Homework #1
Microwave I
deadline : 2/8/1391
1. The current on a transmission line is given as i(t)= 1.2cos(1.5×1010t - 80.3z) A .
Determine (a) the frequency,( b) the wavelength(, c) the phase velocity, and (d) the
phasor representation of this current.
2.
Show that the following T-model of a transmission line also yields the telegrapher
equations derived in Section2 .1.
3.
A lossless transmission line of electrical length l=0.3 λ, is terminated with a complex
load impedance as shown below. Find the reflection coefficient at the load. The SWR on
the line. The reflection coefficient at the input of the line, and the input impedance to the
line.
4.
A lossless transmission line is terminated with a 100  load. If the SWR on the line is
1.5, find the two possible values for the characteristic impedance of the line.
5.
A 100  transmission line has an effective dielectric constant of 1.65. Find the
shortest open-circuited length of this line that appears at its input as a capacitor of 5 pF at
2.5 GHz. Repeat for an inductance of 5 nH.
6.
Calculate SWR, reflection coefficient magnitude, and return loss values to complete
the entries in the following table:
7. (optional) Use the Smith chart to find the following quantities for the transmission line
circuit below:
(a) The SWR on the line.
(b) The reflection coefficient at the load.
(c) The load admittance.
(d) The input impedance of the line.
(e) The distance from the load to the first voltage minimum.
(f) The distance from the load to the first voltage maximum.
8. Design a quarter-wave matching transformer to match a 40  load to a 75  line. Plot the
SWR for 0.5 < f /f0 < 2.0, where f0 is the frequency at which the line is ,λ/4 long.
9. Consider the quarter-wave matching transformer circuit shown below. Derive expressions
for V+ and V-, the amplitudes of the forward and reverse travelling waves on the quarterwave line section, in terms of Vi, the incident voltage amplitude.