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ECE 166 – Microwave Circuits and Systems
Homework #4– Due Tuesday November 9, 2010
Problem 1:
Plot the loci of S
11
and S
21
on the Smith Chart from DC to very high frequencies for all the time
domain circuits in Problem 2/Hwk2. Do not calculate all the points, just a decent sketch of the loci.
Make sure to label the frequency points that can be easily calculated (0, high f, wo, etc.).
Note that S
21
can be plotted on the Smith Chart just as a vector with a center at (0,0) (ie, the location for
=0). In other words, the S
21
vector tip does not correspond to an impedance, but is just a vector. S
21
can be > 1 in active circuits and therefore, can be outside of the Smith chart.
Problem 2:
Consider the 3port network shown below.
The line impedance is Z
o
.
a)
Calculate the scattering matrix.
Use symmetry and reciprocity to simplify your calculations.
What
is the power dissipated in the network when all ports are matched? You can do the power loss
using the Smatrix and not circuit analysis.
b)
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This note was uploaded on 01/08/2011 for the course ECE 166 taught by Professor Staff during the Fall '08 term at UCSD.
 Fall '08
 staff

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