Page 243 - Analog and Digital Filter Design

240 Analog and Digital Filter Design

equations to find the VS WR are different. Let XI be the reactance of the shunt
arm and X2 be the reactance of the series arm. These reactance values must be
scaled in the same way as described for the type A network.

The real part of the impedance seen looking into the matching network is
given by:

R = sgn
(X1+ 12)' + RL
The imaginary part is now given by:
(X1+ X2) + RL ' I
[
I=sgn XI .(RL2 + X2 .(X1+ X2))

The reflection coefficient, and hence the VSWR, can be found using the same
equations as for the type A network.

VSWR of T Matching Networks
Matching T networks can be broken down into real and imaginary impedance,
looking towards the load. The real impedance is given by:

X22. R,'
R=sgn 1
(X2 + X3)' + RL'
The imaginary impedance is:

[ (X2 + X3)' + RL2
I = sgn XI + (X2. RL2 + X2 .X3.(X2 + X3)) 1

The reflection coefficient, and hence the VSWR, can be found using the same
equations as for the type A network.

VSWR of PI Matching Networks
Matching PI networks can be broken down into real and imaginary impedance,
looking from the source into the load. The real impedance is given by:
[ ((Xl+X2).X3)' +((XI+X2+X3).RL)' 1
X1'.X3'.RL
R=sgn

The imaginary impedance is more complicated to show, because of the number
of terms. I have broken the numerator into two equations, which must be added
together.