Page 241 - Analog and Digital Filter Design

238 Analog and Digital Filter Design

also, that component values of a load are lOpF in parallel with 75Q. The shunt
capacitor of the load can be considered as part of the matching network, since
it is in parallel with the shunt capacitor of the impedance matching circuit. Thus
replacing the lOOpF shunt capacitor by one with a value of 90pF (100pF - 10pF)
enables the circuit to be matched with a simple L network. Similar arrangements
can be considered for PI matching networks.

Where the load is an inductor in series with a resistor, an L matching network
of type B could be used to give parasitic absorption, provided that the load
inductance is less than the matching network inductance. This L network has a
series inductor between the source and load, and its value can be reduced by an
amount equal to the load inductance. Thus a load of 25 Q in series with a 1 nH
would be matched as though it were purely resistive. Then once the series induc-
tor has been found for the matching network its value can be reduced by 1 nH.
A similar technique can be used with T matching networks.

Simple Networks and VSWR
Matching networks of type L, PI, and Tare intended to match resistive imped-
ance at a single frequency. At the design frequency, the VSWR is equal to unity
(the reflection coefficient is zero, in other words). However, I have already shown
that it is possible to absorb reactive loads into the network design. It is also pos-
sible to match impedance over a band of frequencies if there is a limit of accept-
able VSWR (or reflection coefficient).

The VSWR and bandwidth are related to the matching impedance ratio. For
example, consider matching to a 50Q source and limiting the VSWX to 1.1. The
frequency range over which matching is achieved for a lOOQ load is 6%. If the
matching network is redesigned for a load of 200Q the frequency range is
reduced 3%. The matching network used in the above example was an L type
A, designed for a center frequency of 100MHz.

VSWR of L Matching Network (Type A)
The VSWR of an L matching network, of type A, can be calculated from the
reactance of the series and shunt arms. Let X1 be the reactance of the series
arm connected between the source and load, and let X2 be the reactance of the
shunt arm across the load; the values given at the center frequency. At fre-
quencies above or below this center frequency the values of these reactances will
be different, depending on whether the reactance is positive (inductance) or
negative (capacitance). The reactance values of Xl and X2 must be scaled in
proportion to the frequency ratio: