Jawad Chowdhury- 7641617

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Artificial Line Laboratory

Objectives: The aim of this experiment was to be able to study the behaviour of a transmission line,

with sinusoidal and step signal input under different terminating conditions. Also to analyse the

output waves produced by the transmission line and to study there reflections, reflective co-efficient

and the effects of the different termination conditions.

By studying these different behaviours we should be able to determine the characteristic impedance

and the length of the artificial transmission line with step input signal, using the time domain

measurement technique based on the reflection concept, and with a sinusoidal excitation signal.

Background Theory:

General Information-

The artificial line that was used in the lab consists of a number of sections and was used to simulate

a length of power line spanning approximately 6000 meters. The sections were built up with

inductive elements twisted around ferrite rings to provide an inductance of 300µH and capacitors of

approximately 3500pF.

Artificial transmission lines are discrete lumped circuit elements designed to represent real

transmission lines. If it was possible to have an infinite number of circuit elements within our

artificial line then we would be able to give a perfectly accurate simulation of a long transmission

line, however this is not possible so we only have a finite number of sections with our artificial line

and this allows us to only represent a transmission line below a high frequency limit.

For our resonant condition of the artificial line is such that the reflected wave exactly opposes the

applied input waveform. Also the lowest frequency for resonance is when the line length is one

quarter of the wave length.

Reflection Co-efficient-

: Reflection Co-efficient, : Load Resistance, : Characteristic Impedance

The reflection co-efficient is a very important concept for transmission lines.

Termination Conditions-

For (short circuit)

For (open circuit)

For (Match- load resistance is same as characteristic impedance)

Impedance match is the proper termination if we don’t want any reflections.

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Characteristic Impedance-

Using KVL and KCL for a small section of the line and having the limit we arrive at

‘Telegraphers equations’:

When the equations are linked together we derived the wave equation:

The wave equation shows that the currents and voltages on the transmission line satisfy the one

dimensional wave equation.

Therefore since current satisfies the wave equation:

And current and voltage are related by equation (1), so for the general function this gives:

And since the forward waves are independent of the reverse waves we have:

Where

√

Within a constant we have:

√

is equal to the Characteristic impedance of the line.

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Length of Line-

Time Domain:

In the time domain to calculate the length of line = speed of light x wave time from input to output

Length = ( m

Frequency Domain:

To calculate the length of line we first have to find out the wave time by using the equation:

So by using this equation we get the time as:

Now that we know the time we can calculate the length of the line:

Length of line = m

Propagation Velocity-

We know that √

for the velocity of wave propagation. So we can calculate the velocity as

we know :

√

Knowing this we can calculate the transit time of the transmission line.

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Experimental Procedure-

Equipment: Agilent oscilloscope, Adjustable Frequency Signal generator, artificial line apparatus,

Digital Multi-Meter (DMM)

Part 1- Time Domain Measurement:

(a) We set the switches on the artificial line apparatus so that it produces a full element line.

We set the line termination to the open circuit setting and connected the oscilloscope to the

end of the line so we could monitor the output. The source potentiometers were then

adjusted so that the output waveform matched the input meaning there was no reflection.

We then determined the time taken for the step input signal to travel from input to output

and sketched the wave forms and estimated the time taken for reflections to travel back to

the input.

(b) Next with the load still on the open circuit setting and the source potentiometers adjusted

so as to remove any reflections of the output wave we disconnected the output and

connected one channel of the oscilloscope at the first element of the transition line. We

then drew the wave forms at the signal input and at the true input. Then we switched the

setting of the load to short circuit setting and drew the waveforms.

(c) The input signal was disconnected and the source potentiometers were measured using the

DMM.

(d) The input signal was then reconnected and the termination setting was set to variable

resistance (load) and we modified the load resistance till we found the value of termination

resistance which gave the minimum reflection at the input. The resistance was then

measured with the DMM and recorded.

Part 2- Frequency Domain Measurement:

(a) The adjustable frequency signal generator was connected up to the input and the

oscilloscope was also connected in parallel. The signal generator was set to an input signal of

5V pk-pk with 0V d.c. offset.

(b) Then the termination setting of the line was set to open circuit setting and we modified the

frequency to find the lowest frequency at which the line is resonant. Once this value was

found the DMM was used to plot the voltage distribution (pk-pk) along the line by measuring

the voltage at each signal point along the line.

(c) We then switched the termination setting to short circuit and measured the voltage

distribution along the line without changing the frequency already set.

(d) The termination setting was changed to the variable resistance and the resistance was

adjusted so that the voltage distribution at each point along the line was as uniform as

possible. By doing this the variable load resistance should be the same as the characteristic

impedance of the line. This value was then measured by the DMM and recorded.

(e) Finally we switched the setting back to the open circuit setting and recorded as many

resonant frequencies as we could.

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Results-

Part 1- Time Domain Measurement

Time events:

The time taken for the input step signal to go from input to output was . So the time taken for

the reflection to come back to the input is equal to:

Wave Forms:

1) Open Circuit setting- No Reflections

From our pictures we see that the time taken for the wave to travel from input to output in 1) is

approximately 20µs and this would mean that the time for the reflection to return to input should

equal where our reflective wave takes approximately 40µs to return to the input.

2) Signal input and the true input:

When the termination setting is set to open circuit and the reflective wave comes back after 40µs

the true input is the same as the signal input as

Time taken for signal to

travel from input to

output.

Each

interval Signal

Voltage

1) Input

signal

2) Output

signal

Input

signal

True

input

signal

Time taken for reflections

to travel back to the input

Step

Input

Time for Reflected wave

to comes back- 40µs

40µs

Start of

input signal

Start of output

signal

Start of

input signal

Start of true

input signal

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3) Signal Input and True Input- Short Circuit:

With the termination condition set to short circuit we see that the signal input wave is shown as the

reflection at the true input when the wave returns to input after 40µs as when short circuit setting

.

–

In the time domain in part 1 of our experiment we measured the source potentiometer using the

DMM to get the resistance, we then set the termination setting to variable resistance (load) and we

then changed the value of the termination resistance until we got minimum reflection at the input.

Once we got this we took the measurement of the resistance using the DMM.

40µs

Start of

input signal

Start of true

input signal

Time taken for

input signal to be

reflected and return

back to input

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0

2

4

6

8

10

12

0 5 10 15 20 25

Vo

ltag

e p

k-p

k (V

)

Section

Open Circuit Voltage Distribution

Part 2- Frequency Domain Measurement-

Resonant Frequency-

We set the termination setting to open circuit setting and then modified the frequency till we found

the lowest value at which the line is resonant.

Lowest Resonant Frequency- 13.96 kHz

Voltage Distribution (pk-pk) for open circuit at lowest resonant Frequency

Section

Voltage- Open Circuit (V)

0 0.073

1 0.791

2 1.533

3 2.277

4 3.01

5 3.718

6 4.41

7 5.086

8 5.724

9 6.327

10 6.895

11 7.415

12 7.907

13 8.34

14 8.691

15 8.983

16 9.226

17 9.414

18 9.55

19 9.635

20 9.66

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0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 5 10 15 20 25

Vo

ltag

e p

k-p

k (V

)

Section

Short Circuit Voltage Distribution

Voltage Distribution (pk-pk) for Short Circuit at lowest resonant Frequency

Section

Voltage- Short Circuit (V)

0 1.826

1 1.814

2 1.792

3 1.76

4 1.718

5 1.666

6 1.605

7 1.534

8 1.455

9 1.367

10 1.271

11 1.171

12 1.067

13 0.955

14 0.826

15 0.696

16 0.561

17 0.427

18 0.292

19 0.151

20 0.021

Value for for Frequency Domain Measurement

The termination setting was set to variable resistance (load) and the resistance was adjusted so that

the voltage distribution across each section was the same. The value measured was:

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Other Resonant Frequencies

The termination setting was set once again to open circuit setting and we then used the oscilloscope

to see the other resonant frequencies by varying the frequency. From our experiment we saw that it

was quite difficult to see the value all the time as the wave was so small and also the equipment we

used was not sensitive enough to be able to increase the frequency by a small amount once you

reached a high number therefore you are unable to see all the values. However we noticed there

was a pattern and the resonant frequency was linear so the same value increased each time would

give a line that was resonant.

Resonant Frequencies (kHz)

44.3

69.0

98.1

126.5

145.9

172.9

The resonant Frequencies occur at each interval of approximately 27 kHz.

Data Analysis and Discussion-

Part1:

Explanation of waveforms:

1) In part 1 for our First waveform we set the termination condition to open circuit and connected a

signal at the input and had a connection at the output to see the output wave compared to the

input. Once we saw the output wave we modified the value of till we had an output wave that

matched the input so that it had no reflections.

The output wave starts after 20µs as that is the time taken to go from input to output.

The value of remained the same through out the rest of the measurements in part 1.

2) For our second condition the termination setting remained as open circuit. However we

disconnected the channel from the output and connected it to the true input to see the true input

wave form. We see that there is no reflection at the true input. The reason for this can be explained

using the equation for the reflection co-efficient:

When the circuit is set to the open circuit setting the value for is very large, ideally the value for

will be infinite, and the value for is very small, negligible, therefore the value for the reflection

co-efficient so when the signal is multiplied by the reflection co-efficient when the signal

returns to the input we see that the true input signal is almost identical to the input with no

reflection. We also see that the true input wave starts after 40µs as that is the time taken for the

reflection to come back to the input.

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3) For our third condition the termination setting is set to short circuit setting. We see that the true

input is a reflection of the input. This can also be explained using the equation for the reflection co-

efficient.

While in short circuit setting the value for is very small, ideally 0, and therefore making the value

for

= -1. So as the value for the reflection co-efficient the wave we see at the true

input will be multiplied by the value and therefore give us a wave that is a reflection of the input at

the true input. That is why we see a reflection.

Also the reflection wave at the true input begins after 40µs as that is the time it takes for the

reflected wave to come back to the input.

Explanation why

In part 1 when we took measurements of the source resistance we saw that it was not the same

value as the load resistance . The values we got were not the same as there is impedance in the

oscilloscope and in the wires which caused the values not to be the same. Also the reflections

caused by the load resistance are visible on the input signal; where as the reflections caused by the

source resistance are visible on the output signal. This means we can’t match them identically and

therefore there would be a difference between the output and input causing the values of

not to be the same. However the values were not far off each other.

Part 2-

Short circuit like behaviour at resonance-

When the line is resonant the inductance and capacitance are equal so they cancel each other out

causing the circuit to behave as if it was short circuit.

Comparison between resistance values taken in parts 1 and 2

The value we measured for in part 1 is very close to the value for measured in part 2,

but not exact. The value would not be exact because of impedance in the circuit and other losses but

the value from part 2 is very close to the values from part 1.

Part1: Part2:

All the values are quite similar to each other.

Analysis of the length of line

Already in the report I have analysed the length of line by calculating the length of the line in the

time domain and the length of line in the frequency domain.

In the time domain we calculated the length to be 6000m and in the frequency domain we

calculated it to be 5373m.

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We can also use another method to calculate the transit time of the line and also its length. We can

do this by using the propagation velocity. We previously in the report calculated the propagation

velocity to be . We also know that there are 21 sections on the artificial line

that we used, so we can use both these values to calculate the transit time:

So the value we have calculated for the transit time . Using this value we can calculate

the maximum length of the real transmission line the apparatus we used simulated:

m

So the maximum length of line of the real transmission line this apparatus represents is 6450m. This

value is similar to the values calculated in the frequency and time domain.

Why at resonant frequency amplitude of the input goes down to almost zero?

At resonant frequency the amplitude of the input almost goes down to zero as the impedance of the

line is the same and the reflected wave cancels out the input making it almost zero as the reflected

wave has the same magnitude and phase as the forward wave.

Relationship between Resonant Frequencies

The values we got for the resonant frequencies showed a pattern, in the table under other resonant

frequencies, where it increased every 27 kHz approximately. The lowest resonant frequency we

measured was 13.96 kHz. So as the values increased at every 27kHz we saw that the relationship

between the resonant frequencies was that:

So if you follow this pattern you can calculate every resonant frequency of the line.

Conclusion-

After performing this experiment and completing this report I believe this artificial line experiment is

a very helpful and useful experiment in understanding transmission lines in the way they work and

the fundamental concepts about them. This experiment is very important in understanding

transmission lines as it allows you to have a practical experience with them as well as seeing and

being able to understand the different functions and why transmission lines are so important in our

everyday life. Also by performing this experiment it gave me good understanding of transmission

lines and why they work in the way they do.

This experiment shows how the different functions of a transmission line works in open circuit, short

circuit and variable resistance termination setting. Also how the transmission line can work in the

time domain and the frequency domain. It also shows the effects of resonance on the line and how

the line has different resonant frequencies. Furthermore it allowed us to see the different ways we

can determine the length of the line and also how to calculate the propagation velocity. We were

able to see how the equations we have learnt are practically used.

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In conclusion I believe the artificial line experiment is a very good experiment and is fundamental in

being able to understand and to see how a transmission line actually works. Being able to see how it

works is what makes the experiment so useful and helpful in the understanding of transmission

lines.

Reference-

Lab Manual