Page 242 - Analog and Digital Filter Design

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Impedance Matching Networks

X' = Lr.b, ifx is positive.
.fc

X'=X.- JC , if x is negative.
f-i5C,,R
Thus, if the frequency at which the VSWR value is required is greater than
the center frequency, the capacitive reactance is reduced while the inductive
reactance is increased.

Next, find the impedance looking into the matching network. This is a combi-
nation of series and parallel impedance, containing real and imaginaiy parts.
The real part is given by:

The imaginary part is given by:

spz(X2.R;)
1 = sgn(X1) - . where sgn(x) means the magnitude of x.
(X2)' + R?

Signum(x), or sgn(s), actually denotes that if x is negative, the value of .Y is mul-
tiplied by -1 (which is really the same thing as saying 'Take the magnitude of s").

The reflection coefficient can now be found:

Now F'SLt'R is simply given by:

The VSWR equals I for a perfect match, but in the real world it is invariably
greater.

VSWR of L Matching Network (Type B)
The series and parallel arms are in the opposite order for a type €3 network;
that is, the shunt arm is across the source instead of the load. Therefore the