RF power amplifier: The low-powered FM signal is amplified by the RF power amplifier, ready to be transmitted. Antenna: The antenna is driven by the high power RF amplifier and changes the RF signals into electromagnetic waves that are transmitted into the atmosphere.
The receiver The AM receiver Below is an example of a simple AM receiver with its functional blocks
AM Demodulator
Local Oscillator
Figure 12.20: AM receiver
Antenna: The antenna is the receiver of the electromagnetic waves and converts them back to an RF signal. RF amplifier: The low-powered RF signal is amplified by the RF amplifier. Local oscillator: The oscillator is responsible for the generation of a fixed high frequency that is then fed to the mixer. Mixer: This high-frequency signal from the oscillator is mixed with the amplified RF signal, giving two sets of signals. The one signal is the sum of the two frequencies and the other signal is the difference between the two signals. One only works with the difference between the two signals, which gives what is known as the intermediate frequency or the IF. This concept of mixing the two frequencies is also called heterodyning. IF amplifier: The IF amplifier just amplifies the IF signal received from the mixer. AM demodulator/detector: This circuit is responsible for recovering the audio signal and removing the RF carrier. AF amplifier: The audio signal is amplified by the AF amplifier before it is fed to the speaker. Speaker: The speaker converts the audio signals to sound (music or speech).
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The FM receiver Did you know? The FosterSeeley discriminator is a common type of FM detector, invented in 1936 by Dudley E. Foster and Stuart William Seeley.
Take note The IF signal for most FM receivers is a fixed frequency of 10.7MHz.
Below is an example of a simple FM receiver with its functional blocks. This FM receiver works much like the AM receivers mentioned above, except for the way it detects the IF signal. This FM receiver makes use of a FM discriminator called a Foster-Seeley discriminator. Antenna
Local Oscillator
Figure 12.21: FM receiver
Antenna: The antenna receives the electromagnetic waves and converts them back to an RF signal. RF amplifier: The low-powered RF signal is amplified by the RF amplifier. Local oscillator: The oscillator is responsible for the generation of a fixed high frequency that is then fed to the mixer. Mixer: The high frequency signal from the oscillator is mixed with the amplified RF signal, giving two sets of signals. The one signal is the sum of the two frequencies and the other signal is the difference between the two signals. One only works with the difference between the two signals, which gives what is known as the intermediate frequency or the IF. The IF signal, for most FM receivers, is a fixed frequency of 10.7 MHz. This concept of mixing the two frequencies is also called heterodyning. IF amplifier: The IF amplifier just amplifies the IF signal received from the mixer. FM discriminator (Foster-Seeley discriminator): This is a special type of discriminator responsible for recovering the audio signal and removing the RF carrier. It uses a tuned RF transformer to convert frequency changes into amplitude changes. Foster-Seeley discriminators are sensitive to both frequency and amplitude variations, unlike some detectors. The discriminator compares the incoming FM signal with a reference signal, and the difference between the two signals is the original audio signal. AF amplifier: The audio signal is amplified by the AF amplifier before it is fed to the speaker. Speaker: The speaker converts the audio signals to sound (music or speech).
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Activity 1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
What is a repeater system? Give three applications of this type of system. Name the four main parts of a cellular system. What are the main advantages of the cellular system compared to other communication systems? What is the main function of an antenna? Draw a labelled polar diagram of a dipole antenna. Write down the difference between an omni-directional antenna and a directional antenna. In your own words, explain why there is a need for a carrier wave in radio communication. With the aid of a simple diagram explain what you understand by the term frequency modulation. Write down the main advantages of amplitude modulation (AM). What is the main difference between amplitude modulation (AM) and single-sideband suppressed carrier modulation (SSBSCM)? Name the main difference between an FM transmitter and an AM transmitter. Make a neat, labelled diagram of a simple FM receiver. What is the main function of the mixer of an FM receiver? Identify the block diagram below and fill in the missing blocks; also state the function of each block.
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15. With reference to the electromagnetic spectrum, what is the relationship between frequency and wavelength? 16. Briefly explain the working principle of a Foster-Seeley discriminator. 17. Identify the antenna represented by the polar radiation pattern below.
18. Explain the term modulation and name three types of modulation.
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Electrical Technology Acknowledgement to: 1. 2. 3. 4. 5. 6. 7.
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Stefan Wahl, a learner who was at Fish Hoek High 2011 (Matric) www.allcircuits.com www.allaboutcircuits.com www.electronics-tutorial.com Occupational Health and Safety Act (Act 85, 1993) SANS 10142-1 2003 Wiring code as amended DBE CAPS documents
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