EASA Part 66 - Module 3 - Electrical Fundamentals - Part B
Short Description
EASA Part 66 - Module 3 - Electrical Fundamentals - Part B...
Description
JAR 66 CATEGORY B1
uk
engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Index 1
DC GENERATION ........................................................................ 1-1 1.1 SIMPLE SINGLE LOOP GENERATOR ........................................... 1-2 1.1.1 Induced emf ........................................................... 1-2 1.1.2 Output frequency ................................................... 1-3 1.2 COMMUTATION ...................................................................... 1-3 1.3 RING WOUND GENERATOR ...................................................... 1-4 1.4 PRACTICAL DC GENERATOR .................................................... 1-7 1.4.1 Construction ........................................................... 1-7 1.4.2 Lap wound generator ............................................. 1-9 1.4.3 Wave wound generator .......................................... 1-10 1.4.4 Internal resistance .................................................. 1-11 1.4.5 Armature reaction .................................................. 1-11 1.4.6 Reactive sparking .................................................. 1-13 GENERATOR CLASSIFICATIONS ................................................ 1-15 1.5 1.5.1 Series generator .................................................... 1-15 1.5.2 Shunt generator ..................................................... 1-16 1.5.3 Self excitation......................................................... 1-16 1.5.4 Compound generator ............................................. 1-17
2
DC MOTORS ................................................................................ 2-1 2.1 SIMPLE SINGLE LOOP MOTOR .................................................. 2-2 COMMUTATION ...................................................................... 2-2 2.2 2.3 PRACTICAL DC MOTORS .......................................................... 2-3 2.3.1 Construction ........................................................... 2-3 2.3.2 Back emf ................................................................ 2-3 2.3.3 Starting d.c. motors ................................................ 2-3 2.3.4 Torque.................................................................... 2-4 2.3.5 Armature reaction .................................................. 2-4 2.3.6 Reactive sparking .................................................. 2-4 2.3.7 Speed control ......................................................... 2-4 2.3.8 Changing the direction of rotation .......................... 2-5 2.4 MOTOR CLASSIFICATIONS ....................................................... 2-5 2.4.1 Series motor........................................................... 2-6 2.4.2 Shunt motor ........................................................... 2-7 2.4.3 Compound motor ................................................... 2-9 2.4.4 Split field motor ...................................................... 2-9 2.5 RATING ................................................................................. 2-10
3
STARTER GENERATORS ........................................................... 3-1
4
AC THEORY ................................................................................. 4-1
Issue 1 - 1 January 2002
Page 1
JAR 66 CATEGORY B1
uk
engineering 4.1 4.2
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
PRODUCTION OF A SINEWAVE .................................................. 4-1 THE SINEWAVE ...................................................................... 4-2
4.2.1 4.2.2 4.2.3 4.2.4 4.2.5 4.2.6 4.2.7 4.2.8
Peak and Peak-to-Peak values .............................. 4-3 Average values ...................................................... 4-3 RMS values ............................................................ 4-4 Form Factor............................................................ 4-4 Periodic time .......................................................... 4-4 Frequency .............................................................. 4-4 Angular Velocity. .................................................... 4-5 Phase Difference (Angular Difference). .................. 4-5 4.3 PHASOR OR VECTOR DIAGRAMS .............................................. 4-6 4.3.1 Addition of phasors ................................................ 4-7 4.4 ADDITION OF AC & DC ............................................................. 4-8 4.5 MEASURING AC USING OSCILLOSCOPES ................................... 4-8 4.5.1 The cathode Ray oscilloscope ............................... 4-8 4.5.2 Types of oscilloscopes ........................................... 4-11 4.5.3 using the oscilloscope ............................................ 4-15 4.6 OTHER TYPES OF WAVEFORMS ................................................ 4-27 4.6.1 Square waves ........................................................ 4-27 4.6.2 Triangular or sawtooth waves ................................ 4-27 4.7 AC VOLTAGE & CURRENT ........................................................ 4-28 4.7.1 Resistive loads ....................................................... 4-28 4.7.2 Capacitive loads ..................................................... 4-28 4.7.3 Inductive loads ....................................................... 4-30 4.7.4 Impedance ............................................................. 4-31 4.8 AC POWER ............................................................................ 4-32 4.8.1 Resistive loads ....................................................... 4-32 4.8.2 Inductive loads ....................................................... 4-33 4.8.3 Capacitive loads ..................................................... 4-34 4.8.4 The total load on a generator ................................. 4-35 4.8.5 Apparent Power & actual current ........................... 4-35 4.8.6 True power & Real Current .................................... 4-36 4.8.7 Reactive power & reactive current ......................... 4-37 4.8.8 Power Factor .......................................................... 4-37 4.9 SERIES L/C/R CIRCUITS ........................................................... 4-38 4.9.1 Inductance and resistance in series ....................... 4-38 4.9.2 Capacitance and resistance in series ..................... 4-39 4.9.3 Inductance, capacitance and resistance in series .. 4-39 4.9.4 Series resonance ................................................... 4-40 4.9.5 Voltage magnification ............................................. 4-41 4.9.6 Selectivity ............................................................... 4-42 4.9.7 Bandwidth .............................................................. 4-43 4.10 PARALLEL L/C/R CIRCUITS ....................................................... 4-44 Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1 MODULE 3 (part B)
uk
ELECTRICAL FUNDAMENTALS
engineering
4.10.1 4.10.2 4.10.3 4.10.4 4.10.5 4.10.6
Inductance and capacitance in parallel .................. 4-44 Parallel resonance ................................................. 4-45 Impedance ............................................................. 4-46 Current magnification ............................................. 4-47 Bandwidth .............................................................. 4-47 Selectivity ............................................................... 4-48
5
TRANSFORMERS ........................................................................ 5-1 5.1 POWER TRANSFORMERS ........................................................ 5-1 5.2 CIRCUIT SYMBOLS & DOT CODES ............................................. 5-2 5.3 LOSSES ................................................................................ 5-4 5.3.1 Iron losses.............................................................. 5-4 5.3.2 Copper losses ........................................................ 5-4 5.3.3 Flux leakage losses ............................................... 5-5 5.3.4 Skin Effect .............................................................. 5-5 5.4 TURNS RATIO ........................................................................ 5-5 5.5 POWER TRANSFERENCE ......................................................... 5-6 5.6 TRANSFORMER EFFICIENCY .................................................... 5-6 TRANSFORMER REGULATION................................................... 5-6 5.7 5.8 APPLYING LOADS TO A TRANSFORMER ..................................... 5-7 5.8.1 No load conditions ................................................. 5-7 5.8.2 Resistive loads ....................................................... 5-8 5.8.3 Inductive load ......................................................... 5-8 5.8.4 Capacitive load ...................................................... 5-9 5.8.5 Combination loads ................................................. 5-9 5.9 REFLECTED IMPEDANCE ......................................................... 5-9 5.10 IMPEDANCE MATCHING TRANSFORMERS .................................. 5-10 5.11 AUTOTRANSFORMERS ............................................................ 5-11 5.12 MUTUAL REACTORS ............................................................... 5-12 5.13 CURRENT TRANSFORMERS ..................................................... 5-13 5.14 THREE PHASE TRANSFORMERS ............................................... 5-15 5.15 DIFFERENTIAL TRANSFORMERS ............................................... 5-16
6
FILTERS & ATTENUATORS ........................................................ 6-1 6.1 FILTERS ................................................................................ 6-1 6.1.1 High pass filters ..................................................... 6-1 6.1.2 Low pass filters ...................................................... 6-2 6.1.3 Band pass filters .................................................... 6-3 6.1.4 Band stop filters ..................................................... 6-4 6.1.5 Smoothing & decoupling circuits ............................ 6-5 6.2 ATTENUATORS ...................................................................... 6-6 6.2.1 ‘T’ type attenuator .................................................. 6-7 6.2.2 Two section attenuator ........................................... 6-8
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JAR 66 CATEGORY B1
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engineering 6.2.3 6.2.4 6.2.5 6.2.6
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Variable attenuators ............................................... 6-9 'π' type attenuators ................................................. 6-9 Balanced & unbalanced networks .......................... 6-10 Attenuator symbols ................................................ 6-10
7
AC GENERATION ........................................................................ 7-1 7.1 PRINCIPLES ........................................................................... 7-1 7.1.1 Output voltage ........................................................ 7-2 7.1.2 Output frequency.................................................... 7-2 7.1.3 Effects of a resistive load ....................................... 7-3 7.1.4 Effects of an inductive load .................................... 7-4 7.1.5 Effects of a capacitive load..................................... 7-4 7.2 PRACTICAL GENERATOR CONSTRUCTION .................................. 7-5 7.2.1 Rotating armature type ........................................... 7-5 7.2.2 Rotating field type .................................................. 7-5 7.2.3 Single phase generator .......................................... 7-6 Two phase generator .......................................................... 7-7 7.2.5 Three phase generator ........................................... 7-7 STAR & DELTA SYSTEMS ......................................................... 7-8 7.3 7.3.1 Delta connection .................................................... 7-9 7.3.2 Star connection ...................................................... 7-9 7.3.3 Power in ac systems .............................................. 7-10
8
AC MOTORS ................................................................................ 8-1 8.1 PRODUCTION OF A ROTATING FIELD ......................................... 8-1 8.1.1 Single phase .......................................................... 8-1 8.1.2 Two phase.............................................................. 8-2 8.1.3 Three phase ........................................................... 8-3 8.2 TYPES OF AC MOTOR .............................................................. 8-3 8.2.1 Induction motor ...................................................... 8-3 8.2.2 Synchronous motor ................................................ 8-5 8.2.3 Shaded pole motor ................................................. 8-6 8.2.4 Hysteresis motor .................................................... 8-7
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JAR 66 CATEGORY B1
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engineering 1
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
DC GENERATION
If a conductor is moved at right angles to a magnetic field, an emf is induced in the conductor. If an external circuit is then connected to the conductor a current will flow. The direction of the current flow depends on two factors, the: direction of the magnetic field direction of relative movement between the conductor and the field and can be determined by using Fleming’s right hand rule.
The size of the generated emf depends on three factors, the: strength of the magnetic field - B effective length of the conductor in the field - l linear velocity of the conductor - v The three are related in the formula
Issue 1 - 1 January 2002
E = Blv
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JAR 66 CATEGORY B1
uk
engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
1.1 SIMPLE SINGLE LOOP GENERATOR In its simplest form, a generator consists of a single loop of wire rotated between the poles of a permanent magnet. The rotating part of the machine is called the rotor or armature, it is connected to the stationary external circuit via two slip rings, thus allowing a current flow.
1.1.1 INDUCED EMF
As the loop rotates an emf is induced in both sides of the conductor. Using Fleming’s right hand rule, it can be seen that the resultant currents flow in opposite directions on each side, but in the same direction around the loop.
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
An emf is only induced in a conductor when it is moved at right angles to the lines of flux in a magnetic field. Therefore, the loop will only have an emf induced in it when it is moving at right angles to the lines of flux, when moving parallel with the lines of flux, no emf will be induced. At any direction in between, there will be a proportion of maximum emf induced in the loop. The instantaneous value of emf induced in the loop is given by: e(instant) = E(max) sin θ where E(max) = Βlv and θ is the angle of the conductor with respect to the lines of flux. As the loop passes the neutral point, the conductors direction of travel through the field reverses. The conductor that was moving upwards through the field is now moving downwards, therefore, the emf's induced in the conductors must change direction, as must the resultant current flow. 1.1.2 OUTPUT FREQUENCY
As the loop rotates, the emf rises to a maximum in one direction, then falls to zero and then rises to a maximum in the opposite direction, before once again falling to zero. One complete revolution is one cycle, the loop having returned to its start position. The number of cycles per second gives the frequency. The faster the loop is rotated, the more cycles per second and the higher the frequency. In this simple generator the frequency depends on the number of loop revolutions per second. The output from this generator changes polarity every time the loop rotates 180 degrees and is therefore of little use as a direct current generator. 1.2 COMMUTATION In order to make the current flow in the same direction through the load, the connections to the external circuit must be switched every time the loop moves past its neutral position. This can be achieved using a commutator. The commutator is used in place of the slip rings and connects the rotating loop to the stationary external circuit.
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
uk
engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
A commutator has 2 functions: Firstly, to transfer current from the rotating loop to the stationary external circuit. Secondly, the periodic switching of the external circuit to keep the current flowing in the same direction through the load. Switching takes place when the loop is moving parallel to the field and has no emf induced in it.
Using a single loop generator and two segment commutator, the output will be as shown above. Although current now flows in the same direction through the external circuit, it is still of little practical use, because the voltage and current fall the zero twice every cycle. Using several loops and a multi-segment commutator, a more constant output can be produced. 1.3 RING WOUND GENERATOR The simple construction of the ring wound generator makes it ideal for explaining the operation of a multi-coil machine. The rotor consists of a laminated iron cylinder onto which is wound 8 equally spaced coils. The junction between each pair of coils is connected to a segment of the commutator. The number of segments equals the number of coils, this being true for all d.c. generator armature windings. Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The brushes are drawn inside for clarity and are positioned so that when they short circuit a coil, that coil is moving parallel to the magnetic field and has no emf induced in it. The metal used for the rotor has a very low reluctance, therefore the flux of the main field flows through it, rather than through the airgap in the centre. The parts of the coils on the inside of the rotor are therefore not cutting any flux and have no emf’s induced in them.
The low reluctance rotor creates a radial field in the airgap as shown above. The radial field means that the conductors are moving at right angles to the flux for a longer period of time and are therefore producing maximum emf for longer. This results in a flat top to the output waveform as shown above. The 8 coils are split into two parallel paths of four, each group of four coils being connected in series, because one set of four coils is moving up through the main field and the other set is moving down through the field, the emf's induced in each set of four coils is in the opposite direction, but it is in the same direction with respect to the brushes.
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The emf induced in four coils is as shown below. The emf in the other four coils is in the opposite direction, but in the same direction with respect to the brushes. It can be seen that the emf no longer falls to zero and only has a small ripple on it.
The ring wound generator is no longer used. Although simple in construction, there are difficulties in winding the coils through the rotor, also, half of each coil is wasted because it has no emf induced in it.
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JAR 66 CATEGORY B1
uk
engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
1.4 PRACTICAL DC GENERATOR 1.4.1 CONSTRUCTION
The size and weight of generators vary considerably, but all are constructed in a manner similar to that shown above. The field assembly consists of a cylindrical frame, or yoke, onto which the pole pieces are bolted. Generators generally have at least four pole pieces, although small machines may have only two. Wound around each pole piece is a field coil. The yoke has a low reluctance and provides a path for the main field of the machine. To reduce eddy currents the yoke is usually laminated. The armature core also provides a path for the main field and is therefore also of low reluctance and laminated.
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
uk
engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The armature windings are located in slots cut in the core, being wedged in with insulation to prevent them being thrown out by centrifugal forces. The coils are normally wound so they return along a slot in the rotor that is one pole pitch away (see diagram below).
Pole pitch is a term used to describe the angle between one main pole and the next main pole of the opposite polarity.
The emf induced in each side of the coil is again in opposite directions, but assisting around the coil. This type of winding is called a drum winding and has the advantage that the coils can be wound and insulated before being fitted into the rotor. There are two types of drum winding, Lap wound and wave wound. The armature windings are connected to risers attached to the commutator. The commutator consisting of copper segments separated by mica insulation. The brush gear assembly consists of a holder and rocker. The holder allows the brushes to slide up a down, whilst preventing them from moving laterally. The rocker allows the brushes to be rotated around the commutator so they can be positioned on the magnetic neutral axis.
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
It should be noted that the output power from a d.c. generator is governed primarily by its ability to dissipate heat. Methods of cooling vary, a large, low power generator would normally be cooled naturally by convection and radiation. Smaller, higher power generators will need some form of cooling system that blows or draws air through the generator. The cooling system may use ram air from a propeller slipstream or from movement of the aircraft through the air, or more commonly, a fan attached to the rotor shaft of the generator. 1.4.2 LAP WOUND GENERATOR
In a lap wound generator, the end of each coil is bent back to the start of the next coil, the two ends of any one coil being connected to adjacent segments of the commutator (see diagram above). This form of construction is used on large heavy current machines. The number of parallel paths for current always equals the number of brushes and the number of field poles (see diagram).
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
1.4.3 WAVE WOUND GENERATOR
In a wave wound generator, the end of each coil is bent forward and connected to the start of another coil located in a similar position under the next pair of main poles (see diagram above). The two ends of one coil are connected to segments two pole pitches away. This type of machine has two parallel paths and uses only two brushes irrespective of the number of poles (see diagram).
This type of winding is used in smaller machines and is therefore more common on aircraft generators.
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
1.4.4 INTERNAL RESISTANCE
A d.c. machine has resistance due to the: armature windings brushes brush to commutator surface contact
This is called internal resistance and can be measured across the terminals of the generator. For the purposes of calculation, the internal resistance is represented as a single value in series with the generated emf. Internal resistance causes the generators terminal voltage to vary with changes in the load current. As the load current increases, the voltage dropped across the internal resistance increases and the terminal voltage decreases. The generated emf E = Ir + V 1.4.5 ARMATURE REACTION
When armature current is flowing, a field is produced around the armature conductors. The overall field of the machine is then produced by interaction between the main field and the armature field.
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
uk
engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The armature field is at 90 degrees to the main field of the machine and therefore distorts it as shown below.
This distortion of the field is called armature reaction and has the effect of weakening the field at points A and strengthening the field at points B. The machine is working near to saturation and therefore the overall effect is a weakening of the field and a reduction in the generators output voltage. Distortion of the field also means that the magnetic, or electric neutral axis is moved around in the direction of rotation, away from the machines geometric neutral axis. When the brushes now short an armature coil, it is no longer at the point where zero emf is induced in it, therefore the brushes must be moved. The position they are moved to depends on the size of the armature current, the greater the current, the further the brushes must be advanced. Armature reaction can be reduced by fitting compensating windings. Compensating windings are small windings wound in series with the armature and fitted into slots cut in the pole faces of the main fields. When armature current flows, current flows in the compensating windings and produces a magnetic field that cancels the armature field. With careful design, correction is applied for all values of armature current, bringing the magnetic neutral axis back onto the geometric neutral axis and restoring the overall strength of the machines field.
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
uk
engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
1.4.6 REACTIVE SPARKING
The diagrams above represent the movement of the commutator under the brush. Prior to being shorted by the brush, current in coil A is at a maximum value left to right. After leaving the brush, current will be flowing at maximum value in the opposite direction through the coil, as shown in coil B. Whilst the coil is shorted by the brush, the current must drop to zero ready for it to go to maximum value in the opposite direction when it comes off the brush. Unfortunately, the coil has inductance, when shorted, a back emf is produced that tries to maintain current flow. When the coil comes off the brush, the current has not reduced to zero, resulting in an excess of current that jumps as a spark from the commutator to the brush. The sparking produced is called reactive sparking. Not all sparking at the commutator is reactive sparking, sparks may also be caused by: • worn or sticking brushes • incorrect spring tension • commutator flats • proud mica Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
One way of overcoming the problem is to increase the resistance of the brushes, this reduces the time constant of the inductive circuit and enables the current to collapse to zero during commutation. However, increasing the resistance of the brushes produces a power loss and increases the overall resistance of the machine. The increase in internal resistance causes greater fluctuations in output voltage with changes in load current. 1.4.6.1
EMF Commutation
Another way of overcoming reactive sparking is to use emf commutation. The purpose of emf commutation is to neutralise the reactance voltages that lead to reactive sparking. One way of achieving this is to advance the brushes beyond the magnetic neutral axis, this means the coils are under the influence of the next main pole before being shorted and will therefore have an emf induced in them. The induced emf will be of opposite polarity to the reactance voltage and will reduce it, reducing the reactance voltage reduces the current in the coil and allows time for it to drop to zero whilst the coil is shorted. Unfortunately, advancing the brushes is only good for one value of armature current, if the current increases, the brushes must be advanced further. Advancing the brushes also increases the demagnetising effects of armature reaction. A better way of applying emf commutation is to fit commutating or interpoles between the main poles of the machine. Interpoles have the same polarity as the next main pole and are connected in series with the armature.
The interpoles induce emf’s in the short circuited coils that exactly cancels the back emf, thus allowing the current to fall to zero instantly. Being in series with the armature means that the reactance voltage is always eliminated irrespective of the value of armature current. By careful design, the interpoles can also be used to eliminate armature reaction in the interpole region.
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
1.5 GENERATOR CLASSIFICATIONS Generators are usually classified by the method of excitation used. There are three classifications; permanent magnet, separately excited and self excited. A permanent magnet generator has a limited output power and an output voltage that is directly proportional to speed. A separately excited generator has its field supplied from an external source. The output voltage being controlled by varying the field current. Self excited generators supply their own field current from the generator output, again the output voltage is controlled by varying the field current. This group may be subdivided into three sub-groups; series, shunt and compound. 1.5.1 SERIES GENERATOR
The series generator has a field winding consisting of a few turns of heavy gauge wire connected in series with the armature.
On "No-load" there is no armature current and therefore no field current. The only voltage generated is due to residual magnetism within the fields. As the load current increases, the field current increases and the terminal voltage rises, the increase in voltage more than compensating for the loss due to armature reactance and internal resistance. The voltage continues to rise until saturation of the field occurs. A series generator therefore has a rising characteristic and is generally only used as a line booster.
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
1.5.2 SHUNT GENERATOR
The shunt generator has a field consisting of many turns of fine wire connected in parallel with the armature. On "No-load" the terminal voltage is a maximum. As the load current increases, the terminal voltage decreases due to the resistance of the armature and armature reactance. The shunt generator has a falling characteristic and is used for d.c. generation on aircraft. 1.5.3 SELF EXCITATION
For a d.c. generator to self excite, certain conditions must be met: • The generator must have residual magnetism. • The excitation field, when formed, must assist the residual magnetism. For shunt generators, additional criteria need to be met: • The field resistance must be below a critical value. • The load resistance must not be too low. Due to the first two points above, the only way to reverse the output voltage of a d.c. generator is to reverse the polarity of the residual magnetism. If the supply to the field winding, or the drive direction is reversed, the excitation will oppose the residual magnetism and the field will be lost.
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
1.5.4 COMPOUND GENERATOR
Compound generators have both series and shunt field windings and fall into one of two categories: differential compound generators, in which the two fields are wound so as to oppose each other. cumulative compound generators, in which the fields are wound so as to assist each other. Differential compound generators are generally used where a high initial voltage is required, but only a low running voltage. Devices such as arc welders or arc lighting may use this form of generator. Cumulative compound machines can be wound to produce over, level or under compounding. Under compounding is more common in aircraft generators, the output voltage falling as the load current is increased.
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
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JAR 66 CATEGORY B1
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engineering 2
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
DC MOTORS
If a current carrying conductor is placed at right angles to a magnetic field, a force will be exerted on it, causing it to move.
The direction of the force and the resultant movement depends on two factors, the : • direction of current flow in the conductor • direction of the magnetic field
The direction of the force and the resultant movement can be found by using Fleming’s left hand rule as shown below:
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JAR 66 CATEGORY B1 MODULE 3 (part B)
uk
ELECTRICAL FUNDAMENTALS
engineering
2.1 SIMPLE SINGLE LOOP MOTOR
The simplest form of motor consists of a single loop of wire able to rotate between the poles of a permanent magnet. If current is applied to the loop through slip rings, a motor torque will be produced, and the loop will start to rotate. As the loop rotates past vertical, the current appears to change direction, this causes the torque to change direction, so the direction of rotation changes. When the loop passes vertical, the current appears to change direction again, causing rotation to revert to its original direction. If left, the loop will simply oscillate back and forth either side of the vertical position.
2.2 COMMUTATION To make the loop rotate, the current must be made to change direction as the loop passes the vertical position, this is achieved using a commutator and brushes.
When current is applied to the loop a motor torque is produced and the loop starts to rotate. When the loop is vertical no rotational torque is produced, however, momentum keeps it moving. At the vertical position, the direction of current in the loop is reversed by the commutator, so that as the vertical position is passed, the torque produced is in the original direction, thereby maintaining rotation. Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
To improve the torque and produce smoother running, more loops or coils are added to the armature, each having its own commutator segment. The construction is as described earlier in d.c. generators. 2.3 PRACTICAL DC MOTORS 2.3.1 CONSTRUCTION
Direct current generators are constructed in the same manner as d.c. generators, therefore further description is unnecessary. The similarities are such that one machine can be operated as the other with only minimal adjustment. In the case of starter generators, the only adjustment necessary is achieved electrically. Most motors have some form of rating, this being a limit on their performance. Ratings take various forms depending on the type, size and use of the motor, but are generally based on a limit on the speed, duration or altitude of operation. As with generators, the limit on a motors performance depends very much on the ability of the machine to dissipate heat. Cooling may be natural, by convection and radiation, or assisted by rotor mounted fans, blast air or slipstream. 2.3.2 BACK EMF
When a conductor moves in a field, an emf is induced in the conductor. The armature coils of the motor are moving in a magnetic field and therefore must have an emf induced in them, this emf acts against the applied voltage and is called back emf. The resultant of the two voltages is called the effective voltage. The armature current is due to the effective voltage, not the applied voltage. When running, the back emf is almost equal to the applied voltage, therefore the effective voltage and the current taken from the supply are both small. 2.3.3 STARTING D.C. MOTORS
On starting, the rotor is stationary and therefore producing no back emf, this results in a high effective voltage and a large current being taken from the supply. To limit the current, a starting resistor is often used, the resistor being removed from the circuit once the motor is running. Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
2.3.4 TORQUE
The torque produced by a d.c. motor is directly proportional to the armature current and the magnetic field strength. T = Φ × IARMATURE Some torque is lost within the motor, especially if a fan is fitted to the rotor shaft. The torque lost is not constant, usually increasing with an increase in speed. 2.3.5 ARMATURE REACTION
The overall field of a d.c. motor consists of the armature field and the stator field. The two fields react, as in the d.c. generator, producing armature reaction. Armature reaction causes the magnetic neutral axis of the motor to be moved around in the opposite direction to that of the generator, against the direction of rotation. The problem can be overcome as in d.c. generators, by fitting compensating windings. 2.3.6 REACTIVE SPARKING
d.c. motors also suffer from reactive sparking. For fixed load motors, the problem is overcome simply by moving the brushes onto the magnetic neutral axis. For variable load motors, interpoles are used as in d.c. generators. 2.3.7 SPEED CONTROL
The effects of back emf make a d.c. motor a self regulating machine. If the load is increased, load torque exceeds motor torque and the motor slows down, the reduction in speed causing a decrease in back emf and an increase in the effective voltage across the armature. The increase in effective voltage causes an increase in the current drawn from the supply and an increase in motor torque, which increases the motor speed to cope with the load increase. The speed of a d.c. motor can be varied by controlling the field current or by controlling the armature current. Issue 1 - 1 January 2002
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Field control
With field control, a decrease in field current causes an increase in motor speed; main field decreases back emf across armature decreases effective voltage increases armature current increases motor torque increases over load torque motor speed increases This occurs because a small change in the main field strength causes a large change in the armature current. Of course, this cannot continue uncontrolled because eventually the field will be lost. Field control is generally used for speed control of normal running speed and upwards. 2.3.7.2
Armature control
With armature control, an increase in armature current causes an increase in motor torque over load torque and an increase in motor speed. A decrease in armature current causes a decrease in motor speed. Armature control is generally used for control of normal running speed and downwards. 2.3.8 CHANGING THE DIRECTION OF ROTATION
To change the direction of rotation it is only necessary to change the direction of the main field or the armature current. If both are changed, the motor will rotate in the same direction. In the majority of cases where a bi-directional d.c. motor is required on an aircraft, a split field motor is used. This motor will be examined in more detail later in the notes, suffice to say it has two fields windings, one for clockwise rotation, the other for anti-clockwise rotation. 2.4 MOTOR CLASSIFICATIONS The construction of d.c. motors is the same as d.c. generators, with armatures being either wave wound or lap wound. Motors are also classified in a similar way to generators - shunt, series and compound. Each type having its own operating characteristics and uses.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
2.4.1 SERIES MOTOR
A series motor has a low resistance, heavy gauge field winding in series with the armature winding. On light loads its speed is high, the armature current is low and the field is weak. On heavy loads. speed is low, the armature current is large and the field is strong. Series motors have a wide speed variation with load.
The armature torque is proportional to the field strength and armature current. In series motors the field strength depends on the armature current, so the torque produced is approximately proportional to the square of the armature current. In practice it is slightly less (particularly on heavy loads) due to armature reaction and saturation of the magnetic circuit. As speed increases, the torque decreases, until the load torque and motor torque balance. If the load of a series motor is removed, the speed may become dangerously high. It is not normal practice to run series motors off-load . When starting a series motor, it is normally connected straight to the supply, the initial current being limited by the combined resistance of the field and armature windings and by the inductance of field winding. The field strength builds up quickly, giving a high starting torque, a fast acceleration and a rapid back-emf build up. There is a short period of high current drain on the supply. Where a large change in operating speed is required, as in turbine engine starting, a starter resistor is initially connected in series with the motor and removed when the motor is required to increase speed. The starter resistor must be able to withstand the large initial current. Applications include starter motors, winches and aircraft actuators. Some series motors are fitted with two separate windings. This enables motor rotation to be quickly reversed. Applications include fuel valves and landing lights.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
2.4.2 SHUNT MOTOR
Shunt wound motors have a high resistance field winding connected in parallel with the armature. The field current will be constant if the input voltage is constant and no field control resistor is used.
When the load torque is increased, the motor slows down. The decrease in speed, causes a fall in the back-emf and an increase in armature current which produces more motor torque. When the motor torque and load torque are again balanced, the speed becomes constant. Small decreases in speed cause relatively large increases in armature current. Between no-load and full-load, the variation in speed of a d.c. shunt motor with a low resistance armature is small enough for it to be considered a constant speed motor. With a high resistance armature, there is a more noticeable variation in speed with load. When a shunt motor has a constant input voltage: on light loads, the magnetic field is constant and the torque is directly proportional to the armature current. on heavy loads the magnetic field is reduced by armature reaction and the torque does not rise in direct proportion to the armature current. If a shunt motor does not increase speed when connected to the supply, then no back-emf is produced. This results in a very high armature current, a large armature reaction and a reduced torque and the motor will not start. Several options are available to overcome the problem: use the motor only on a small load start the motor with no load connected to it increase the armature resistance use a starter resistor
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
A low resistance shunt motor is normally started with a variable resistor, set to maximum resistance, placed in series with the armature. This reduces the armature current and armature reaction, thereby increasing the starting torque. As the speed increases, the back emf increases and armature current decreases. As the speed builds, the resistance is gradually decreased until at normal running speed it is totally removed from the circuit. An automatic method used to insert a resistor is series with the armature for starting, and to remove it once the back-emf has been developed is referred to as a 'T’ Start circuit. At the instant the motor is switched ‘on’, the armature is stationary and producing no back-emf, therefore the voltage at A is almost zero and the relay is deenergized. The resistance is in circuit limiting the current. As the rotor starts to turn and the back-emf increases, the potential at point A starts to increase. At a pre-determined speed the potential at point A and the current through the relay coil will be sufficient to cause the relay to energize, removing the resistor from the armature circuit. Speed control - The speed of a shunt motor is normally controlled by a variable resistor placed in series with the field winding. When the resistance is increased, the field current is reduced, the back-emf decreases and the effective voltage increases. The increase in effective voltage produces an increase in armature current and an increase in speed. When required to reduce the speed of the motor, the field resistance is decreased. Separately excited shunt motors - Separately excited d.c. shunt motors have the same operating characteristics as self excited shunt motors and therefore require no additional consideration. Applications - Shunt motors are used where a constant speed is required and will be found in inverter drives and windscreen wipers.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
2.4.3 COMPOUND MOTOR
These are used to meet specific requirements, we may require a motor: • that has a high starting torque, but will not race off-load. • to increase, decrease or maintain speed as the load on it varies. These requirements can be met with suitable compounding. As with generators, there are two forms of compound motor. • Differential compound - fields connected to oppose each other • Cumulative compound - fields connected to assist each other 2.4.4 SPLIT FIELD MOTOR
In certain applications it is necessary to change the direction of rotation of a motor. Typical examples would be in valves and actuators. We have already seen that this can be achieved by reversing the direction of the armature or field current, however, there is also a special form of reversible series motor known as a split field motor.
A split field motor is simply a series motor with two field windings. The fields are wound in opposite directions, with one being used for each direction of rotation. The direction is usually controlled by a single pole, double throw switch as shown above. The circuit above is in fact that of an actuator and includes not only a split field motor, but also a selector switch, limit switches and a brake solenoid. The motor is shown as having driven to position 1, this can be seen because limit switch A is not connected to the field winding. Whether this position is fully open, fully closed, extended or retracted depends on the device being driven.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
When it is required that the actuator drive to position 2, the selector switch is moved to position 2. Current flows through the field winding, brake solenoid and armature winding. The brake is released and the motor starts to turn. As soon as the motor moves, it is no longer in position 1, so switch A moves across. This allows the direction to be reversed (by returning the selector switch to position 1) should the need dictate. When the motor reaches the limit of travel at position 2, switch B moves across, removing the motor power supply. The brake solenoid, field winding and armature de-energise, the brake is applied and the motor stops. If the selector switch is now moved to position 1, the upper field winding, brake solenoid and armature are energised. The brake is released and the motor runs in the opposite direction towards position 1. Again as soon as the motor turns, it is no longer at position 2 so the lower switch moves over to contact the field winding. 2.5 RATING Most motors have a rating - a limit on performance or operation. Ratings take various forms - output, time, speed, altitude. As with generators, the output depends very much on the machines ability to dissipate heat. All machines require some form of cooling. Low output motors, or those that are not used for continuous operation may be cooled naturally. Others may be fitted with centrifugal or straight fans to drive air through machine, this being usual on small machines. Others use air ducted from slipstream.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
STARTER GENERATORS
Many gas turbine aircraft are equipped with starter-generator systems. These starting systems use a combination starter-generator which operates as a starter motor to drive the engine during starting, and after the engine has reached a selfsustaining speed, operates as a generator to supply the electrical system power. The starter-generator unit shown below left, is basically a shunt generator with an additional heavy series winding. This series winding is electrically connected to produce a strong field and a resulting high torque for starting. Starter-generator units are desirable from an economical standpoint, since one unit performs the functions of both starter and generator. Additionally, the total weight of starting system components is reduced, and fewer spare parts are required. The starter-generator shown below right has four windings; (1) series field, (2) shunt field, (3) compensating, and (4) interpole. During starting, the series, compensating, and interpole windings are used. The unit is operating in a similar manner to a direct-cranking starter, since all the of the windings used during starting are in series with the source. While acting as a starter, the unit makes no practical use of its shunt field. A source of 24 volts and 1,500 amperes is usually required for starting. When operating as a generator, the shunt, compensating and interpole windings are used. The output voltage is controlled in the conventional manner, by connecting the shunt field in the voltage regulator circuit. The compensating and interpole windings provide almost sparkless commutation from no-load to fullload.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The following diagram illustrates the external circuit of a starter-generator with an undercurrent controller. This unit controls the starter-generator when it is used as a starter. Its purpose is to ensure positive action of the starter and to keep it operating until the engine is rotating fast enough to sustain combustion. The control block of the undercurrent controller contains two relays; one is the motor relay which controls the input to the starter, the other, the undercurrent relay, controls the operation of the motor relay.
To start an engine equipped with an undercurrent relay, it is first necessary to close the engine master switch. This completes the circuit from the aircraft's bus to the start switch, the fuel valves, and the throttle relay. Energising the throttle relay starts the fuel pumps, and completing the fuel valve circuit provides the necessary fuel pressure for starting the engine.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
When the battery and start switches are turned on, three relays close. They are the motor relay, ignition relay and battery cut-out relay. The motor relay closes the circuit from the power source to the starter motor; the ignition relay closes the circuit to the ignition units; and the battery cut-out relay disconnects the battery. On this particular aircraft opening the battery circuit is necessary because the heavy drain of the starter motor would damage the battery, this is not the general case. The majority of aircraft are designed to be started using the battery so as to make the aircraft independent of ground resources, the battery will however be disconnected from the bus when ground power is connected and care must be taken to ensure the ground power unit is capable of supplying the current required by the starter motor. Closing the motor relay allows a very high current to flow to the motor. Since this current flows through the coil of the undercurrent relay, it closes. Closing the undercurrent relay completes a circuit from the positive bus to the motor relay coil, ignition relay coil, and battery cut-out relay coil. The start switch is allowed to return to its normal "off" position and all units continue to operate. As the motor builds up speed, the current draw by the motor begins to decrease, as it decreases to less than 200 amps, the undercurrent relay opens. This action breaks the circuit from the positive bus to the coils of the motor, ignition and battery cut-out relays. The de-energising of these relay coils halts the start operation. After the procedures described are completed, the engine should be operating efficiently and ignition should be self-sustaining. If however, the engine fails to reach sufficient speed, the stop switch may be used to break the circuit from the positive bus to the main contacts of the undercurrent relay, thereby halting the start operation. On a typical aircraft installation, one starter-generator is mounted on each engine gearbox. During starting, the starter-generator unit functions as a d.c. starter motor until the engine has reached a predetermined self-sustaining speed. Aircraft equipped with two 24 volt batteries can supply the electrical load required for starting by operating the batteries in a series configuration. The following description of the starting procedure used on a four-engine turbojet aircraft equipped with starter-generator units is typical of most starter-generator starting systems.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Starting power, which can be applied to only one starter-generator at a time, is connected to a terminal of the selected starter-generator through a corresponding starter relay. Engine starting is controlled from an engine start panel. A typical start panel (see diagram below) contains an air start switch and a normal start switch.
The engine selector switch shown has five positions ('1, 2, 3, 4, and off'), and is turned to the position corresponding to the engine to be started. The power selector switch is used to select the electrical circuit applicable to the power source being used (ground power unit or battery). The air-start switch, when placed in the "normal" position, arms the ground starting circuit. When placed in the "air-start" position, the igniters can be energised independently of the throttle ignition switch. The start switch, when in the "start" position, completes the circuit to the starter-generator of the engine selected, and causes the engine to rotate. The engine start panel shown above also includes a battery switch. When an engine is selected with the engine selector switch, and the start switch is held in the "start" position, the starter relay corresponding to the selected engine is energised and connects that engine's starter-generator to the starter bus. When the start switch is placed in the "start" position, a start lock-in relay is also energised. Once energised, the start lock-in relay provides its own holding circuit and remains energised providing closed circuits for various start functions. An overvoltage lockout relay is provided for each start-generator. During ground starting, the overvoltage lockout relay for the elected start-generator is energised through the starting control circuits. When an overvoltage lockout relay is energised, overvoltage protection for the selected started- generator is suspended. A bypass of the voltage regulator for the selected starter-generator is also provided to remove undesirable control and resistance from the starting shunt field.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
On some aircraft a battery lockout switch is installed in the external power receptacle compartment. When the door is closed, activating the switch, the ground starting control circuits function for battery starting only. When the door is open, only external power ground starts can be accomplished. A battery series relay is also necessary in this starting system. When energised, the battery is connected in series to the starter bus, providing an initial starting voltage of 48 volts. The large voltage drop which occurs in delivering the current needed for starting, reduces the voltage to approximately 20 volts at the instant of starting. The voltage gradually increases as the starter current decreases with engine acceleration and the voltage on the starter bus eventually approaches its original maximum of 48 volts. Some multi-engine aircraft equipped with starter-generators include a parallel start relay in their starting system. After the first two engines of a four-engine aircraft are started, current for starting each of the last two engines passes through a parallel start relay. When starting the first two engines, the starting power requirement necessitates connecting the batteries in series. After two or more generators are providing power, the combined power of the batteries in series is not required. Thus, the battery circuit is shifted from series to parallel when the parallel start relay is energised. To start an engine with the aircraft batteries, the start switch is placed in the "start" position. This completes a circuit through a circuit breaker, the throttle ignition switch and the engine selector switch to energise the start lock-in relay. Power then has a path from the start switch through the "bat start" position of the power selector, to energise the battery series relay, which connects the aircraft batteries in series to the starter bus. Energising the No 1 engine's starter relay directs power from the starter bus to the No. 1 starter-generator, which then cranks the engine. At the time the batteries are connected to the starter bus, power is also routed to the appropriate bus for the throttle ignition switch. The ignition system is connected to the starter bus through an overvoltage relay, which does not become energised until the engine begins accelerating and the starter bus voltage reaches about 30 volts. As the engine is turned by the starter to approximately 10% r.p.m. the throttle is advanced to the "idle" position. This action actuates the throttle ignition switch, energising the igniter relay/ When the igniter relay is closed, power is provided to excite the igniters and fire the engine. When the engine reaches about 25 to 30% r.p.m., the start switch is released to the "off" position. This removes the start and ignition circuits from the engine start cycles, and the engine accelerates under its own power.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
AC THEORY
4.1 PRODUCTION OF A SINEWAVE The only practical way of generating an electromotive force (emf) by mechanical means is to rotate a conductor in a magnetic field. As the conductor rotates in the magnetic field, its direction of motion relative to the magnetic field is continually changing, therefore, the emf induced in the conductor is continuously changing. The emf will start at zero when the conductor is moving parallel with the lines of flux, it will rise to a maximum value when the conductor is moving at 90° to the lines of flux, before decaying back to zero rising to a maximum value in the opposite direction. In this way, an alternating emf is produced which, when connected to a circuit, produces an alternating current flow.
By making the conductor in the form of a loop, we have the basis of the simple ac generator. All generators, both dc and ac, have this basic design. In a dc machine the output to the load is continually switched by the commutator, so that the load current always flows in one direction. In an ac machine the output to the load is continually reversing it direction.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
If the generated emf of the loop is measured and plotted as the loop rotates, the result will be as shown in the diagram below.
It can be seen that when the conductors are moving parallel to the lines of flux, and not cutting them, the induced emf is zero. When the conductors are cutting the lines of flux at right angles, maximum emf is induced in them. By convention, the part of the waveform above the zero line is labelled positive and the part below the line is labelled negative. 4.2 THE SINEWAVE If the conductor is rotated at uniform speed in a uniform magnetic field, the output waveform is said to be ‘sinusoidal’ and we refer to this type of waveform as a sine wave. There are many other wave shapes that can be generated or developed, but it is the sine wave that is used for main power supply systems. It is therefore necessary for the engineer to be very familiar with this particular waveform and he is expected to be able to remember and use the various figures and formulae associated with it. The wave generated is called a sine wave because its amplitude (height) at any instant can be calculated from sine tables, i.e. by plotting the sine’s of all angles between 0º and 360º. When the conductor has completed 360º of rotation, it is said to have completed one cycle. Issue 1 - 1 January 2002
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
4.2.1 PEAK AND PEAK-TO-PEAK VALUES
Amplitude values and their calculation apply equally to current and voltage measurement. The Peak or Maximum Value. The maximum value attained by the wave in either direction is called the maximum value, or more usually, the peak value.
The Peak-to-Peak Value. The maximum value in one direction, to the maximum in the other direction is called the Peak-to-Peak value. It must not be confused with peak value, which is measured in one direction only. Peak-to-peak values are often used on oscilloscopes because it is easier to measure from top to bottom of the waveform, but the majority of calculations require the use of the peak value. It must be remembered to divide the peak-to-peak value by two in order to obtain the peak value for calculations. The Instantaneous Value. As previously stated, the value at any instant can be calculated by multiplying the peak value by the sine of the angle (from 0º) through which the conductor has rotated. 4.2.2 AVERAGE VALUES
The amplitude of an ac waveform may be defined in terms of its average values. Over one complete cycle, this would mathematically be zero (the wave goes as far positive as it does negative) If the pulses of voltage or current are always in one direction, the average value can be calculated from: For single-phase full-wave rectification Average Value = Peak Value × 0.637 For single-phase half-wave rectification Average Value = Peak Value × 0.318
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engineering
4.2.3 RMS VALUES
Whilst the Peak and Average values of ac have their place and uses, they are not a lot of use for everyday work on ac. What is required is a value of ac which relates to an equivalent value of dc. Suppose an electric fire is operating with 5 amperes of d.c. current flowing through it and it is giving out a certain amount of heat. We want to know the value of a.c. which will produce the same amount of heat. Such a value is given by the Root Mean Square (rms) value of an a.c. current. For a sinusoidal waveform, the rms value = peak value × 0.707. In other words, a sine wave of peak value ‘y’ produces a certain amount of heat when passed through a given resistor. To produce the same heating effect, in the same resistor using d.c., would require a d.c. with a steady current of only 0.707 of ‘y’. By convention, it is not necessary to add ‘rms’ to a voltage or current value but, if peak or average values are being referred to, then the word ‘peak’ (Pk) or ‘average’ (Av) must be added after the value. 4.2.4 FORM FACTOR.
The form factor of a waveform is a number which indicates its shape: Form Factor =
rms value average value
For a sine waveform, this works out at 0.707 / 0.637 = 1.11. For any other waveform, the values will be different and so the Form Factor will be a different number. (This is given in these notes for information only as the aircraft engineer should not have to concern himself with the form factor). 4.2.5 PERIODIC TIME
The time taken to complete one cycle is called the ‘periodic time’ (t). It is measured in seconds or fractions of a second. 4.2.6 FREQUENCY
In electrical terms, frequency is the number of cycles completed in one second (cycles per second) and is expressed in Hertz (Hz). 1 Hz = 1 cycle / sec. 10 Hz = 10 cycles / sec. etc. 1,000 Hz
(103 Hz) = 1 Kilo-Hertz
(1 kHz)
6
1,000,000 Hz
(10 Hz) = 1 Mega-Hertz (1 MHz)
1,000,000,000 Hz
(109 Hz) = 1 Giga-Hertz (1GHz)
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Periodic time and frequency are related. T = 1/f
and
f = 1/T
4.2.7 ANGULAR VELOCITY.
The velocity at which a phasor rotates is very important and can be calculated from: Distance Speed = Time Distance (one revolution) = 2π radians. Time (periodic time) = 1/f. Angular Velocity (ω) (omega)
2π = 1/f radians per second = 2πf radians per second.
(A proper understanding of this formula is essential as it is used in other formulae). Referring back to our simple loop it can be seen that, if the loop was rotating at 120 revolutions per second, the output frequency would be 120 Hz. It therefore follows, that the frequency of the output of an ac generator is directly proportional to its speed of rotation. 4.2.8 PHASE DIFFERENCE (ANGULAR DIFFERENCE).
If two conductors are caused to rotate at the same angular velocity, then two waves would be generated. Any angle between them is said to be their phase difference. In the following diagram, the phase difference is 90º. As the conductors rotate in an anti-clockwise direction, the dotted wave is said to lead the solid wave by 90º.
When two waves are 90º apart, they are said to be in ‘quadrature’ with each other. When two waves are 180º apart, they are said to be in ‘antiphase’ with each other. Issue 1 - 1 January 2002
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
4.3 PHASOR OR VECTOR DIAGRAMS Waveform diagrams are difficult to visualise and engineers have devised a diagrammatic method known as a phasor or vector diagram to simplify the problem. The terms vector and phasor are interchangeable, however, the term vector is more general, being used to denote any quantity that has both magnitude and direction, whereas the term phasor, tends to be associated with electrical engineering. To avoid repetition, the word phasor will be used in these notes. Imagine a phasor of length of Vm rotating in an anticlockwise direction, rather like the conductor rotating in the magnetic field. If you plot the vertical displacement of the tip of the line at various angular intervals, the curve traced out is a sinewave.
When the line is horizontal, the vertical displacement of the tip of the line is zero, corresponding to the start of the sinewave at point A. After the line has rotated 90° in an anti-clockwise direction, the line points vertically upwards, point B on the diagram. After 180° of rotation the line points to the left of the page, and the vertical displacement is again zero. Rotation through a further 180° returns the line to its start point. A phasor is a line representing the rotating line Vm, frozen at some point in time. Although line Vm was drawn to represent the maximum values, a phasor is normally scaled to represent r.m.s. values, and can be used to represent voltage current, power or indeed flux. One rotation of the phasor produces one cycle of the waveform, therefore the number of rotations completed per second gives the frequency. The 3 'o-clock position on a phasor diagram is considered to be the reference point of the diagram. Whether the current, voltage, mmf or flux is drawn pointing in this direction depends on the circuit under consideration. If two or more phase displaced waveforms are to be drawn on the same phasor diagram they must have the same frequency, their angular displacement is indicated by the angle between the phasors. It must be remembered that phasors rotate anti-clockwise, therefore if a voltage leads a current by 90°, the two phasors should be drawn so that as they are rotated, the voltage phasor is leading.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
4.3.1 ADDITION OF PHASORS
The addition of sine waves is greatly simplified by the use of phasor addition, however it should be remembered that, phasors can only be used to add sinewaves of the same frequency. To add two phasors, a parallelogram is produced, the two extra sides being drawn parallel to the phasor already present.
Each extra side should start at the end of each phasor as shown. Once the parallelogram has been produced, the resultant voltage is represented by a line from the origin to the intersection of the two new lines. The length of this new phasor represents the magnitude of the new voltage and the angle between it and the other phasor is the phase angle between them. When adding more than two phasors, it is simply a matter of reducing pairs to a single phasor, as described, until a single resultant remains.
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4.4 ADDITION OF AC & DC
It is possible for both ac and dc to exist in the same circuit or conductor. In such cases the ac is said to be superimposed on the dc, or the dc has an ac ripple. The resultant waveform depends on the relative values of ac and dc, as shown in the diagrams above. 4.5 MEASURING AC USING OSCILLOSCOPES 4.5.1 THE CATHODE RAY OSCILLOSCOPE
Cathode ray oscilloscopes are analogue-graphical instruments which enable electrical waveforms to be displayed for analysis and measurement purposes. A typical instrument is represented in the diagram below.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
With reference to the above diagram, the grids g1, g2 and g3 of the cathode ray tube (CRT) form an electron gun which projects a stream of electrons between deflecting plates onto the screen. The screen is coated with a phosphorescent material so that a luminous spot is produced on the screen. A property of the screen coating material allows the spot to persist for a period of time when the stream of electrons is moved or interrupted. The amount of illumination depends on the quantity of electrons in the stream and their velocity on impact with the screen. The potential at grid g1, which is negative with respect to the cathode, controls the quantity of electrons emitted from the cathode. Adjusting R1 varies the potential at g1, hence R1 controls the brightness of the illuminated spot. Positive potentials at g2 and g3 accelerate the electrons towards the screen. The potential difference between g2 and g3, varied by adjusting R2, sets up an electrostatic field which enables the electron stream to be focused at the screen. The position of the spot on the screen is determined by the simultaneous effect of voltages applied to the X and Y deflecting plates. A potential difference between the X deflecting plates causes the spot to move across the screen in the horizontal direction, through a distance proportional to the potential difference. A potential difference between the Y deflecting plates exerts a similar control over the vertical movement of the spot. The outputs of the X and Y amplifiers establish the potential differences between corresponding pairs of deflecting plates. If these voltages vary in magnitude the spot moves over the screen to produce a continuous trace. Since one voltage controls horizontal deflection and the other controls vertical deflection, the trace forms a graphical representation of one voltage as a function of the other. 4.5.1.1
The Time Base
Most applications require that a signal waveform is displayed as a function of time. To meet this requirement a time base circuit supplies a voltage which varies linearly with time, usually, to the horizontal (X) deflecting plates whilst the signal to be observed is usually applied to the vertical (Y) deflecting plates. A time base (sawtooth) voltage synchronised with a time dependent signal are depicted in the diagram.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The period t1, is the sweep, that is the time the spot takes to move linearly from left to right across the screen. During the much shorter period t2, called the flyback time, the spot returns rapidly to the left of the screen to start a new cycle. During flyback the screen may blacked out by a negative pulse generated by the time base circuit and applied to g1, the control grid. If the sweep period (T) of the time base is equal to, or is a multiple of, the periodic time of the signal applied to the Y deflecting plates, a stationary display of the signal voltage variations with time will be obtained. In the diagram above, the 1 sweep period (T) equals the periodic time f of the signal waveform. In practice the time base is adjusted so that signals over a wide frequency range may be displayed against a convenient time scale. 4.5.1.2
Synchronisation
The time base and the displayed waveform may be synchronised by employing a trigger circuit actuated by the signal itself, that is, by using the output of the Y amplifier. Alternatively, an external signal source or the mains supply may be used for this purpose. The trigger circuit generates a pulse to initiate one sweep of the time base when the voltage applied to the circuit reaches a predetermined value. The circuit is adjustable so that a particular trigger point on either the positive or negative half cycle of the displayed waveform may be selected. Where the signal to be observed is nonperiodic, or when the signal appears infrequently, the time base is triggered by the signal, performs one sweep and then waits for the next signal to appear. In order that the beginning of a non-periodic signal can also be examined, the vertical deflecting voltage is delayed relative to the trigger pulse so that the time base is started before the signal to be observed appears on the screen. The time relationship is shown in the diagram.
4.5.1.3
MOD
On many oscilloscopes, a terminal marked Z MOD is provided. The terminal is connected through a blocking capacitor, to the control grid (g1) of the cathode ray tube. The facility enables a suitable voltage pulse to be applied to the grid so that selected portions of the display can be blacked out or brightened for the duration of the pulse. Issue 1 - 1 January 2002
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Amplifiers & Attenuators
The X and Y amplifiers and attenuators provide the voltage scaling required to ensure that the instrument and the measured signal are compatible. Since the oscilloscope is required to display complex voltage waveforms, it is essential that fundamental and harmonic frequencies must undergo the same amplification or attenuation, and that the time relationships between different frequencies must be maintained. It therefore follows that both the amplifier and the attenuators, must have flat amplitude against frequency and transit time against frequency, characteristics. 4.5.2 TYPES OF OSCILLOSCOPES 4.5.2.1
Sampling Oscilloscopes
At very high frequencies, say above 300MHz, it is not possible using existing techniques to produce a continuous display on an oscilloscope. To obtain a satisfactory display a sampling technique must be used. As shown in the diagram below, in a sampling oscilloscope the time base circuit produces a stepped voltage waveform to deflect the electron beam in the horizontal direction. Prior to each step, a pulse is generated which initiates the sampling process.
The input signal is sampled later during each successive cycle to produce the vertical deflection of an illuminated spot. In this way the display, which may consist of 1,000 spots, is progressively built up over a number of cycles of the input signal. An obvious limitation of the sampling oscilloscope is that it cannot be used to display transient waveforms.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Multiple Trace Display
Oscilloscopes equipped with multiple trace facilities enable two or more signals to be displayed simultaneously. Essential features of these instruments are a separate input channel for each signal and a means of separating the electron beams for display. The most widely used instruments enable two signals to be compared, although four beam instruments are quite common. Cathode ray tubes equipped with two electron guns and two sets of deflecting plates, so that each channel is completely independent, are employed in instruments known as Dual Beam Oscilloscopes. Alternatively, a single gun may be used to produce two traces by switching the Y deflecting plates from one input signal to the other for alternate sweeps of the screen. Although the signals are sampled, the display appears to the eye as a continuous, simultaneous, display of both signals. Oscilloscopes employing this techniques, which is called the alternate mode, can only be used as single channel instruments to investigate transient waveforms. 4.5.2.3
Dual Trace CRO
4.5.2.3.1
Alternate Mode
The electronic switch alternately connect the main vertical amplifier to the two vertical preamplifiers. The switching takes place at the start of each sweep. The switching rate of the electronic switch is synchronised to the sweep rate, so that the CRO spot traces channel 1 signal on one sweep and channel 2 signal on the next sweep. This is used for viewing high frequency signals.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Chopped Mode
The electronic switch is free running at 100 - 500KHz and is independent of the frequency of the sweep generator. The switch successively connects small segments of the 1 and 2 waveforms to the vertical amplifier. If the chopping rate is much faster than the horizontal sweep rate, the individual little segments fed to the vertical amplifier reconstitute the original 1 and 2 waveforms on the screen, without visible interruptions in the two images. 4.5.2.4
Delayed Sweep
Both time bases in operation. A - delaying sweep B - delayed sweep
Either or both (alternate) signals can be fed to X plates. This allows a closer examination of part of the waveform. CRO contains two linear calibrated sweeps, a main sweep and a delayed sweep. The main sweep is initiated by its trigger pulse at time t0. The delayed sweep will be triggered at time t1, intensifying the original display. If the CRO sweep control is now set to delay position, the intensified portion will be shown expanded on the screen.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Direct Viewing Storage C.R.T.
The dielectric storage sheet consists of a layer of scattered phosphor particles capable of having any portion of its surface area written to. This dielectric sheet is deposited on a conductive coated glass faceplate called the "storage target backplate". The flood electrons are distributed evenly over the entire surface area of the storage target. After the write gun has written a charge image on the storage target, the flood guns will store the image. The written portions of the target are bombarded by flood electrons that transfer energy to the phosphor layer in the form of visible light. This light pattern can be viewed through the glass faceplate. 4.5.2.6
The Digital Storage CRO
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The digital storage CRO stores the data representing the waveforms in a digital memory. The input signal is "digitised", i.e. it is sampled and then converted into binary numbers by the A/D converter. The resolution of the system depends on the number of bits used by the converter. Converters are said to have a resolution of 1 part in 2 or 'n bit resolution' where n is the number of bits, i.e. 10 bit resolution would digitise to 210 (1024) discrete levels: the resolution would be 1 part in 1024 or 0.098%. This digitised input is then converted back to an analogue signal for display by the D/A converter. (1-2MHz which may be extended to 200MHz using sampling techniques). 4.5.3 USING THE OSCILLOSCOPE
An oscilloscope is an extremely comprehensive and versatile item of test equipment which can be used in a variety of measuring applications, the most important of which is the display of time related voltage waveforms. Such an item probably represents the single most costly item in the average service shop and it is therefore important that full benefit is derived from it. The oscilloscope display is provided by a cathode ray tube (CRT) which has a typical screen area of 8cm × 10cm. The CRT is fitted with a graticule which may be an integral part of the tube face or on a separate translucent sheet. The graticule is usually ruled with a 1cm grid to which further bold lines may be added to mark the major axes on the central viewing area. Accurate voltage and time measurements may be made with reference to the graticule, applying a scale factor derived from the appropriate range switch. A word of caution is appropriate at this stage. Before taking meaningful measurements from the CRT screen it is absolutely essential to ensure that the front panel variable controls are set in the calibrate (CAL) position. Results will almost certainly be inaccurate if this is not the case!
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The use of the graticule is illustrated by the following example: An oscilloscope screen is depicted below. This diagram is reproduced actual size and the fine graticule markings are shown every 2mm along the central vertical and horizontal axes. The oscilloscope is operated with all relevant controls in the 'CAL' position. The timebase (horizontal deflection) is switched to the 1ms/cm range and the vertical attenuator (vertical deflection) is switched to the 1V/cm range. The overall height of the trace is 5cm × 1V = 5V. The time for one complete cycle (period) is 4 × 1ms = 4ms. One further important piece of information is the shape of the waveform, which in this case is sinusoidal.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Layout of Controls
Layouts of the controls and display provided by a typical dual-channel oscilloscope are shown in the diagrams above and below. The majority of the controls identified in the above diagram are those associated with the position and appearance of the display (e.g. vertical shift horizontal shift, intensity and focus) whilst those shown in the diagram below include the vertical gain and attenuator controls.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The dual-channel oscilloscope has three BNC coaxial input connectors: •
Channel 1. This is the primary vertical input, but it is also used for the horizontal (X) input when the mode switch is set to the 'X-Y' position.
•
Channel 2. This is the second vertical input which is also used for the vertical input (Y) when the mode switch is set to the 'X-Y' position.
•
External trigger. This input is only used when the trace is to be locked to an external trigger signal (both 'CH1' and 'CH2' trigger selector buttons must be depressed on the trigger selector).
In addition, a voltage calibrator test point is provided (marked 'CAL 1V' on the front panel). This connector provides an accurate 1V square wave signal which may be used to calibrate the two vertical deflection channels.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Basic Adjustments
The basic adjustments for single-channel waveform measurements are shown in the diagram below. The sequence of adjustments is as follows: 1. The input signal is applied, via a suitable probe, to the Channel 1 (CH1) input connector. 2. The intensity and focus controls are adjusted for a satisfactory display. 3. The display is centred on the graticule using the vertical and horizontal shift controls. 4. The variable gain (Var) and variable sweep (Var Sweep) controls are set to the calibrate (Cal) positions. 5. The trigger selector (TRIGGER) is set the Channel 1 (CH1). 6. Positive edge trigger is selected '+' (note that negative edge trigger may also be selected - in practice the sharpest edge of the waveform will produce the most effective triggering). 7. The display mode switch (MODE) is set to Channel 1 (CH1). 8. The Channel 1 input selector is set to 'AC'. 9. The vertical attenuator (VOLTS/CM) control is adjusted to produce a suitable height display. 10. The trigger level control (Trig Level) is adjusted to obtain a stable (locked) display. 11. The timebase selector (TIME/CM) control is adjusted to produce a suitable number of cycles on the display (usually two to five cycles).
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The basic adjustments for dual-channel waveform measurements are shown in the diagram below. The sequence of adjustments is as follows: 1. The first input signal is applied, via a suitable probe, to the Channel 1 (CH1) input connector. 2. The second input signal is applied, via a suitable probe, to the Channel 2 (CH2) input connector. 3. The intensity and focus controls are adjusted for a satisfactory display. 4. The displays are centred using the horizontal shift control. 5. The displays are adjusted (vertically separated into the upper and lower parts of the display) using the two vertical shift controls. 6. The two variable gain (Var) and variable sweep (Var Sweep) controls are set to the calibrate (Cal) positions. 7. The trigger selector (TRIGGER) is set to either Channel 1 (CH1), or Channel 2 (CH2), as necessary. 8. Positive or negative edge triggering is selected as required. 9. The display mode switch (MODE) is set to dual-channel (Dual). 10. Both input selectors are set to 'AC'. 11. The vertical attenuator (VOLTS/CM) controls are adjusted to produce displays of a suitable height. 12. The trigger level control (Trig Level) is adjusted to obtain a stable (locked) display. 13. The timebase selector (TIME/CM) control is adjusted to produce a suitable number of cycles on the display (usually two to five cycles).
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The basic adjustments for measurement of DC offset voltages are shown in the diagram below. The sequence of adjustments is as follows: 1. The input signal is applied, via a suitable probe, to the Channel 1 (CH1) input connector. 2. The intensity and focus controls are adjusted for a satisfactory display. 3. The display is centred on the graticule using the horizontal shift control. 4. The variable gain (Var) and variable sweep (Var Sweep) controls are set to the calibrate (Cal) positions. 5. The trigger selector (TRIGGER) is set to Channel 1 (CH1). 6. Positive edge trigger is selected '+' (note that negative edge trigger may be also be selected - in practice the sharpest edge of the waveform will produce the most effective triggering). 7. The display mode switch (MODE) is set to Channel 1 (CH1). 8. The Channel 1 input selector is set to 'GND'. 9. The vertical shift control is adjusted so that the trace is exactly aligned with the horizontal axis of the graticule (this line will then correspond to 0V) 10. The Channel 1 input selector is set to 'DC'. 11. The vertical attenuator (VOLTS/CM) control is adjusted to produce a suitable height display. 12. The trigger level control (Trig Level) is adjusted to obtain a stable (locked) display. 13. The timebase selector (TIME/CM) control is adjusted to produce a suitable number of cycles on the display (usually two to five cycles).
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
4.5.3.3
Waveform Measurements
Examples of some basic waveform measurements using an oscilloscope are shown in the diagram to the left. In (a), a square wave is displayed. One complete cycle of this waveform occupies 2cm on the display. Since the timebase range selector (TIME/CM) is set to 1ms/cm, the time for one complete cycle of the waveform is 2 × 1ms = 2ms. The vertical size of the waveform (i.e. its peak-peak value) measures 2cm on the graticule. Since the vertical attenuator (VOLTS/CM) is set to 1V/cm the peak-peak voltage is 2 × 1V = 2V. A sine wave is shown in (b). One complete cycle of this waveform occupies 2.5cm on the display. Since the timebase range selector (TIME/CM) is set to 2ms/cm, the time for one complete cycle of the waveform is 2.5 × 2ms = 5ms. The vertical size of the waveform (i.e. its peakpeak value) measures 3cm on the graticule. Since the vertical attenuator (VOLTS/CM) is set to 50mV/cm the peakpeak voltage is 3 × 50mV = 150mV.
An irregular pulse is shown in (c). The display is 'low' for 3.4cm measured on the graticule. Since the timebase range selector (TIME/CM) is set to 0.1s/cm, the 'low' time shown on the display is 3.4 × 0.1s = 0.34s. Similarly, the period for which the wave next goes 'high' is 1.5 × 0.1s = 0.15s. The vertical size of the waveform (i.e. its peak-peak value) measures 4cm on the graticule. Since the vertical attenuator (VOLTS/CM) is set to 1V/cm the peak-peak voltage is 4 × 1V = 4V, equally distributed either side of 0V.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Pulse Rise and Fall Times
The rise and fall of a pulse can be easily measured using the techniques previously described (note that this measurement is only valid if the oscilloscope is fitted with a properly compensated probe). The diagram shows the parameters of a pulse including: • Rise time (10% to 90%) • Fall time (90% to 10%) • On time (time above 50%) • Off time (time below 50%)
4.5.3.5
Pulse Delay
A dual-channel oscilloscope can be easily used to measure pulse delay (see diagram below). Note that this measurement should be performed with the timebase mode switch set to 'CHOP' rather than 'ALTERNATE' on oscilloscopes that offer an alternate sweep facility.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
4.5.3.6
Sine Wave Performance checks
An oscilloscope can provide a very rapid assessment of the performance of an amplifier. A pure sinewave (of appropriate frequency and amplitude) is applied to the input of the amplifier (or other system under test) and the output is displayed on the screen of the oscilloscope. The effects of non-linearity, clipping noise, distortion, etc. and be easily seen (see diagram).
4.5.3.7
Square Wave Performance Checks
An alternative, but equally revealing assessment of an amplifier can be made using a square wave test. An accurate square wave (of appropriate frequency and amplitude) is applied to the input of the amplifier (or other system under test) and the output is once again displayed on the screen. The effects of poor frequency response, 'ringing', etc. can be easily detected (see diagram).
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Phase Measurement
A number of useful measurements can be made with an oscilloscope in X-Y mode. It is possible to carry out reasonably accurate measurements of phase angle using Lissajous figures (see diagram to the left). In order to obtain these displays, the two signals must be applied with identical gain/attenuation and it is usually necessary to calibrate the instrument by applying the same sine wave signal to the X and Y inputs and adjust the gain controls to obtain a straight line at exactly 45º (see diagram). Thereafter, the signal to be measured is applied to vertical channel (Y) whilst the reference signal is applied to the horizontal channel (X). The shape of the display indicates the phase shift between the two signals. This technique is ideal for rapidly checking the phase shift produced by a network, filter or amplifier.
4.5.3.9
Frequency Measurement
Lissajous figures can also be used to determine the frequency relationship between two signals (see diagram). The frequency ratio is given by the ratio of the number of 'peaks' produced in the horizontal direction to the number of 'peaks' produced in the vertical direction.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
4.5.3.10
Modulation Measurement
Finally, the depth of amplitude modulation (AM) can be easily determined using an oscilloscope (see diagram). The depth of modulation (per cent) is given by the relationship: VM Modulation depth = V × 100% C
4.5.3.11
Do's and Don'ts of using an Oscilloscope
•
Do ensure that the vertical gain and variable time/cm controls are placed in the calibrate (CAL) positions before making measurements based on the attenuator/timebase settings and graticule.
•
Do ensure that you have the correct trigger source selected for the type of waveform under investigation.
•
Do remember to align the trace with the horizontal axis of the graticule with the input selector set to 'GND' before making measurements of DC levels.
•
Do make use of the built-in calibrator facility (where available).
•
Do use a properly compensated oscilloscope probe.
•
Don't leave the intensity control set at a high level for any length of time.
•
Don't leave a bright spot on the display for even the shortest time (this may very quickly burn the screen's phosphor coating).
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
4.6 OTHER TYPES OF WAVEFORMS Fourier (1768-1830), a French mathematician was one of the first to realise that all periodic waves could be built-up by combining sinewaves of the appropriate amplitude, frequency and phase. When considering waveforms made up of a number of sinewaves it is customary to call the sinewave with the lowest frequency, the fundamental. The resultant waveform will have the same frequency as the fundamental frequency. The harmonics are those sine waves with frequencies that are twice, three-times, four times etc. the harmonic frequency. 4.6.1 SQUARE WAVES
A perfect square wave has vertical sides and a flat top. Such a theoretically perfect wave has an infinite number of odd harmonics and no even harmonics. Such a waveform is not possible to achieve in electronic circuits, however, by using the fundamental and the lowest nine odd harmonics (3rd to 19th) a good resemblance can be obtained. Limiting the number of harmonics causes a sloping of the sides of the wave. A voltage with a square waveform is often used as a test signal applied to the input of a system. If the system does not respond well to higher frequencies, the sides will slope, if it does not respond well to lower frequencies the flat portions will become curved. If an amplifier does not function correctly when a square wave is applied to the input, it is unlikely to function correctly when other periodic waves are applied. A skilled experimenter can make deductions about the response of an amplifier by observing the output waveforms. 4.6.2 TRIANGULAR OR SAWTOOTH WAVES
A perfect sawtooth wave contains an infinite number of both odd and even harmonics, again this is not possible practically. The lower harmonics affect the rising portion of the wave, the higher harmonics, the decay time.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
4.7 AC VOLTAGE & CURRENT The type of load (resistive, capacitive or inductive) placed on an a.c. power supply affects the phase angle relationship between the voltage and current. Each type of load produces a different effect, so they are examined individually. 4.7.1 RESISTIVE LOADS
When a pure resistance is placed in an a.c. circuit, the instantaneous current is given by the instantaneous voltage divided by the resistance (i.e. it follows Ohms Law). This means that the current waveform is in-phase with the voltage waveform. If the voltage and current values are known, then resistance may be VPK VAK VRMS calculated from I or I or I . PK PK RMS 4.7.2 CAPACITIVE LOADS
The diagram shows a pure capacitance or capacitor connected in an ac circuit. This cannot actually happen in practice as there must always be some resistance, but we will introduce the resistive element later in these notes.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
A capacitor will always charge up to, or discharge down to, the voltage which is being applied to it. In other words, it follows the supply voltage. If we take the point where the capacitor is charged in one direction, when connected across an ac supply and the ac supply voltage starts decreasing, then a discharge current will flow (conventionally) from the capacitor’s positive plate through the supply source to the negative plate. This current flow will be small at first as the supply voltage starts to drop but will increase to a maximum value when the supply is at zero volts. It will continue to flow in the same direction but decrease as the capacitor is charged up in the reverse direction, becoming zero at the point of full charge. The following diagram illustrates this point and it can be seen that the current is leading the supply voltage by 90º.
The operation of the capacitor produces an opposition to the flow of current. It will therefore act in a similar manner to a resistance in a circuit. It is a form of ‘ac resistance’. The word ‘resistance’ is kept for the physical resistance as we already know it, so this form of ‘ac resistance’ is called ‘reactance’. It is calculated in Ohms and is given the symbol X. The opposition to current flow produced by a capacitor is known as capacitive reactance and given the symbol XC. Capacitive reactance is dependent on frequency, such that XC varies inversely with frequency. If frequency increases, XC decreases and so the current flow increases. If frequency decreases, XC increases and so the current flow decreases. (This is why, after the initial charge current, no current flows through a capacitor on dc). Capacitive reactance, XC =
1 2π πfC
ohms
Ohms Law still applies XC = V/I ohms It should be clearly understood that, although we refer to alternating currents and signals flowing ‘through’ capacitors, no current actually passes through the dielectric between the plates. Electrons circulate from plate to plate through the circuit, being affected by the electrostatic fields on the plates.
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4.7.3 INDUCTIVE LOADS
The diagram shows a pure inductance or inductor connected across an ac supply. The notes assume that there is no resistance in the circuit. This is a situation which cannot exist in practice, but we shall introduce the resistive element later. An inductance always opposes any change in current flow. When the current is a.c. and constantly changing in value, the result is that it always lags behind the supply voltage. For a pure inductance the angle of lag is 90º.
The constantly changing current means that the magnetic field produced by the inductance is also constantly changing. This gives rise to an emf being induced into the inductor’s own windings in such a direction as to oppose the applied emf. This self-induced emf is therefore known as a back-emf. The back-emf is dependent on the rate of change of current and on the value of the inductor (in Henrys). Back-emf = -L × Rate of Change of Current
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Note that, the ‘minus’ sign indicates that the back-emf is in opposition to the applied emf. Note also that point F on the following diagram is a maximum ‘negative’ value because the current at that instant (point A) is changing at maximum rate.
The appearance of this back-emf in the circuit means that there is an opposition to the flow of current from the supply. The opposition due to an inductance, L, is called inductive reactance, and given the symbol XL It has already been stated that back-emf and therefore reactance, depends on the rate of change of current in the circuit, but this is obviously dependent on the frequency of the a.c. supply. As frequency increases, XL will increase and so current flow will decrease. As frequency decreases, XL will decrease and so current flow will increase. It can thus be seen that equipment marked ‘For use on a.c. only’ is depending on the reactance to control the current flow. If it was used on dc at the same voltage, XL would not exist, the current flow would be too high and the equipment would burn out. Inductive Reactance, XL = 2π πfL ohms. Ohms Law still applies XL = V/I 4.7.4 IMPEDANCE
When inductance, capacitance and resistance appear together in an a.c. circuit, in any combination, the total opposition to current flow is referred to as impedance and given the symbol Z. Resistance, inductance and capacitance in a circuit can be represented by phasors in the same way as currents and voltages. The position of each phasor relative to the reference position (3 o'clock) depends on whether a series or parallel circuit is being considered.
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ELECTRICAL FUNDAMENTALS
For the purpose of deriving the impedance formula shown, it is only necessary to understand that phasors for XL and R or XC and R are at 90° to each other and as such form a right angled triangle. In a circuit containing all three components, the values of XL and XC oppose each other, leaving one dominant value that again forms a right angled triangle with R. The resultant in each case is the circuit impedance, which can be calculated quite easily using Pythagoras. The total impedance in a circuit containing resistance R, inductance L and capacitance C, is calculated using the formula: Impedance Z =
R2 + (XL - XC)2
4.8 AC POWER Alternating current power also needs to be examined under the three headings of resistive loads, inductive loads and capacitive loads, as the calculation of power in each type of load produces different results. 4.8.1 RESISTIVE LOADS
Power in a Resistive Circuit. When the instantaneous values of voltage and current are multiplied, the resultant power waveform is as shown in this diagram below.
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ELECTRICAL FUNDAMENTALS
engineering
It can be seen that all of the power waveform is above the ‘zero’ line, indicting that it is all being dissipated in the resistance. The shaped area under the power graph is the product of power × time and represents the electrical energy consumed in the circuit. • Peak Power
= V(Pk) × I(Pk)
• Average Power = Peak Power 2 = V(Pk) × I(Pk) 2 = V(Pk) × I(Pk) √2
√2
= V(rms) × I(rms) = VI watts 4.8.2 INDUCTIVE LOADS
Power in a purely inductive circuit. No power is developed in a pure inductance. Power is calculated by multiplying the instantaneous values of voltage and current. If this is done for the two waveforms when they are 90º outof-phase , then the resultant power waveform will be as shown below.
It can be seen from the above diagram that each half-cycle of voltage and current produces one full cycle of power. (Power wave frequency is twice the supply voltage frequency).
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When the power curve is ‘positive’, the inductor takes power from the supply source. When the power curve is ‘negative’, the inductor returns power to the supply source. Over a complete cycle, the net absorption of power is zero watts. It must be fully understood that current is flowing in the circuit but that no work is being done when that current is 90º out-of-phase with the voltage. 4.8.3 CAPACITIVE LOADS
As with pure inductance, a pure capacitance also produces a current flow which does ‘no work’. On one half-cycle, power is delivered to the capacitor (charging) from the supply source but the on the next half-cycle the capacitor returns power to the supply source (discharging).
Each half cycle of the voltage and current again produces a full cycle of power. When the power curve is positive, the capacitor takes power from the supply source. When the power curve is negative the capacitor returns power to the supply source. Over a complete cycle, the net absorption of power is zero watts. Again it must be understood that the current is flowing in the circuit, but no work is being done.
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4.8.4 THE TOTAL LOAD ON A GENERATOR
The following facts regarding power in a.c. circuits have already been established in these notes: • In a purely resistive circuit, all of the current does work. • In a purely inductive circuit, none of the current does work. • In a purely capacitive circuit, none of the current does work. We have also established that, depending on the relative values of resistance, inductance and capacitance, the current can be at any angle, from 0º to 90º, leading or lagging the supply voltage. If any number of individual loads are switched onto an a.c. generator, the individual currents will all combine to give one load current on the generator at one particular angle of lead or lag. As the angle is usually designed to be one in which the current lags the voltage, we will concentrate on that, but the same arguments we are going to use also apply to a leading current. If the instantaneous values of two sinewaves are added together, the result will be another sinewave. Conversely, any sinewave can be thought of as being comprised of two separate sinewaves. If therefore, we assume the generator’s load current is lagging the voltage by an angle θ, we can say that (irrespective of the individual loads that produced it) it is comprised of one current which is in phase with the voltage and one current which is 90º lagging the voltage. 4.8.5 APPARENT POWER & ACTUAL CURRENT
The load current (lagging the voltage by θ) is called the actual current. This is the current that would be indicated on an ammeter inserted into the circuit, or would be detected by a current transformer (see transformer notes). If the supply voltage is multiplied by this current, the power that is ‘apparently’ being dissipated is found. This however, is not the true power being dissipated and so it is called the ‘apparent power’ and is given the units of volts-amps. Apparent power = V × I(actual) volts amps Issue 1 - 1 January 2002
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If the rating plate on an a.c. generator is examined, it will be seen that the generator is rated at, say 200 volts (rms); 30 kVA. The rating is not given in watts because the designer has no way of knowing what the phase angle will be when it is loaded. 4.8.6 TRUE POWER & REAL CURRENT
The component of the actual current that is in phase with the voltage is known as the ‘Active’ or ‘Real’ load current, because it is the part of the load current that is doing all the work. This component can only be calculated, as it is not possible for a device such as an ammeter or current transformer to measure anything other than actual current. In order to find the real load current, it is necessary to multiply the actual current by the Cosine of the angle θ. If the supply voltage is multiplied be the real load current, the ‘true power’ being dissipated in the circuit is found. The unit of true power is the watt (as in d.c.). True power
= V × I(actual) × Cos θ Watts. = V × I(real) Watts.
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4.8.7 REACTIVE POWER & REACTIVE CURRENT
The component of the actual current that is lagging the supply voltage by 90º is known as the ‘Reactive’ or ‘Wattless’ load current, because it is the part of the load current that does no work at all, even though it exists and has to be carried by the cables, etc. It is brought into being by the nature of the capacitive and inductive loads. Again, it can only be calculated by multiplying the actual load current by the sine of the angle θ. If the supply voltage is multiplied by the reactive load current, the reactive power is found, reactive power is given the units of Volt Amps Reactive (VAR). Reactive power
= V × I(actual) × Sin θ VARs = V × I(reactive) VARs.
4.8.8 POWER FACTOR
The angle which the actual load current makes with the supply voltage is known as the power factor of the circuit. The power factor is given by the Cosine of the angle θ. When the current is in phase with the voltage, the angle is 0º. The Cosine of 0º = 1 and so the power factor = unity (1).
When the current is in quadrature with the voltage, the angle is 90º. The Cosine of 90º = 0 and so the power factor = zero (0). Issue 1 - 1 January 2002
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Because of considerations of automatic control over varying conditions, the power factor in aircraft systems is kept well away from unity. It is usual to operate at power factors in the order of 0.75 or 0.8 on aircraft. Power factor can be obtained from anything that gives the Cosine of the angle. For example, Power factor = R/Z (resistance divided by impedance). It is also given by Power Factor =
True Power Apparent Power
It also follows that True Power = Apparent Power × Power Factor. 4.9 SERIES L/C/R CIRCUITS It has already been stated that it is not possible to have an ac circuit consisting only of inductance, or only capacitance. There must be some resistance in each of these circuits and this resistance can be thought of as being in series with the inductance, or in series with the capacitance. Of course, many circuits have resistors deliberately inserted in series with the other components and some circuits have all three components in series. It is these combinations of series circuits that we will now consider: 4.9.1 INDUCTANCE AND RESISTANCE IN SERIES
As L and R are in series, the current I is the same through each component. The current passing through the inductance gives rise to a potential across it, which leads the current by 90º. At the same time, the voltage developed across the resistor is in phase with the current. As I is the common value in the circuit, it is called the ‘reference phasor’ and is usually drawn horizontally when drawing the phasor diagram. This is shown below, along with the circuit diagram.
The applied voltage V is the phasor sum of VL and VR and leads I by phase angle θ, which can be any angle between 0º and 90º depending upon the ratio of XL to R. If required, the phasor diagram could now be re-drawn with the supply voltage V in the horizontal position and showing the current lagging this voltage.
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Z(ohms) =
R2 + XL2 = V/I = Total opposition to the flow of current.
4.9.2 CAPACITANCE AND RESISTANCE IN SERIES
As C and R are in series, the current through each component is the same. The current applied to the capacitance gives rise to a potential across the capacitance which lags the current by 90º. At the same time, the voltage developed across the resistor is in phase with the current. As I is the common value in the circuit, it is called the reference phasor and is drawn horizontally when drawing the phasor diagram. This is shown below, along with the circuit diagram.
The applied voltage V is the phasor sum of VC and VR and lags I by the phase angle θ, which can be any angle between 0º and 90º depending upon the ratio of XC to R. If required, the phasor diagram could now be re-drawn with the supply voltage V in the horizontal position and showing the current lagging this voltage. In this instance: Z(ohms) =
R2 + XC2 = V/I = Total opposition to the flow of current
4.9.3 INDUCTANCE, CAPACITANCE AND RESISTANCE IN SERIES
As in the paragraphs above, the current is again common all three components and so is used as the reference phasor when drawing the phasor diagram. This will obviously be a combination of the two diagrams shown previously and is drawn above, along with the circuit.
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In this example, XL is greater than XC and therefore VL is greater than VC. Resolution of the diagram results in the applied voltage V being shown to lead the current I by phase angle θ. The circuit is therefore acting as though it were inductive. The opposite effect would be obtained if XC was greater than XL and the circuit would then act as though it were capacitive. In this instance, the impedance (Z) is given by: Z(ohms) =
R2 + (XL - XC )2 = V/I = Total opposition to current flow
4.9.4 SERIES RESONANCE
It has already been shown that XL varies directly with frequency and that XC varies inversely with frequency. If therefore, the frequency applied to the above circuit was altered to decrease XL and at the same time increase XC, then at one particular frequency XL would be equal to XC. This frequency is called the resonant frequency and is denoted by the symbol fo. At the resonant frequency, the applied voltage and the circuit current are in phase, as shown in this phasor diagram below and the impedance of the circuit equals the resistance.
In a Series Circuit at Resonant Frequency (fO): • XL = XC • VL = VC • VL and VC are in antiphase and therefore cancel each other out. • VR = Applied Voltage V. • Z = R. The only opposition to the flow of current comes from the resistive element of the circuit, therefore current rises to a maximum value. • Because I is a maximum, this series resonant circuit is known as an ‘acceptor circuit’.
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• Also, because I is at a maximum value, VL and VC rise to very high values. They can be far higher than the supply voltage and can therefore be very dangerous. For this reason, it is very rare for this type of circuit to be operated continuously at resonant frequency. • Because XL = XC, then 2π foL =
1 1 by transposition fo = 2πfoC 2π π LC
If graph of current against frequency is made for a series circuit containing both inductance and capacitance, the result is as shown below.
4.9.5 VOLTAGE MAGNIFICATION
At resonance, VL and VC can rise to very large values and be greater than the supply voltage. This is known as voltage magnification and given the symbol QO. Off resonance the magnification factor is represented by the symbol Q. The XL XC VL VC amount of magnification is expressed by the fractions R , R , V or V which S S VL VC equals V or V since VS = VR and is sometimes called the ‘Q’ factor of the R R circuit. Qo
Thus
And
=
XL XC = R R
=
2πfL 1 = R 2πfCR 2πfL 1 1 L R × 2πfCR = R2 × C
QO2 =
QO =
1 R
L C
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The actual increase in voltage depends on the resistive element of the circuit.
Below fO the circuit is capacitive, at resonance it is resistive and above fO inductive. 4.9.6 SELECTIVITY
Selectivity is the ability of a tuned circuit to respond strongly to its resonant frequency and to give a poor response to nearby frequencies. A sharp response curve indicates high selectivity, a flat response curve indicates low selectivity.
High selectivity may be obtained by: • Either making XL and XC large, that is by using large L and small C, or in L other words using a large C ratio. This increases the circuit impedance off-resonance. • Or by making R smaller. This reduces Z at resonance.
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1 1 Therefore selectivity ∝ L, ∝ C , ∝ R Since both selectivity and QO are proportional to L and inversely proportional to C and R the QO may be used as a measure of selectivity. 4.9.7 BANDWIDTH
The bandwidth (B) of a circuit is the difference between two frequencies either side of the resonant frequency at which the power has fallen to half its value at resonance, i.e. the half power points (these are also called the –3db points: see Decibel notation later in the course). If the power has fallen to half its value at resonance, then since: P ∝ I2 P I2 2∝2 I P 2∝ 2 ×
I I ( = 0.707I) 2 2
The current has fallen to 0.707 of its value at resonance.
By definition Bandwidth (B) = f1 - f2 The narrower the bandwidth of a circuit, the higher the selectivity. Thus bandwidth may also be used as a measure of selectivity, as well as the magnification factor (QO). •
A useful relationship is: B =
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
4.10 PARALLEL L/C/R CIRCUITS The effects of connecting these three components in series was studied in the previous section, they can however be connected in parallel. This section studies the effects of connecting the three components in parallel. 4.10.1 INDUCTANCE AND CAPACITANCE IN PARALLEL
As with the series circuit, changes of frequency will again effect the inductive reactance and the capacitive reactance and there will again be one particular frequency at which the two will be equal for a given capacitor and inductor. This is the resonant frequency of the circuit. The formula for this is the same as for the series circuit, providing that the resistive element of the circuit is small. At resonant frequency, the current circulating between the capacitor and the inductor is high, but the current drawn from the supply is low. This type of circuit is therefore commonly known as a ‘rejector circuit’. The best way of understanding its operation is to imagine a capacitor and an inductor connect as shown in the diagram.
Imagine also that the capacitor is charged to a given voltage and that there is no resistance in the circuit. When the switch is closed, the capacitor will discharge through the inductor, transferring energy to it. The inductor field will then collapse, charging the capacitor up in the reverse direction. This action will repeat itself ad infinitum and the current will continue to circulate backwards and forwards at a natural frequency which, of course, is the resonant frequency of the circuit. This ideal condition would need no external force to keep operating. In practice, however, there must be some resistance in our circuit and so the current will oscillate at resonant frequency, but will gradually die away as power is lost across the resistance. In order to keep our circuit oscillating, it is only necessary to keep the circulating current ‘topped-up’ from the supply. The current drawn from the supply at resonant frequency is therefore very small. At supply frequencies less than resonance, the current through the inductor increases and that through the capacitor decreases. The reverse occurs at supply frequencies above resonance.
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If a graph is drawn of supply current (or line current, as it is sometimes known) against frequency, the result will be as shown below.
The very high impedance at resonance associated with parallel circuits is most often used in the tuning circuits of radio or television receivers. When tuned to a particular frequency, that frequency will not pass through the parallel circuit. It is therefore available for the amplifier to amplify and use. All the other (unwanted) frequencies coming in at the aerial are passed through the parallel circuit to the chassis, thereby by-passing the amplifier. At frequencies above resonance, the circuit acts as though it were capacitive and at frequencies below resonance, as though it were inductive. 4.10.2 PARALLEL RESONANCE
Unlike the series tuned circuit, the resistance does have an effect on the resonant frequency of a parallel tuned circuit, the equation being: fo =
1 R2 LC - L2
1 2π
However, if R is very small, the term involving resistance may be ignored and for most practical purposes the resonant frequency is given by: fo =
1 2π LC
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At resonance, the supply current (IS) is a minimum and is in phase with the applied voltage. The value of the resonant current, as shown in the diagram Vs VsCR below, is given by Z or L D
In a Parallel Circuit at Resonant Frequency (fO): • XL = XC • VL = VC and are in antiphase and therefore cancel each other out • VR = Applied Voltage V. L • Z = CR and current is a minimum. • Because the impedance is a maximum, the parallel resonant circuit is known as a ‘rejecter circuit’. 4.10.3 IMPEDANCE
The impedance of a parallel circuit can be calculated using the formula shown below, although knowledge of this formula is not essential on this course.
1 2
1 1 1 − + R XL X C
2
At resonance, the impedance is a maximum and called the dynamic impedance (ZD) of the circuit. If the supply frequency is increased above or decreased below fO then the circuit impedance will decrease. The dynamic impedance is given by the equation: Issue 1 - 1 January 2002
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4.10.4 CURRENT MAGNIFICATION
In a parallel tuned circuit at resonance, current magnification occurs, that is IL and IC will be very large compared with IS. At any instant IL and IC act in the same direction round the ‘internal’ circuit, and IS flowing in the ‘external’ circuit is the difference between IL and IC. Thus, if IL and IC are large and very nearly equal, IS will be small. At any instant Kirchoff’s first law applies, that is: I S = IL + L C The circulating current is the smaller of the two currents (IL or IC) and IS is the make-up current. Remember that QO for a series tuned circuit is its voltage magnification whereas QO for a parallel tuned circuit is its current magnification at the resonant frequency. QO =
1 R
L C
4.10.5 BANDWIDTH
Bandwidth is defined as the difference between two frequencies f1 and f2, one either side of resonance, at which the impedance has fallen to 0.707 of the maximum value. As for the series circuit: Bandwidth B =
fO QO
1 where QO = R
L C
L If R is increased, or the ratio C decreased, then the impedance at resonance is decreased, QO is decreased and hence bandwidth increased.
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4.10.6 SELECTIVITY
As for the series circuit, selectivity is the ability of the tuned circuit to respond strongly to its resonant frequency and to give a poor response to nearby frequencies. Again, as for the series circuit, QO is used as a measure of selectivity. Below fO
Above fO
1. Z small due to small XL
1. Z small due to small XC
2. XC > XL
2. XL > XC
3. Thus IL > IC
3. Thus IC > IL
4. Thus circuit inductive
4. Thus circuit capacitive
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
TRANSFORMERS
Transformers have no moving parts and are very efficient pieces of electrical equipment. Transformers operate by mutual inductance, the flux from one coil of wire linking with another coil. Because the flux must be changing state, static transformers can only be used on alternating current. In order for a transformer to be used on direct current, part of the transformer must be rotated. 5.1 POWER TRANSFORMERS The main elements of a power transformer are: •
The primary and secondary windings
•
A laminated core and coil former
•
A mounting and terminal strip
The windings consist of insulated wire wound onto a former. The secondary winding is generally wound on top of the primary winding, the two being separated by a layer of insulating material. The wire gauge used depends on the current rating of the transformer. The ends of both primary and secondary windings are connected to the terminal strip for connection into the circuit.
The core is made up of thin strips of iron approximately 07mm to 3mm thick, the thickness being determined by the intended frequency of operation. Each sheet is insulated from the next. This laminated form of construction is used to prevent eddy currents joining together and producing large circulating current within the core.
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The core is invariably one of two types, core or shell. A core type core has ‘U’ shaped and either ‘I’ or ‘L’ shaped laminations , staggered when assembled to provide a single circular magnetic circuit. The windings may be wound on one limb or split between the two. The laminations of a shell type core are usually ‘T’ and ‘U’ shaped, staggered when assembled to produce a three-limbed core. When made for single phase operation, both windings are wound on the centre limb, when made for three phase operation, each phase is wound on a separate limb. Whilst more expensive, the provision of two magnetic paths make the shell type former more suitable for large current use. All of the energy transferred from the primary winding to the secondary must be stored in the magnetic field created in the core, therefore, sufficient iron must be provided to store the energy of each half cycle of the a.c. waveform. If the total power is kept the same, there will be less energy in half a high frequency cycle than in half a low frequency cycle, therefore, the higher the supply frequency, the smaller and lighter the transformer. 5.2 CIRCUIT SYMBOLS & DOT CODES The basic symbol used for a transformer with one primary winding and one secondary winding is as shown below. The two dots are used to indicate the phase relationship between the two windings, the terminals marked with a dot are always in phase with each other. In the diagram shown, when the top of the left winding is positive, the bottom of the right winding is positive and vice versa.
Whilst it should be understood that there is a phase shift of 180º between the primary and secondary voltages, the polarity of the secondary winding (at any instant in time) with respect to the primary, depends purely on the way the transformer is wound.
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To indicate the type of core material used, additional markings are added to the basic transformer symbol. The core material is determined primarily by the frequency of the supply on which the transformer is to be operated. Three lines drawn between the primary and secondary windings on the transformer below indicate that it has a laminated iron core. As such, the transformer would be used at low frequencies and may be found on a.c. power supply systems. The two coils drawn on the right show that this transformer has two secondary windings, and the dot notation indicates that these two windings are wound in opposite directions. The top of one winding being positive whilst the top of the other is negative.
The dashed lines drawn between the windings of the transformer below indicate that it has a ferrite core and as such it would be used on medium to high frequencies.
When there are no lines between the two windings, the transformer is air cored and as such would be used on very high frequencies (VHF) and above.
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5.3 LOSSES Transformer losses are very small, 98% efficiency being easily attained, however some losses occur in all transformers. Generally the losses can be divided into three groups; copper losses, iron or core losses and flux leakage losses. 5.3.1 IRON LOSSES
Iron or core losses are divided into two groups; hysteresis and eddy current. •
Hysteresis losses arise through continually magnetising and demagnetising the transformer core, the energy required for this is dissipated as heat. Hysteresis loss is dependent on the operating frequency and type of material used for making the core. The higher the frequency, or the greater the flux density within the core, the greater the loss. Transformers are therefore designed to operate on a specific frequency and the material used to make the core has a narrow hysteresis loop. Typical materials used are stalloy, permalloy or mumetal.
• Eddy current loss is due to the formation of eddy currents within the transformer core, the energy again being dissipated as heat. Any metal located within the field of a transformer has emf's induced in it, these emf's produce small circulating currents called eddy currents. The core of the transformer is metallic and therefore has eddy currents flowing in it. Providing the currents are small, loss is minimal, but if they are able to join together, large circulating currents are produced. These large circulating currents result in a power loss, the loss being proportional to the square of the supply frequency. Eddy currents are kept to a minimum by laminating the transformer core, thus preventing the small eddy currents joining into large circulating currents. 5.3.2 COPPER LOSSES
Copper losses are the I2R losses in the windings. Part of the applied voltage is used to overcome the resistance of the primary winding, this reduces the flux available for inducing an emf in the secondary winding. Also, when the secondary circuit is connected, the secondary voltage falls due to the resistance of the secondary winding. Copper losses are dependent on the primary and secondary currents and the resistance of the windings and are independent of the supply frequency.
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5.3.3 FLUX LEAKAGE LOSSES
Flux leakage losses as the name implies, result from the fact that not all of the primary flux links with all of the secondary coils. The reduction in flux linkages results in a reduced secondary voltage. With modern production methods this loss is negligible. 5.3.4 SKIN EFFECT
Another loss that occurs at high frequencies is caused by skin effect. Any current carrying conductor has a field around it. In a conductor carrying a.c. current, the field expands from and collapses to the centre of the conductor, and also changes direction every half cycle. This alternating flux induces a back-emf in the conductor. As the field is denser at the centre of the conductor, the back emf at the centre of the conductor is larger than the back-emf at the surface of the conductor. Consequently, the current tends to flow in the surface region of the conductor rather than the centre, almost as thought the cable were a hollow tube. The higher the frequency the greater the skin effect. Although skin effect cannot be eliminated, the associated problems can be reduced by using Litz wire (multiple stranded cable – the current being divided between the strands), or by reducing the resistance of the surface region of the cable, this can be achieved by silver plating the conductor. 5.4 TURNS RATIO A simple transformer consists of two coils, a primary and a secondary, wound on a high permeability, soft iron core. The changing current in the first coil creates a changing magnetic field that induces an alternating voltage in the secondary coil.
The size of the secondary voltage compared to the voltage applied to the primary depends on turns ratio, or transformation ratio. That is, the number of turns of wire in the secondary winding compared to number of turns in the primary. If losses are small, the turns ratio may be expressed as: VSecondary NSecondary = T (transformation ratio) = V Pr imary N Pr imary
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If the number of turns on the secondary is less than the number of turns on the primary, the output voltage will be less than the input voltage, and the transformer is called a step-down transformer. If the number of turns on the secondary is greater than the number of turns on the primary, the transformer is a step-up type and the output voltage will be greater than the input voltage. By convention, when writing the transformation ratio, the secondary voltage is put before the primary, therefore a 4:1 transformer is a step-up transformer, the secondary voltage being 4 times the primary voltage. 5.5 POWER TRANSFERENCE If losses are ignored, the power in the secondary winding equals the power in the primary winding. IPrimary = ISecondary × T therefore:
VSecondary but T = V Primary
IPrimary × VPrimary = ISecondary × VSecondary
In practice there are some losses in a transformer and the output power can never equal the input power. 5.6 TRANSFORMER EFFICIENCY A transformers efficiency, η, is given by the ratio of output power to input power. output power × 100% η (eta) = input power The value of eta ranges from about 90% for small power transformers in receivers, to 98-99% for large power transformers. 5.7 TRANSFORMER REGULATION As the load on the secondary is increased, the output voltage falls. The amount by which the voltage falls is expressed as a percentage of the no-load voltage, and is termed the % regulation. % regulation =
no load voltage - full load voltage × 100% no load voltage
Regulation of power transformers is generally less than 4%.
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5.8 APPLYING LOADS TO A TRANSFORMER 5.8.1 NO LOAD CONDITIONS
In a practical transformer there are losses in the primary winding due to; resistance, hysteresis and eddy currents. These losses produce a current flow within the primary winding that is in phase with the applied voltage, and is termed loss current. The iron core and coils of the primary winding make the circuit highly inductive. The resistance of the primary winding is by comparison very small. The magnetising current therefore lags the applied voltage by 90 degrees. The total current flowing in the primary, with the secondary winding off-load, is the vector sum of the magnetising current and the loss current. Due to the large reactance of the primary circuit, the primary current is very small. If however, the transformer is operated at a lower than rated frequency, the inductive reactance will be less, and a larger primary current will flow, therefore, transformers should not be operated below their rated minimum frequency without reducing the applied voltage. It is the magnetising current that produces the primary field, and it is this alternating field that induces an emf in the secondary winding. The induced emf depends on the rate of change of flux, and therefore lags the primary field by 90°. As the primary field already lags the applied (primary) voltage by 90°, the emf induced in the secondary winding will lag the applied voltage by 180°. The secondary voltage is anti-phase with respect to the applied voltage. When a load is connected to the transformer, a current is set up in the secondary winding and a flux is produced. The secondary flux opposes the primary flux and effectively decreases the inductance of the primary winding. If the applied voltage is kept constant, the decrease in inductance results in an increase in the primary current. This increase in current is known as the load component of primary current. The load current in the primary winding sets up a flux that is equal and opposite to the secondary flux. The ampere turns of the primary flux equalling the ampere turns of the secondary flux. NPrimary × IPrimary = NSecondary × ISecondary
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
IPrimary NPrimary ISecondary × NSecondary = T (the transformation or turns ratio)
The total primary current is the vector sum of the no-load current and the load current. The larger the secondary current, the larger the primary current. Under normal conditions, the load current is so much larger than the no-load current that the latter can be ignored. 5.8.2 RESISTIVE LOADS
If the load on the secondary is purely resistive, the secondary voltage and secondary current are in phase. The secondary current decreases the inductance of the primary circuit and the primary current increases, the increase being the load element of primary current. The load element of primary current is anti-phase with respect to the secondary current and equal to the secondary current × the turns ratio. The primary current consists of the vector sum of the no-load and load current. From the diagram it can be seen that the primary voltage and current become more in phase as the resistive load applied to the secondary is increased. It appears as though the secondary load has been reflected back into the primary winding. 5.8.3 INDUCTIVE LOAD
If a purely inductive load is applied to the secondary winding, the secondary current will lag the secondary voltage by 90°. The load element of primary current, equal to the secondary current × T, will still be anti-phase with respect to the secondary current and will therefore be in phase with the magnetising current. The primary current is again the vector sum of the no-load and load currents. From the diagram it can be seen that the primary current now lags the applied voltage by almost 90°. Again it appears as though the load on the secondary has been reflected back into the transformer primary winding. Issue 1 - 1 January 2002
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5.8.4 CAPACITIVE LOAD
If a purely capacitive load is applied to the secondary, the load will again appear to be reflected back into the primary winding, and the primary current will lead the applied voltage by 90°. 5.8.5 COMBINATION LOADS
Introducing resistance into the purely inductive and capacitive circuits examined, simply has the effect of reducing the phase angle between the primary voltage and current. The greater the resistance, the greater the reduction in the angle. Or put another way. The more resistance there is in the secondary circuit, the more in phase the primary voltage and current. 5.9 REFLECTED IMPEDANCE The load placed on the secondary winding of a transformer always affects the primary current by altering its phase angle in relation to the primary voltage. Neglecting losses the reflected values of L / R / C can be shown to depend on the transformation or turns ratio. Iprimary × Vprimary = Isecondary × Vsecondary (1) now
Vsecondary = Isecondary × Zsecondary (2)
where Z equals the load applied to the secondary winding. Substituting (2) in (1) Iprimary × Vprimary = I2secondary × Zsecondary but
NPrimary ISecondary = IPrimary × N Secondary
so
Iprimary × Vprimary =
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2 IPrimary
×
2 Nprimary 2 Nsec ondary
× Z sec ondary
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Vprimary = Iprimary ×
2 Nprimary 2 Nsec ondary
× Z sec ondary
But the effective impedance in the primary is given by: Z primary =
so
Z primary =
Vprimary Iprimary 2 N primary 2 N sec ondary
× Z sec ondary
NSecondary writing the transformation ratio N =T Primary 1 ZPrimary = T2 × ZSecondary
ZPrimary =
T2 =
ZSecondary T2
ZSecondary ZPrimary
In a step down transformer T is less than unity and Z primary is greater than Z secondary. The fact that the impedance reflected from the secondary winding into the primary winding depends on the transformers turns ratio, makes it useful for impedance matching. 5.10 IMPEDANCE MATCHING TRANSFORMERS Maximum power is transferred from the source to the load only when the load impedance is equal to the internal impedance of the source. If this is not the case, an impedance matching transformer can be used. The necessary turns ratio being calculated using the formula: T2 =
ZSecondary ZPrimary
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For example a transformer could be used to match a pre-amplifier of 20 000 ohms input impedance to a moving coil microphone of 200 ohms. The turns ratio required would be calculated as follows: Z
20000
T2 = ZSecondary = 200 Primary
=
100 1
10 N Therefore T = 1 = NSecondary Primary 5.11 AUTOTRANSFORMERS Auto transformers have only one winding, this serving as both the primary and secondary. They may be used as "step up" or "step down" transformers.
When the primary terminals are connected to an a.c. source, current flows between P1 and P2. The alternating flux produced, links with all of the turns on the former, inducing a voltage in each. The output is taken from terminals S1 and S2. The voltage ratio is calculated from the turns ratio: VSecondary NSecondary VPrimary = NPrimary
In the step up transformer shown, the number of turns on the primary are those between points A and B, the turns on the secondary, those between points A and C. If the transformer were a step down type, the input and output terminals would be reversed. The effects of different loads on the transformer are as for the power transformer, however it should be noted that the primary and secondary currents oppose each other in the common portion of the winding. This enables smaller conductors to be used in the common portion of the transformer, producing a weight saving, especially if the input and output voltages are almost the same.
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Auto transformers are used for: •
line boosters to compensate for the voltage drops in long cable runs
•
motor starting. Several tappings being used in sequence to apply an increasing voltage to the motor
•
impedance matching
•
to step the 115V a.c. aircraft supply down to 26V for lighting circuits
The major disadvantage of auto transformers, especially step down types, is that should the common portion of the winding go open circuit, the primary voltage is applied directly to the load on the secondary. It was for this reason that autotransformers were rarely used on aircraft, however, improved reliability through modern manufacturing methods has made them increasingly more common. 5.12 MUTUAL REACTORS Mutual reactors or Quadrature transformers are devices that have been known about for many years, however, until the introduction of constant frequency a.c. systems, little use was made of them.
In order to detect the difference between the real and reactive loads on an a.c. generator, there was a requirement for a device that produced a voltage signal, that was at 90° to the current being sensed in a circuit. For all practical purposes this is achieved in a mutual reactor or quadrature transformer. When a current is passed through the primary winding, the voltage across the secondary lags the primary current by almost 90°.
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In order to explain the operation of a mutual reactor, it is necessary to examine the "off-load" vector diagram of a basic power transformer. Under no-load conditions a small, lagging current flows in the primary winding. If an air-gap is cut in the former, the reluctance of the magnetic circuit is increased and more current is required to magnetise the core. The magnetising element of the primary current lags the primary voltage by 90°. Therefore, as the magnetising current is increased, the total "no-load" current is increased and moved around until almost at 90° to the primary voltage. It also follows that the primary current leads the secondary voltage by almost 90°. In understanding the mutual reactor it is best to forget the applied voltage, and remember that, the voltage across the secondary will be in quadrature (at 90°) with any current passed through the primary winding. When physically examining a quadrature transformer it looks very much like a power transformer. The air-gap has to be of optimum size and is normally located under the windings. Unlike power transformers, mutual reactors can only be used to produce signal voltages and cannot be used supply a load. 5.13 CURRENT TRANSFORMERS Current transformers (CT's) are designed to enable circuit currents to be measured without breaking the circuit. The outputs are applied directly to instruments, or used in control circuits. Although working on the same principles as power transformers their construction and operation are vastly different.
Some have a primary winding comprising a few turns of wire capable of carrying the load current that is to be measured, others known as bar primary current transformers use the load supply cable as the primary. The bar primary type is more common on aircraft.
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The secondary former consists of a continuous strip of metal wound on itself to form a ring, although not laminated in the true sense, this gives the effect of laminations. The secondary winding is toroidally wound on the former, with the two ends brought out for connection to the load. When a power transformer is designed, the designer only needs to know the: • supply on which the transformer will operate • the output voltage required • maximum current that the transformer will be expected to supply This is not the case with a CT. A CT is designed to operate on one particular load, if a different load is attached, it will give a false indication. The CT designer needs to know the load and the supply source, and then designs a CT to link the two together. When writing the turns ratio, the primary is written before the secondary, the opposite to a power transformer. A 400:1 CT will have 1 ampere flowing in its secondary winding and load, if 400 amps is flowing through the primary cable. A bar primary counts as a single turn. When a current passes through the supply cable it causes a magnetic field along its entire length, this flux induces an emf into the coils of the secondary winding. The ring former and the secondary winding only take up a very short length of the primary conductor, therefore whatever happens to the secondary will have virtually no effect on the primary. The voltage induced in the secondary winding causes a current to flow through its load, this produces a secondary flux that opposes the primary flux, keeping the core flux to a very low level. If the primary is operated with the secondary disconnected from its load, there will be no secondary flux to oppose the primary flux, this results in; a high core flux, increased eddy currents, and increased voltages in the individual secondary coils, which can result in the CT overheating and burning out. Even if the CT is switched off before it burns out, the core may become pre-magnetised or biased, resulting in an inaccurate output. If it is necessary to operate a CT off-load, the secondary terminals must be shorted. If a CT is supplying a load such as an ammeter, the polarity of the connections may not matter, this is not however the case when used in control circuits. If the connections are crossed, or the CT is fitted the wrong way around on the primary, the output is phase shifted by 180°. This will cause control circuits to operate in the opposite sense. A CT should never be operated on anything other than its designed load, in some instances the CT and its load are a matched pair and may have the same serial number, in this case they must be changed as a pair.
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5.14 THREE PHASE TRANSFORMERS Although it is possible to use three, interconnected, single phase transformers for three phase a.c. it is more common to use a single, three limbed, transformer. Using a three limbed transformer, the primary and secondary windings for each phase are allocated a single limb.
Once the layout of the transformer has been established, it is only necessary to decide how to interconnect the primary and secondary windings. There are four possible alternatives:
The preferred methods of connection are the last two, however, the requirements of the circuit must come first. Issue 1 - 1 January 2002
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5.15 DIFFERENTIAL TRANSFORMERS Linear variable differential transformers (LVDT's), rotary variable differential transformers (RVDT's) and E and I bar transducers all use transformer principles to produce electrical signals from mechanical movement. The magnitude of the signals produced is dependent on the amount of movement, and the phase of the signal on the direction of movement. All three devices are used in control systems, and will be studied in more detail in module 4.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
FILTERS & ATTENUATORS
6.1 FILTERS Filter circuits are four terminal networks designed to pass a band of frequencies from the input to the output terminals, and to filter-off or attenuate, the remaining unwanted frequencies present at the input terminal. Such circuits are made from capacitors and inductors whose reactance changes with change in frequency. Filter circuits take four main forms: • High pass • Low pass • Bandpass • Bandstop 6.1.1 HIGH PASS FILTERS
High pass filters allow all frequencies above a certain cut-off frequency to be passed from the input terminals to the output terminals. All frequencies below the cut-off frequency are filtered off or attenuated. The diagrams above show a simple high pass filter together with its circuit symbol. The capacitor C allows the high frequencies to pass onto the output terminals, but offers a high reactance to the low frequencies. The inductance L offers a low reactance to low frequencies, so they are filtered off through it, but it offers a high reactance to the high frequencies and thus does not filter them off. A typical attenuation/frequency graph for a simple high pass filter is shown below.
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In practice a number of high-pass filter circuits are used in succession (cascade) as shown. This improves the attenuation of the lower frequencies and so the cutoff region becomes more abrupt and clearly defined. 6.1.2 LOW PASS FILTERS
Low pass filters allow all frequencies below a certain cut-off frequency to be passed from the input terminals to the output terminals. All frequencies above the cut-off frequency are filtered off or attenuated. The circuit symbol and an attenuation / frequency graph for a simple low pass filter are shown below.
In this circuit, L offers a low reactance to the low frequencies, allowing them to pass easily onto the output terminals, but offers a high reactance to the higher frequencies. The capacitor C offers a low reactance to the high frequencies, so they are filtered off through it, but it offers a high reactance to the required low frequencies and therefore does not attenuate them appreciably.
In practice a number of these filter circuits are used in succession. This improves the attenuation of the higher frequencies, and so the cut off region becomes more sharply defined.
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6.1.3 BAND PASS FILTERS
These circuits allow a certain narrow band of frequencies to be passed onto the output terminals and filter off, or attenuate the frequencies above and below this band. A simple bandpass filter is shown above. Rejecter circuit L1 C1 and acceptor circuit L2 C2 are tuned to the same frequency, the centre frequency of the required band. No mutual coupling exists between L1 and L2. The acceptor circuit offers low impedance to the resonant frequencies and passes them onto the output terminals, but offers high impedance to all the other input frequencies. The rejecter circuit offers low impedance to the unwanted frequencies either side of the band and so they are filtered off through it. The circuit symbol and attenuation / frequency curve for a band pass filter are shown below. A more practical band pass filter circuit is shown above. This 'π type' band pass filter circuit will give more clearly defined cut off regions.
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6.1.4 BAND STOP FILTERS
These circuits pass onto the output terminals all frequencies except a certain narrow band which is attenuated or filtered off. The circuit below is a simple bandstop filter.
Acceptor circuit L1C1 and rejecter circuit L2C2 are tuned to the same frequencies; the midpoint frequency of the unwanted band. No mutual coupling exists between L1 and L2. The rejecter circuit offers low impedance to all the required frequencies and therefore passes them onto the output terminals, but it offers a high impedance to the unwanted band of frequencies. The acceptor circuit L1C1 offers a low impedance to the unwanted band of frequencies and so they are filtered off through it. The acceptor circuit offers high impedance to the wanted frequencies and so, does not attenuate them appreciably. The circuit symbol and frequency / attenuation graph for a simple band stop filter are shown below.
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A more practical 'π type' band stop filter is shown above, again this will give more clearly defined cut-off regions. 6.1.5 SMOOTHING & DECOUPLING CIRCUITS
Smoothing and Decoupling circuits are special applications of filters. A smoothing circuit changes a pulsating d.c. to a smooth d.c. in power supply circuits. In order to achieve this, the filter circuit offers a high reactance to a.c. and a low reactance to d.c.
A Decoupling circuit removes any unwanted a.c. from a d.c. voltage. Such a circuit offers a high reactance to d.c. and a low reactance to a.c.
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6.2 ATTENUATORS When a source is connected to and supplying power to a load, it may be necessary to reduce the voltage, current or power in the load. This process is called ‘attenuation’. Attenuation can be achieved by adding a resistor in series with the load. The addition of the attenuator section (ABCC) in the circuit below, results in the load voltage and current being reduced by half, and the power in the load being reduced to a quarter.
This simple method of attenuation however causes a mismatch. To the source, (terminals AC) the load appears to be 180Ω. The load (terminals BC) sees a power source with an internal impedance of 180Ω. For proper matching, the supply should see a load of 60Ω and the load should see a supply with an internal impedance of 60Ω. This mismatch may cause a deterioration in the performance of the source and/or load, eg; the frequency response may be affected, particularly where impedances with reactance are involved. To avoid mismatch, an attenuator must match the load and the source impedances, ie; the source must ‘see’ an impedance equal to its own internal resistance and the load must ‘see’ an impedance, looking back into the attenuator, equal to its own value. Such attenuators are called matching attenuators and different types now follow, although only the first will be examined in the course.
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6.2.1 ‘T’ TYPE ATTENUATOR
If the output terminals of the circuit above are open-circuited, the impedance across the input terminals AC is 100Ω (Ra and Rc in series) or Zoc. If the output terminals are short-circuited, the impedance at the input terminals is 36Ω (Ra plus parallel combination Rb and Rc) or Zsc. The impedance of the input terminals can be any value between 36Ω and 100Ω, depending on the load placed across BC. The geometric means of these values is equal to: ZSC x ZOC =
36 x 100 = 60Ω
and is called the ‘characteristic impedance (Zo) of the network. By suitable choice of resistor values, a network with any value of characteristic impedance can be built. The significance of Characteristic Impedance may be seen if the ‘T’ type attenuator above is connected between the source and the load in the first diagram. This arrangement is shown below, with the appropriate values of voltage, current and power shown. The source (of 60Ω internal resistance) will ‘see’ a load of 60Ω, ie; it will be matched (Load + Rb in parallel with 80Ω, in series with Ra = 60Ω). Looking back, the load will ‘see’ an impedance of 60Ω, ie; will be matched (Source resistance + Ra in parallel with 80Ω, then in series with Rb = 60Ω).
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60V Action. Across the input terminals AC, the impedance is 60Ω: 1A , and 60 Watts is applied as input power to the attenuator. However, at the load, the power has reduced to 15 W (30V × 0.5A) i.e. one quarter of the input power. (In units of decibels, which will be discussed later in the course, this is a reduction of 6 dBs). The source and load are matched; only a controlled reduction of power, voltage and current has occurred at the load. Being matched, the performance of the source and the load has not been affected in any other way. 6.2.2 TWO SECTION ATTENUATOR
Two identical attenuators may be used to reduce the input power by 1/16 at the load. i.e. attenuation of 12 dBs. Such an arrangement is below.
It will be seen that the input power is progressively reduced and that the impedance at each of the junctions X, Y and Z is the same. Calculated values are shown in the table below. Voltage
Current
Impedance
Power
At X
60V
1A
60Ω
60W
At Y
30V
0.5A
60Ω
15W
At Z
15V
0.25A
60Ω
3.75W
Any number of such sections may be added to give the required attenuation. The extra sections may be switched in, to give manual control of the amount of attenuation.
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6.2.3 VARIABLE ATTENUATORS
Fine adjustment of an attenuator may be achieved by having a section with all three resistors variable as shown below. If the attenuator resistors were changed to the values Ra = 36Ω ; Rb = 36Ω ; Rc = 32Ω The impedances across AC and BC would be 60Ω as before.
If Ra and Rb were varied from 20 to 36Ω and at the same time Rc is varied from 80 to 32Ω, the attenuator would reduce the input power from 1/4 to 1/16 at the load, i.e. attenuation would vary from 6dBs to 12dBs, whilst the impedances seen by the load and the source would remain constant. 6.2.4 'π π' TYPE ATTENUATORS
In the π type attenuator, the components are arranged to form the Greek letter π (Pi), as shown below. The same general principles apply to this network, as to the T type.
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6.2.5 BALANCED & UNBALANCED NETWORKS
All the attenuators shown so far have a common line (the bottom line in the diagrams), such as earth. These networks are said to be ‘unbalanced’ because the voltages in each line are different due to the different impedances in each line. In a balanced network, the two lines have equal anti-phase voltages and therefore should have equal impedances in each line. Balanced attenuators are shown below.
6.2.6 ATTENUATOR SYMBOLS
Functional diagram symbols for a fixed loss attenuator (pad) and a variable attenuator are shown below.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
AC GENERATION
7.1 PRINCIPLES The generation of an alternating current has already been examined in the section on d.c. generation. The rules concerning the size of the generated emf and the direction of current flow are as previously described. Instead of a commutator being used to ensure the current flows in one direction through the load, the load is connected via slip rings and the current flow is alternating, as shown below.
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7.1.1 OUTPUT VOLTAGE
The instantaneous value of emf induced in the loop is given by: e(instant) = E(max) sin θ where E(max) = Βlv and θ is the angle of the conductor with respect to the field.
7.1.2 OUTPUT FREQUENCY
Referring back to our simple single loop generator, it can be seen that, if the loop were to rotate at 120 revolutions per second, the output frequency would be 120 Hz. It therefore follows that the frequency of the output of an ac generator is directly proportional to its speed of rotation. Another factor which determines the output frequency of an a.c. generator is its physical construction. A generator with 4 field poles will produce two complete cycles of output for each revolution of the shaft.
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Similarly, a generator with six field poles will produce three complete cycles for each revolution and so on. A cycle is complete whenever a conductor has passed under the influence of two dissimilar magnetic poles. So the output frequency of an ac generator is given by: Frequency = Revolutions per second × No. of pairs of poles The speed of rotation is normally given in revolutions per minute (rpm), therefore the output frequency is actually calculated from using: Frequency = Where:
NP 60
N is the speed of rotor rotation in RPM P is the number of pairs of poles
From the foregoing, it will be seen that one cycle is completed in: 360 mechanical degrees for a two-pole machine, 180 mechanical degrees for a four-pole machine, 120 mechanical degrees for a six-pole machine, 90
mechanical degrees for an eight-pole machine, and so on.
It is therefore necessary to use electrical degrees when referring to angular motion in the cycle. One cycle = 360 (electrical) degrees. It is not usual to use the word ‘electrical’ in this respect, but the concept should be clearly understood. 7.1.3 EFFECTS OF A RESISTIVE LOAD
When a resistive load is placed on an a.c. generator, armature reaction occurs. If the generator is a rotating field type, the field is distorted against the direction of rotation as shown below. If the load is increased, armature reaction is increased and the field is distorted further.
A resistive load also places a physical load on the generator causing it to slow down, this results in both the output frequency and voltage decreasing. The only way to restore the output is to provide more drive torque to overcome the extra load.
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7.1.4 EFFECTS OF AN INDUCTIVE LOAD
If an inductive load is placed on an a.c. generator, the current in the stator lags the voltage by 90°, causing the stator field to move around 90°. The stator field now opposes the main field, resulting in a weaker main field and a reduction in output voltage.
The voltage is restored by increasing the field current, however this does generate additional heat in the machine. 7.1.5 EFFECTS OF A CAPACITIVE LOAD
If a capacitive load is placed on an a.c. generator, the stator field is advanced by 90° and now assists the main field, this increases the main field strength and increases the generators output voltage.
This can be corrected without adverse affects, by decreasing the field current. Most aircraft systems have inductive loads and a lagging power factor.
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7.2 PRACTICAL GENERATOR CONSTRUCTION There are two types of alternating current generator, a rotating field type and a rotating armature type. These names stem from the way they are both constructed. Although the rotating field type generator is the one most commonly used for the production of a.c. power on aircraft, both types will be met later in the course. 7.2.1 ROTATING ARMATURE TYPE
A rotating armature generator is constructed in a similar manner to a d.c. generator. The field is located on the stationary part of the machine (stator) and the emf is induced in windings located on a rotating armature (rotor). The output is then taken from the generator using slip rings as previously described.
7.2.2 ROTATING FIELD TYPE
It is possible however, to obtain the same output by rotating the field inside stationary armature (stator) windings located around the frame of the machine. The output is then taken from the stationary armature.
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This type of generator is called a ‘rotating field generator’. It has several advantages over the rotating armature type: •
Because the output windings are now stationary they are no longer subject to high centrifugal forces and can therefore be larger.
•
By having the output windings on the outside of the machine there is more room for good insulation and higher voltages can be used.
•
With the output windings on the outside of the machine they are more easily cooled and can therefore carry larger currents.
•
Using a rotating field only requires the use of two slip rings and two brushes, also the current required is relatively small.
These advantages mean a larger output can be obtained from a smaller machine. 7.2.3 SINGLE PHASE GENERATOR
A single phase a.c. generator consists of a single output winding wound on a pair of stationary poles and a rotor fitted either with a permanent magnet or an electromagnet. The electromagnet is energised from a d.c. supply via two brushes and slip rings.
When the rotor is driven, emf's are induced in the stator windings. When the output windings are connected to a load, load current flows. The output frequency is dependent on the speed of rotor rotation and the number of poles on the rotor. If the generator shown was rotated at the same speed, but had two pairs of field poles, the frequency would double.
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7.2.4 TWO PHASE GENERATOR
A two phase generator has two output windings wound on separate pairs of poles positioned 90 degrees apart as shown. A single, common rotor comprising a permanent or electromagnet is still used.
The 90° angle between the to two output windings means that when maximum emf is induced in one winding, zero emf is induced in the other winding and vice versa. The output from the generator will be two voltages of equal amplitude and frequency, but phase displaced from each other by 90°. 7.2.5 THREE PHASE GENERATOR
A three phase a.c. generator has three sets of output windings, each physically displaced from the other two by 120°. The rotor is the same as that used in a single phase or two phase generator. The Three phase a.c. generator is really three single phase generators on one stator, all using a common field. Due to the construction of the machine, the emf's generated in each of the windings is phase displaced by 120 degrees, as shown below. The normal order of rotation is: Red
Yellow
Blue
1
2
3
A
B
C
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If two phases are reversed then motors and control circuits will try to operate in reverse.
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If required, the three single phases can be used independently, however this is not common practice. The windings are normally connected together in one of two ways, called star or delta. Whether star or delta depends on the way the windings are connected at the generator output terminals.
7.3 STAR & DELTA SYSTEMS The three armature windings of a three phase generator can be connected in two ways. Firstly, the end of one winding can be connected to the start of the next, so that the three windings are connected in series to form a triangle. This form of connection if called a Delta system. The delta system is a three wire system, a single wire being taken from each of the three points of interconnection. The alternative, is to connect the same end of each armature winding to a common point and take the other end of each winding to an output terminal. This form of connection is called a Star system. The star system is a four wire system, as a wire is also taken from the common point to an output terminal.
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MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
7.3.1 DELTA CONNECTION
A Delta system is a three wire system, one wire coming from each of the armature winding interconnection points. In a delta connected system: VLINE = VPHASE ILINE = 3 x IPHASE Or
ILINE = 1⋅73 x IPHASE
A delta connected system has no neutral line and is generally used on small generators supplying virtually fixed, balanced loads. 7.3.1.1
Balanced loads
If the currents in each phase are equal in size and phase displaced from one another by 120 degrees, the loads are said to be balanced. Under balanced conditions, the loads on each phase are identical 7.3.1.2
Symmetrical loads
If the phase voltages are the same in magnitude, and phase displaced from one another by 120 degrees, the system is said to be symmetrical. Aircraft systems are naturally symmetrical. 7.3.2 STAR CONNECTION
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
Although a star connected system is considered to be a four wire system, if the loads are balanced, the neutral line need not be connected. The neutral line only carries out of balance currents. The neutral, although connected to earth, should not be confused with the earth in a three pin mains plug which is there for protection. Under the majority of conditions, a star connected aircraft power system will have current flowing in the neutral line. The voltage from the neutral line, or star point, to the other end of each phase winding is called the phase voltage, the voltage from one phase to another is called the line voltage. In a star connected system: VLINE = 3 x VPHASE or
VLINE = 1⋅73 x VPHASE
and ILINE = IPHASE The frequency is always expressed as the frequency of a single phase. In aircraft a.c. systems, the phase voltage is 115V and the line voltage is 200V. On some aircraft systems the frequency is variable (wild), however, on the majority of modern aircraft, the frequency is kept constant at 400 Hz. With a star connected a.c. power system, two possible systems are available: •
three single phase systems each operating at the phase voltage
•
a single three phase system operating at line voltage
If the instantaneous values of two phases are added together to produce a line voltage and the process is repeated for the other phases, three line voltages will be produced. Each line voltage is displaced 120 degrees from the other two. One point to note is that, there is a 90 degree phase angle between a phase voltage and its opposite line voltage, this relationship is used in several aircraft control and monitoring systems. 7.3.3 POWER IN AC SYSTEMS
In star and delta connected systems, the power dissipated in each phase is given by the formula: PPhase = VPhase x IPhase Cos θ Watts If the system is balanced and symmetrical then the total power is three times the above value.
Issue 1 - 1 January 2002
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JAR 66 CATEGORY B1
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engineering 8
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
AC MOTORS
With few exceptions, the operation of an a.c. motor relies on the production of a rotating magnetic field, therefore, we will examine the production of a rotating field first. 8.1 PRODUCTION OF A ROTATING FIELD Alternating current supplies are generally available in one of three forms, single phase, two phase or three phase. Any of these three supplies can be used to produce a rotating magnetic field, but there are differences in how it is achieved, so they will be examined individually. 8.1.1 SINGLE PHASE
To produce a rotating field from a single phase a.c. supply requires a minimum of two pairs of field windings and a four pole stator, as shown below. However, a single phase supply connected to the windings shown, will only produce an alternating field positioned at 45 degrees to the pole pieces.
To create a rotating field, the current in one pair of field windings must be 90 degrees out of phase with the current in the other pair of field windings. This can be achieved by placing an inductor or capacitor in series with one pair of field windings, whilst connecting the other directly to the supply. A capacitor is generally used because it is more efficient.
Issue 1 - 20 March 2001
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The direction of rotation of the magnetic field depends on the order in which the poles become magnetised.
The direction of rotation of the field can be reversed either by swapping the supply to one pair of field windings, or by switching the capacitor from one field winding to the other. The latter method is often used on aircraft motors. If the supply to both field windings is reversed, the motor will run in the same direction. 8.1.2 TWO PHASE
To produce a rotating field from a two phase supply also requires a minimum of four field poles and two pairs of field windings. A two phase supply comprises two voltages phase displaced from one another by 90 degrees. Therefore no capacitor is required.
Issue 1 - 20 March 2001
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
The only way to reverse the direction of rotation of such a motor is to swap the power supply connections to one pair of field windings. A two phase supply can be obtained from a three phase a.c. supply, by using one phase voltage and the opposite line voltage. 8.1.3 THREE PHASE
To produce a rotating field from a three phase a.c. supply requires the use of a six pole stator and three pairs of field windings. The stator of a three phase a.c. motor is the same as that of a rotating field a.c. generator.
The direction of rotation of the field depends on the order in which the windings are energised. To reverse the direction of rotation, it is only necessary to swap the connection to any two of the field windings. 8.2 TYPES OF AC MOTOR The two main types of a.c. motor used on aircraft systems are the induction motor and the synchronous motor. Hysteresis and shaded pole motors are however often found in instruments, and as they are both a.c. motors, they will also be examined at this time 8.2.1 INDUCTION MOTOR
The rotor of an induction motor consists of a number of copper or aluminium bars connected by two end rings to form a cage. The cage is enclosed in a laminated iron core to reduce its reluctance. This construction is very simple but very strong.
Issue 1 - 20 March 2001
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
When the rotor is placed in a rotating magnetic field, the bars are cut by the rotating flux, causing emf's to be induced in them, because the bars are shorted by the end rings, currents then flow in the bars. Current flow in the bars produces a magnetic field around them, which reacts with the main field of the machine, causing the rotor to turn.
At switch-on, the emf's induced in the rotor bars are at the same frequency as the supply voltage and because the circuit is highly inductive the current lags the voltage by almost 90 degrees. This means, that by the time the rotor field has been produced, the main field has moved on by almost 90 degrees and the rotor field can only react with the trailing edge of the main field, resulting in a small starting torque. As the rotor speed increases, the frequency of the emf's in the rotor decrease, reducing the inductive reactance. The brings the current more in-phase with the induced emf's, producing a good running torque. It is not possible for the rotor to rotate at synchronous speed (the speed of the field), because there would be no emf’s induced in the rotor bars, no current flow and no magnetic field produced. The difference between synchronous speed and rotor speed is called ‘slip speed’ and is usually expressed as a percentage of the synchronous speed.
Issue 1 - 20 March 2001
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
When running, the field around the rotor bars induces an emf into the stator windings, this ‘back-emf’ is almost 180 degrees out of phase with the applied voltage and therefore opposes it, resulting in a small effective voltage across the field and a low current drawn from the power supply. If the load on the motor is increased, it slows down, this causes the phase angle of the back-emf to change, increasing the effective voltage, the current from the supply and the motor torque. The increase in motor torque accelerates the motor back to its original running speed. When first started, the back-emf is almost at 90 degrees to the applied voltage and therefore not opposing the supply voltage. The effective voltage is therefore almost equal to the supply voltage and the current demand is high. In order to reduce the starting current, some motors are designed to be started with the field windings connected in star and run with them connected in delta. This increases the impedance during starting and reduces the current drawn from the supply, but it does not improve the poor starting torque. If it is required that an induction motor be started ‘on-load’, then the poor starting torque must be improved. To achieve this, the rotor current must be made to appear more in phase with the voltage. This can be achieved by increasing the resistance of the rotor windings, however, if the resistance is left in the rotor circuit once the motor is running, there will be: • an increase in the slip speed • a greater speed variation with load changes • an increase the current taken from the supply A compromise often used on aircraft induction motors is to fit a second, high resistance, cage into the rotor. This gives an improved starting torque, with minimal running problems. 8.2.2 SYNCHRONOUS MOTOR
The synchronous motor gets its name from the fact that the rotor runs at synchronous speed (the speed of the field), for it to do this, the rotor must be a permanent magnet or an electro-magnet.
Issue 1 - 20 March 2001
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JAR 66 CATEGORY B1
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engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
In order for the magnet to lock-on to the field, it must be brought up to about 75% of synchronous speed, to achieve this the majority of synchronous motors have the cage of an induction motor built into them. The motor starts as an induction motor and when sufficient speed has been attained, the electromagnet is energised, allowing the rotor to lock onto the field. Once running, no emf's are induced in the rotor bars, however, they are useful in holding the rotor and rotor windings in place and also assist in smooth running during load changes. The rotor, although running at synchronous speed, will lag behind the field, the angle of lag is proportional to the load placed on the motor.
If whilst running the load is increased, the angle of lag increases, changing the angle of the back-emf and increasing the effective voltage. This increase in effective voltage increases the current taken from the supply, producing an increase in torque to cope with the load increase. Should the angle become too great, the magnetic link will snap, the motor will run down, stop, and possibly burn out due to the high current taken from the supply as a result of the loss of back emf. 8.2.3 SHADED POLE MOTOR
The shaded pole motor uses only a single set of poles to create the appearance of a rotating magnetic field. The poles are each cut into two sections. One section of each pole is then shaded by a copper or aluminium ring, or a shorted coil.
Issue 1 - 20 March 2001
Page 8-6
JAR 66 CATEGORY B1
uk
engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
When the field winding is energised, an alternating flux appears across the main poles. The alternating main field induces emf's in the shaded ring or shorted winding and causes a current flow within it that produces a second alternating magnetic field. The field in the shorted ring lags the main field by approximately 90 degrees. The overall effect is to produce a field that appears to move through an angle determined by the relative positions of the two sections of each main pole. The field is not fully rotating, only moving through a small angle, therefore the starting torque is low and the motor can only be used for small, fixed loads. The operation of the rotor is as for an induction motor. 8.2.4 HYSTERESIS MOTOR
The construction of hysteresis motors vary. The motor is so named because the material used for the rotor has a large hysteresis loop. This type of motor requires a two phase a.c. supply and is often used as a servo motor, one phase being supplied from a reference source, the other from a control circuit. The current in the control phase is made to either lead or lag the reference phase by 90 degrees, depending on the direction of rotation required.
The motor shown employs a cobalt steel ring rotor. When the field is energised, a North pole appears at A and a South pole at A1. Poles B and B1 are not magnetised. The field across A-A1 induces a South pole in the rotor at X and a North pole in the rotor at Y. As the supply changes, A and A1 die away as B becomes a North pole and B1 becomes a South pole. The retention of flux by the rotor causes the south pole at X to be attracted by the North pole at B and the North pole at Y to be attracted by the South pole at B1. This causes the rotor to rotate. As the rotor moves to align with the field, the field has moved on, so the rotor moves again to try and align. The rotor continues to rotate following the field. If the phase of the control supply is reversed (made to lag the reference supply instead of lead it), the motor will change direction
Issue 1 - 20 March 2001
Page 8-7
JAR 66 CATEGORY B1
uk
engineering
MODULE 3 (part B) ELECTRICAL FUNDAMENTALS
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