Page 239 - Analog and Digital Filter Design

236 Analog and Digital Filter Design

Component Values for PI and T Networks
Equations for PI and T networks are similar. However, the angle p is not deter-
mined by the source and load resistance ratio. Instead the designer can define
the angle. In fact, it is possible to match equal resistors with a specified phase
angle between input and output. This is particularly useful if a 90" phase shift
circuit is required (at a fixed fi-equency).

A T network has three components, as shown in Figure 8.8d. There is a series
arm (XI), a shunt arm (m), and another series arm (X3). The values of these
are given by the following equations.

Jm cos p
RS
-
2'1 =
sinp

&!7x-RLcosp
x3 =
sin p

A PI network also has three components, as shown in Figure 8.8~. There is a
shunt arm (Xl), a series arm (X), and another shunt arm (X3). The values of
the elements are given in the following equations.

sin p
XI = RS.RL.
RL.cos~-,/~EZZ

sin p
X1= RS.RL.. 1IRs.RL

sin p
XI = RS.RL.
RS.COS~ -JXL!ZE

Scaling of component values for the desired center frequeiicy uses the
same formula as before and is repeated below. As before, a positive element
value denotes an inductor, while a negative element value indicates that
the component is a capacitor. The magnitude of the element value is then
used in the following equations to find the capacitance or inductance
required.