Expt. No. 1 With Answers

Experiment No. 1 WAVE PROPAGATION IN A TRANSMISSION LINE DEMONSTRATING THE EFFECTS OF LOSSES, ATTENUATION AND STANDING WAVES 1. Objective(s): The activity aims to introduce the basic concepts of transmission line and transmission line abnormalities and its effects. The experiment will give the students a close look on how signal propagates inside the transmission line and how it reacts to irregularities on the line. This will also introduce the students to the concepts of characteristics impedance and reflections in transmission line. 2. Intended Learning Outcomes (ILOs): The students shall be able to; 2.1 Explain the propagation of a signal in a match or non-resonating line. 2.2 Determine the effects of loses, attenuation, and dispersion, on the amplitude, frequency and phases of signal. 2.3 Define characteristic impedance and reflections. 3. Discussion Propagation in a Transmission Line There are many situations in which it is desired to connect a generator (or source of electrical power) to distant load (or power – absorbing device). the generator may be of high power, as in a power station, or low power, as with a microphone; it may be low frequency, again as in the power station, or high, as a radio transmitter. But each case a pair (at least) of conductors is required to convey the power from the generator to load. Such a pair of conductors is called a “transmission line” or abbreviated to simply ‘line’ when convenient. When a signal is applied to a transmitter line at one end, the other end is not immediately affected. Instead the signal travels along the line with finite velocity, and reaches the load somewhat later. The potential difference between the conductors is associated with a magnetic field. Those fields interact with each other and with the line to form a guided electromagnetic wave travelling along the line. The maximum speed such a wave can have a speed of light, 3 x10 8m/s; in lines having solid materials around the conductors the speed of propagation can be much less. If a sinusoidal signal is applied to a line, different phases of the sine-wave will be distributed in distance along the line owing to its travel. A complete cycle of the wave occupies a distance λ along the line which is called wavelength. The wavelength is inversely proportional to the frequency f of the wave: they are related to the propagation velocity v by the formula v = λf. Attenuation and Dispersion The flow of current in the conductors’ resistance gives rise to the energy losses. Further losses arise due to imperfections in the isolation between conductors, such as surface leaking across insulator, or dielectric losses. In consequence if the power of a signal is W (watts) at the sending end of the line, it may be reduced to 1/2W at some distance along the line; the same further on again it will be 1/4W. The signal is

said to be attenuated. The diminution in power is exponential: the decrease is by a given factor per unit distance. In mathematical treatment of the line transmission, all the properties (velocity of propagation, attenuation, distortion of signals) are explained in terms of four ‘line constants’. These are: L = the inductance of the line per unit distance (H/m) C = the capacitance of the line per unit distance (F/m) R = the resistance of the line per unit distance (Ω/m) G = the conductance of the line per unit distance (S/m) The line constants are in fact only constant for a particular frequency, and may vary from one frequency to another. However, the variation is not usually so rapid as to spoil the usefulness of the theory. 4. Resources: Equipment: 1 - Function Generator, Sine (e.g. Feedback VPG608) 1 - 0600R Terminator 2 - Links 1 - Extension Cord 5. Procedure: PART A: PROPAGATION IN A TRANSMISSION LINES 1. Set the TLD511 controls as follows: i. hold/run set to ‘run’ ii. line length set to ‘8L’ iii. distributed attenuation set to ‘min’ 2. Set the function generator’s output voltage to zero. The generator frequency should on a range allowing continuous variation between 2 and 0.5 Hz. Set the frequency to 0.75Hz. 3. Connect up the system as shown in Figure 1.1.

Figure 1.1

4. Operate the switch for ‘step input to A’ briefly until the light has appeared in the second column. Observe: The lights are running from left to right . 5. Send a pulse from terminal ‘B’ to ‘A’ by operating “step input to B’. Observe that the pulse disappear at the end. Why? The signal travels along the line with fixed velocity, and reaches the load somewhat later. The other end is not immediately affected by the input signal . 6. Change the line length to 2L and raise the output voltage of the generator to give full height indication in each column. Describe the shape of the wave: The wave is sinusoidal. 7. Operate hold. What part of the wave is shown? The first part of the wave is shown. 8. Release ‘hold’ and operate again at a different part of the input cycle: different parts of the sine wave are displayed, but always the same fraction of a wavelength. 9. Release ‘hold’ again and raise the frequency gradually to 2Hz. Point out the reduce wavelength and operate ‘hold’ again. Observe: The wave moves faster. 10. Take v (for TLD511) as 4L m/s if L is the length in meters. Find the propagation time of the line of length L.

2m ( dt )=( 4 Lm /s )

v=

therefore, t= 0.5s

PART B: ATTENUATION AND DISPERSION 1. Set the TLD511 controls as follows: i. hold/run ii. line length

set to ‘run’ set to ‘2L’

iii. distributed attenuation

set to ‘min’

2. The generator frequency should on a range allowing continuous variation between 2 and 0.5 Hz. Set the frequency to 1.75Hz. 3. Connect up the system as shown in Figure 1.2.

Figure 1.2 4. Raise the generator’s output voltage to give a travelling sine wave display of full column amplitude. Point out that amplitude is the same at all points in the line. 5. Gradually raise the distributed attenuation to ‘max’. Observe: As the signal reaches the other point, the amplitude decreases. 6. Reduce the frequency of the generator. Observe: The attenuation of the signal decreases but the movement of the signal is also slower 7. Disconnect the line connecting to the generator. Set the length to ‘8L’. Set the distributed attenuation control about mid-way. 8. Operate the ‘step input to A’ switch until the second display column lights, to produce a travelling pulse. Observe: The signal is reduced when it comes to the right most of the line. 9. Repeat with various amounts of attenuation. 10. Transfer the 600R terminator to the ‘A’ end of the line. Operate the ‘step input to B’ switch. Observe: The signal is reduced when it reaches the leftmost part of the TLD.

PART C: TERMINATIONS, SIMPLE CASES 1. 1. Set the TLD511 controls as follows: i. hold/run set to ‘run’ ii. line length set to ‘8L’ iii. distributed attenuation set to ‘min’ 2. Set the function generator’s output voltage to zero and its frequency to 1.5Hz. 3. Connect up the equipment as shown in Figure 2.1.

Fig.2.1 4. Operate the switch for ‘step input to A’ briefly until the light has appeared in the second column. A pulse, two columns wide as in Figure 2.2, will then travel to terminal ‘B’ end of the line and disappear. Why? The pulse disappear because of the 600R terminator.

Figure 2.2 5. This time remove the terminator from ‘B’ end of the line and send a pulse from ‘A’. Observe and record results.

Figure 2.3 6. Place a short-circuit link across the line at ‘B’ (where the 600R terminator was) and again send a pulse from ‘A’. Observe and record results.

Figure 2.4 7. Reconnect the set-up of Figure 2.1. Operate the ‘step input to ‘A’ switch to send a pulse from ‘A’, then immediately operate it in the reverse direction to send a pulse from ‘B’. Record results below.

Figure 2.5 8. Operate the ‘step input to A’ switch. Release only the switch after the signal has reached ‘V’. When the line is at rest remove 600R terminator.

Observe: It continues to send the signal to B so when the 600R terminator was removed, all the signals at B bounces back. Meanwhile, the signal which is approaching B collides with the reflected signal that is why there is an increased signal at B. 9. Operate the ‘step input to A’ switch. Release only the switch after the reflected signal has returned to ‘A’. Observe: The observation at number 8 is just the same with this number. It’s just that, the incident occurs twice. 10. Repeat procedure 8 and 9 of part C, using short-circuit link at termination ‘B’. Explain: Since the 600R is not there, therefore nothing receives the signal that is why the tendency is for the signal to bounce back. 11. Set the line length ‘2L’. Replace the 600R terminator at ‘B’ (a value lower or higher than 600R). 12. Raise the function generator output to give a travelling wave of about half-scale amplitude. 13. Remove the terminator from B. Observe the standing wave. 14. Vary the frequency in the range ½ to 2 Hz. Observe the change in the wavelength and always a maximum voltage at terminator ‘B’. 15. Return the frequency to 1.5 Hz. Plug in a short-circuit link in parallel with terminator ‘B’. Observe the places node and antinodes where they have change places.

Course: Group No.: Group Members: Enriquez, Kavin Lusterio, Ma. Olivia T. Mapa, Renaldi Montefalcon, Robert Saja, Odellien

Experiment No.: 1 Section: Date Performed: Date Submitted: Instructor:

Yucot, Marjie 6.Data and Results: 2m ( dt )=( 4 Lm /s )

v=

therefore, t= 0.5s

With 600R

Without 600R (open)

Link instead of 600R (short)

7. Analysis: From the results obtained the amplitude of the travelling pulse which was dependent on the amount of output voltage from the generator supplied to the transmission line demonstrator (TLD), and was determined due to the number of lights that lit up in a column. Pulse propagation on TLD was determined by the orientation of the step input, that the propagation followed the terminal point directed by the step input. When it comes to Attenuation and Dispersion, it was noted that the rate of the pulse propagation or transmission was accounted to the amount of distributed attenuation in the TLD, that as the distributed attenuation control was set at maximum level, the pulse propagation became slower. That was accounted to the effect of the attenuation on the transmission media where in the attenuation blocked the transmission of pulse from one point to another, thus resulting to a lossy line. On the other hand, the decreased in the attenuation was not only done by controlling the distributed attenuation knob, but also

was accounted to the decreasing of frequency, that resulted to fewer frequency components causing less distortion of the pulse brought by the attenuation. It was also noted that in a backward attenuation, the propagation of pulses as it was being transmitted was always dependent on where the load terminator was located, regardless of the orientation of the step input, in order for the maximum power transfer to be achieved, since the characteristic impedance of the transmission line was equal to the purely resistive load terminator. When it comes to Line Terminations, a perfectly matched transmission was accounted at the instance that the characteristic impedance and the load were equal, thus the voltage remained constant all throughout as the pulse propagated. And since the load was a purely resistive load, all of the pulse that was propagated and entered the line from the source was dissipated at the load. That kind of line transmission was also considered to be a line termination at a short circuit link, where there was already a reflected pulse that was seen and that was accounted to the zero value of the resistance while the current was at maximum value. While when pulse were terminated at an open circuit link, the pulses did not propagated back and that was accounted to the maximum value of resistance and minimum value of current, where the maximum resistance stored the pulse in the distributed inductance and capacitance and the line acted as a resistor that dissipated all the energy and none was returned back. 8. Conclusion: Based on the data gathered and by analyzing those data and results, we can now therefore conclude that in Propagation in a Transmission line, when a signal is applied to a transmission line at one end, the other end is not immediately affected. Instead, the signal travels along the line with fixed velocity, and reaches the load somewhat later. The potential difference between the conductors is associated with a magnetic field. Those fields interact with each other and with the line to form a guided electromagnetic wave travelling along the line. If a sinusoidal signal is applied to a line, different phases of the sine-wave will be distributed in distance along the line due to its travel. A complete cycle of the wave occupies a distance λ along the line which is called wavelength. The wavelength is inversely proportional to the frequency f of the wave: they are related to the propagation velocity v by the formula v = λf. The flow of current in the conductors’ resistance gives rise to the energy losses. Further losses arise due to imperfections in the isolation between conductors, such as surface leaking across insulator, or dielectric losses. The line constants are in fact only constant for a particular frequency, and may vary from one frequency to another. However, the variation is not usually so rapid as to spoil the usefulness of the theory. 9. Questions and Problems: 1. Give examples of causes of attenuation.  network devices such as router, hub and repeater.  transmission medium  conductors and connectors 2. Compare the reflected wave of open, short and properly matched line.  In a matched line, the entire signal is absorbed by the load; in an open or short line, the entire signal is reflected back. 3. Why do we need to terminate a line at its characteristic impedance? What are the effects of not doing so?



The idea is that the signals propagate at a finite speed, that is to say a certain signal takes time to get from one end of the transmission line to the other line. The cable also has some intrinsic capacitance/inductance per unit length, which can be approximated with a characteristic impedance (assuming loss-less):

Zo=

√

L C

This is the impedance

initially experienced by the source when the signal changes, with the signal level acting like a voltage divider circuit between R1 and Z0:

Vs=Vin

( R 1+ZoZo )

When the signal

propogates to the end of the cable, it will realize that there's nothing to dump the signal energy into. The signal must go somewhere, so it bounces off the far end and returns to the source. When it reaches the source, the source voltage will be twice the original Vs, which will flow back through R1 to the source. 4. Why an ordinary extension cord is not usually considered a transmission line, while a television antenna of the same length would be?  If you get down to the technical part, an ordinary extension cord is a transmission line. It's not normally thought of in this fashion but it could be. You see the high voltage power transmission lines going across country. There are power transmission lines going through your neighborhood. These may be on poles or underground. The wires in your house are also power transmission lines. This could include your extension cord. They allow transmit the household power to where it's needed. It's just semantics, but thinking of an extension cord as a transmission line is valid. 5. What is the relationship between frequency and attenuation?  In a transmission line, the loss is logarithmic. It is a given number of dB per distance of transmission line. This is also something that increases (sometimes drastically) with frequency, but it is not a simple relationship. However, loss in a transmission line ALWAYS goes up with frequency. 10. Assessment (Rubric for Laboratory Performance):