ECEn 360 Lab 3: Transmission Line Model Using Matlab or Python
1/3/24
I began this lab by testing out the Matlab code provided in the lab procedure. I went
through and added comments to the code to describe what each of the major lines of
code was doing. These comments can be seen in the figure below.
Figure 1. Given Matlab code with added descriptive comments.
After running the model, I was given an animated graph that resembled the figure
below.
Figure 2. Graph of several voltages relative to time and position.
The solid lines in the above figure show the forward and reverse-moving wave voltages.
The blue solid line is the forward wave voltage and the orange solid line is the reverse
wave voltage. The dashed yellow line is the total voltage wave, which is the combination
of the forward and reverse-moving waves. The purple dashed line is the standing wave
voltage.
The load at the end of the transmission line is an open, which can be inferred from the
fact that the reflection coefficient is 1. This can also be seen in the waves in the graph
because the forward-traveling waves are of the same amplitude as the reverse waves.
Without knowing anything about the load, you could determine what the load was from
the plot of these curves. The VSW plot tells us that the reflection coefficient is a positive
value because it is at a peak at 0. It also tells us that the reflection coefficient must only
have a real part because it is not shifted off of a max/min value, so it must be either 1 or
-1. Using this information it can be deduced that the reflection coefficient is 1 and the
load is an open.
Next, I plotted the voltages after changing the reflection coefficient to the following
values: 0, 0.1, 1, -1, .707+j.707. The resulting plots are shown in the figures below.
Figure 3. Graph of several voltages with a reflection coefficient of 0
Figure 4. Graph of several voltages with a reflection coefficient of 0.1
Figure 5. Graph of several voltages with a reflection coefficient of 1
Figure 6. Graph of several voltages with a reflection coefficient of -1
Figure 7. Graph of several voltages with a reflection coefficient of .707+j.707
Each reflection coefficient used in the above examples corresponds to a different load
impedance. The first example corresponds to a load impedance that is equal to the
characteristic impedance of the transmission line. The second example corresponds to
a load impedance that is slightly larger than the characteristic impedance. The third
example corresponds to a load impedance of infinity or an open circuit. The fourth
example corresponds to a load impedance of 0 or a short circuit. The fifth example has
a reflection coefficient with a magnitude of 1, but it also has a phase shift. This leads me
to think that the load impedance corresponds to a purely capacitive or inductive load.
I then adjusted the loss coefficient in the model to be nonzero. I observed that the
forward wave decreased in amplitude as it moved towards the load. Then, the reverse
traveling wave’s amplitude started at the minimum amplitude of the forward wave but
continued to decrease as it traveled away from the load. The standing wave increased
in amplitude as you got closer to the load because this is where the amplitudes of the
forward and reverse travelling waves were the closest in value and could cause the
greatest fluctuation in the total voltage of the wave.
Figure 8. Graph of several voltages with a reflection coefficient of 1 and a loss
coefficient of 0.5.
I then returned the loss coefficient to a value of 0 and changed the reflection coefficient
to a value greater than 1. As shown in the figure below, this resulted in a reverse
voltage with an amplitude greater than the forward-traveling wave. The amplitude of the
standing wave voltage and the total wave voltage also increased. This reflection
coefficient represents having a generator or some other power source at the load that
amplifies the reverse wave.
Figure 9. Graph of several voltages with a reflection coefficient of 2.
I then returned the reflection coefficient to 1 and adjusted the wavelength of the signal
to see how that would impact the signal. I found that it increased the number of
oscillations within a period of time, but it did not change the amplitude or phase of the
signal. After some contemplation, I came to the conclusion that this came as a result of
the fact that the reflection coefficient remained constant. This meant that the relative
size of the characteristic impedance and the load impedance remained the same. In a
real circuit, however, I would expect there to be different results because the change in
wavelength would change how the signal was propagated along the transmission line.
Figure 10. Graph of several voltages with a reflection coefficient of 1 and a wavelength
1/6 of the transmission line length.
Conclusion
From this lab, I have learned how a signal along a transmission line can be affected by
several factors including the characteristics of the load and the transmission line itself. I
have also learned how to model a transmission line signal in Matlab. My intuition about
the effect of wavelength on the overall model was incorrect, but I was able to reach a
clear conclusion about why, having made some assumptions that were incorrect.