EE361
Instructor:
Evan Goldstein
Assignment: 1
Due:
0800 Monday 5 May, 2014
Do this assignment on your own. You are free to discuss the lectures and reading and general approaches to problems with other students.
But you are expected to turn in work that you have done yourself, without checking answers with others. To receive full credit, the answers
must be correct and clear, and it must be apparent how you arrived at them.
1.
Suppose you know a cable’s characteristic impedance Z0, both its magnitude and its phase. But you don’t
know the voltage or current propagating on it.
a. State clearly and precisely what Z0 tells you about the magnitude and phase of the voltage and
current on the line.
b. If Im(Z0) is nonzero, what do you know about the voltage and the current on the line?
c. If Im(Z0) is nonzero, what do you know about the loss properties of the line?
d. In this case, where does the lost propagating electrical energy go?
2.
A given cable has characteristic impedance Z0 = 50 Ohms. At a given position on the line, the total voltage
amplitude is 1 V. State clearly what if anything you know about the total current on the line.
3.
A given cable has characteristic impedance Z0 = 100 Ohms. At a given position on the line, the voltage
amplitude is 1 V.
a.
b.
4.
Draw a sketch (a snapshot at a fixed time) of the forward-traveling voltage and current waves on
the line, showing their amplitudes and phases.
Draw a sketch of the backward-traveling voltage and current waves on the line, showing their
amplitudes and phases.

The meaning of Vo .

a.
What exactly is the meaning—the physical meaning—of the quantity Vo , which has been so
b.
prominent from almost the very start in our discussion of transmission lines?
If you wanted to measure this quantity for a given line, what exactly would you measure and
where would you do it?
c.
Does Vo depend on the load impedance that’s attached to the line? Explain why or why not.
d.
To measure Vo , would you need to turn on the voltage generator? Why or why not?


5. The basic logic thus far.
The point of this problem is to make clear the logic of the subject thus far. As you’ll see in a
moment, there are some pretty important subtleties once you think about it.
a. We proved that voltages and currents on wires travel as waves. We did this by
considering TEM wires and assuming that such wires obey two general laws. What
are those two laws?
b. The result: Waves!
So here’s a transmitter and receiver connected together by a TEM wire whose length
is ¼ of the system’s operating wavelength. It’s a sinusoidal steady-state system.
+
v(z,t)
-
i(z,t)
z
For simplicity (it really doesn’t matter) let the receiver be impedance-matched to the
wire so that there’s no reflected voltage or current wave, and let the wire be lossless.
Draw the above system figure on your page. Then on two separate space axes below
the figure, draw snapshots of the voltage v(z,t’) and current i(z,t’) at an instant t’
when the transmitter voltage is going through a maximum.
c. KVL as applied in circuit theory says that the sum of the voltage drops around any
loop is zero and that the voltage drop along any lossless wire is zero. What does this
imply about the relationship between the transmitter voltage and receiver voltage? Is
this assertion true for the circuit above?
d. KCL as applied in circuit theory says that the net current flow out of any region is
zero and in particular that the current flowing into any wire equals the current
flowing out of it. Is this true for the circuit above?
e. Wait.
Then we have a major problem. We assumed KVL and KCL. From them, we
derived that KVL and KCL are false. What?? Can you explain how the thinking
here is actually sound?
Try this. Redraw the circuit and waveforms of part (b) for a very short system that’s
only, say, 1/100 of an operating wavelength in length. Here it is.
z
f. How are KVL and KCL looking now, for this very short system?
g. Recall that in deriving the Telegraphers’ Equations (and waves) from KVL and KCL,
we took limits as the length of the system z goes to zero. So we were actually
making assumptions about ‘point’ systems—systems in the limit of arbitrarily small
size (Are such assumptions true in this limit?) And we were drawing inferences for
spatially extended systems. In view of this, explain how the logic we’ve employed is
sound. As I said, there are subtleties here—important ones.
6. Consider a lossless wire that’s air-filled and 3-meters long. It has a characteristic impedance
of 100 Ohms. The forward-traveling voltage wave has a zero-to-peak amplitude of 1V and a
frequency of 1 GHz.
Draw a snapshot of the forward-traveling voltage wave on the line at some fixed time t’.
a. Draw a similar snapshot of the forward-traveling current wave at t’, showing the
amplitude and the phase relationship of the current wave and the voltage wave.
b. On your sketch of the current wave, show with arrows at various positions the actual
direction of motion of positive mobile charge at time t’.
c. On the horizontal axis of the current-wave sketch, show the positions at which
positive charge is bunching up. What tells you that it’s bunching up?
d. Using the 
i
Telegrapher’s Equation for line current, show why, in the lossless
z
case, line voltage and current must be in-phase.
e. What basic distributed feature of the line is this equation describing? Explain.
f.
Using the 
v
Telegrapher’s Equation for line voltage, show why, in the lossless
z
case, line voltage and current must be in-phase.
g. What basic distributed feature of the line is this equation describing?
h. Does KCL hold for circuits that use this line as a wire? Explain.
i. Does KVL hold for circuits that use this line as a wire? Explain.
Suppose now that the line’s operating frequency is reduced to 1 kHz, keeping all other
parameters the same.
j. Draw a snapshot of the forward-traveling voltage and current waves on the line now.
k. Does KCL approximately hold for circuits that use the line as a wire?
l. Does KVL approximately hold?
7. We’ve so far learned one colossally large thing: voltages and currents on wires travel as
waves.
a. Exactly what does this statement mean? (Be precise, in 1-2 sentences.)
b. In 3-4 clear English sentences (no math) how do we know this is true?
c. Contrast this result with circuit theory. How, according to circuit theory, do voltages
and currents travel on wires?