1
ECE 166 – Microwave Circuits
Homework #1 – Due Thursday, October 8, 2009
(This problem is to show you how the voltage and impedance change along the line. You need a plotting
routine, MATLAB, Excel, etc. to plot the voltages vs. the zaxis, etc.).
Problem 1:
Consider a load with
Γ
=0.6 (+90deg) and f = 3 GHz in an FR4 medium with
ε
eff
=4.0 and Z
0
=
50
Ω
. The forward wave is V
o
+
=1 V(rms) defined
at the load (z=0)
.
a)
Determine the wavelength of the transmission medium.
b)
Determine the load impedance in Ohms.
c)
Determine the total voltage at the load (complex number). This is V
load
and is
not
V
o
+
.
d)
Find the location of the voltage and current maximum, and the voltage and current minimum on the
line. Determine their amplitudes. Calculate the VSWR. Use the Crank diagram for your solution.
e)
Calculate the forward power (P+), the backward power (P) and the power dissipated in the load.
f)
Determine the voltage, current and impedance at z = 0, 0.05
λ
, 0.1
λ
, 0.15
λ
, 0.2
λ
, 0.25
λ
, 0.3
λ
from the load. You can use the impedance equation on page 5. See how much the impedance changes
vs. position!
g)
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 Fall '10
 CS
 Impedance, Volt, Input impedance, Transmission line, Impedance matching, Electrical parameters

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