Page 235 - Analog and Digital Filter Design

232 Analog and Digital Filter Design

The quality of an impedance matching network is described in terms of the
voltage standing wave ratio (VSWR) or in terms of the return loss obtained.
The relationship between VSWR and return loss is simple, since both are related
to the reflection coefficient (p):

Note that the VSWR equation is usually written with the denominator elements
transposed, but this results in a negative number for reflection coefficients less
than unity.

Z-Ro
p=-
Z+Ro

The return loss = 20. log IpI.
Suppose the characteristic impedance R,, is 50 Q and the load is Z = 50 + j30.

50 + j30 - 50 - j30
p=-p=
50+ j30+50 - 100+ j30
30 90 = 0.28735 L 73.3
’= 104.4116.7

Thus the return loss is 20. log 0.28735 = -10.8dB.

1.28735
TheVSWR=-=1.806
0.71265

To find the impedance Z, given the VS WR, use the following equations:

s-l
IPI = -
s+l
l+P
Z=Ro.-
1-P

For example, suppose the circuit has a VSWR of 1.4 in a 50 st system. The reflection
coefficientp=0.4/2.4=0.1667, and theimpedanceZ=50x 1.667/0.8333= 100Q.

Series and Parallel Circuit Relationships
Before discussing the design of an impedance matching network I would like to
review the relationship between series and parallel circuits. In this case I am con-