READ THESE ASSIGNMENT INSTRUCTIONS: Don’t forget the coversheet! All your plots and graphs must have the
proper labels and units. This ALL answers must be provided below the appropriate question. ALL questions must be
shown in your assignment. If you use the simulator to find your answer mention FROM THE SIMULATOR. You receive
-15 points if you do not turn in the assignment at the beginning of the class!
Assignment
A. Starting with equation 2.76 in the text, derive 2.79. You must show all the intermediate steps.
B. In a matching network (using a shun device), formulate the value for input impedance (Zd). Note that
this is input impedance at any location d from the end of the line after we place the shunt device.
What will be the real and imaginary parts of (Zd). Under what condition we achieve a matched
condition.
C. Assume in the test setup below the load has resistance of 100 ohm and inductive reactance of 50 ohm.
The voltage source starts at t=0. Also assume the transmission line has a length of 670 mm and it is
lossless.
a. Calculate the coefficient of reflection.
b. Calculate VSWR.
c. Calculate the normalized load admittance.
d. Calculate the normalized load impedance.
e. Calculate the normalized input impedance.
f. Use Smith Chart to find the coefficient of reflection.
g. Use Smith Chart to find the normalized load admittance.
h. Use Smith Chart to find the normalized input impedance.
i. Use Smith Chart to find the VSWR.
j. Use the simulator in the text to verify your answers (show a snapshot).
k. What is the expression for the instantaneous voltage [V(z,t)]?
l. What is the expression for the instantaneous current?
m. What is the expression for the instantaneous power?
n. Calculate the average incident power (use any method you prefer).
o. Calculate the average reflected power (use any method you prefer).
p. Find the shunt impedance for the circuit in order to have a matched network (use any method
you prefer).
q. Use the voltage diagram to plot transient voltage v(z,t) at the point midway along the length of
line from t=0 to t=10 nsec. Assume the frequency is 1 GHz. Explain what is happening. This
is similar to Figure 2-42 (c) in the textbook.
r. Use the simulator in the text to verify your answer to (q) (show a snapshot).
s. Use Matlab to plot your expression for V(z,t) in part (k) assuming the point of interest is
located at the point midway along the length of line and time is changing between t=[0 - 10
nsec]. Assume the frequency is 1 GHz. Explain what is happening and how this is different
from part (q).
Length of the line= 670 mm
Zo=50 ohm
Wavelength = 200 mm
D- Assume the load is 75-j50 ohm. Use the Smith chart to determine the input impedance of two
transmission lines L1 and L2 with characteristic of impedances of 100 ohm and 50 ohm, respectively.
Assume L2 is connected to the load. Also, assume the length of L1 is 0.375 and the length of L2 is 0.625.
E- HINT: You can use Module 2.6 or 2.8 in CD to find the answer for this problem: Assume a 200 ohm
transmission line is to be matched to a load measured as ZL = (50− j25) ohm by inserting an appropriate
reactance in parallel with the line. If f = 800 MHz and er = 4, determine the location nearest to the load at
which inserting a capacitor can achieve the required matching, and the value of the capacitor.
F- Assume a 25-ohm load is connected to a 75-ohm transmission line. Assume the transmission line is
lossless. We like to place a shunt impedance Z at a distance l from the load to eliminate the reflection.
Determine the values of shunt impedance and l.