C ALIFORNIA S TATE U NIVERSITY, BAKERSFIELD (CSUB)
D EPARTMENT OF E LECTRICAL & C OMPUTER E NGINEERING & C OMPUTER S CIENCE
ECE 332: F IELDS AND WAVES
Homework 5
Solution
QUESTION 1:(20 POINTS)
At an operating frequency of 300 MHz, it is desired to use a section of a lossless 50 Ω transmission line terminated
in a short circuit to construct an equivalent load with reactance X = 40 Ω. If the phase velocity of the line is
0.75c, what is the shortest possible line length that would exhibit the desired reactance at its input?
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QUESTION 2:(20 POINTS)
A 50 Ω lossless line of length ` = 0.375λ connects a 300-MHz generator with Ṽg = 300 V and Zg = 50 Ω to a
load ZL . Determine the time-domain current through the load for:
a) ZL = (50 − j50) Ω
b) ZL = 50 Ω
c) ZL = 0 (short circuit)
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QUESTION 3:(20 POINTS)
Use the Smith chart to find the reflection coefficient corresponding to a load impedance of
a) ZL = 3Z0
b) ZL = (2 − j2)Z0
c) ZL = −j2Z0
d) ZL = 0 (short circuit)
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QUESTION 4:(20 POINTS)
A lossless 50 Ω transmission line is terminated in a load with ZL = (50 + j25) Ω. Use the Smith chart to find the
following:
a) The reflection coefficient Γ.
b) The standing-wave ratio.
c) The input impedance at 0.35λ from the load.
d) The input admittance at 0.35λ from the load.
e) The shortest line length for which the input impedance is purely resistive.
f) The position of the first voltage maximum from the load.
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QUESTION 5:(20 POINTS)
A 200 Ω transmission line is to be matched to a computer terminal with ZL = (50 − j25) Ω by inserting an
appropriate reactance in parallel with the line. If f = 800 MHz and εr = 4, determine the location nearest to the
load at which inserting:
a) A capacitor can achieve the required matching, and the value of the capacitor.
b) An inductor can achieve the required matching, and the value of the inductor.
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