Page 189 - Analog and Digital Filter Design

1 86 Analog and Digital Filter Design

there will be an equal number of stages resonant above and below the center
frequency. In the example frequency response, illustrated by the graph in Figure
6.10, fR is belowfo.
The gain of the filter at its center frequency can be found from the following
equation, which also requires the stage’s Q to be known. The terms fR and
Q can be found from the bandpass pole positions and using the relationship
GR = 2Q’. The bandpass filter center frequency, fo, is found from the filter’s
specification.

GR 2Q’
, which simplifies to Go =
fR fo

This equation gives the midband gain of the stage being designed. Suppose
the bandpass filter design is required to have unity gain in the passband. The
simplest way to do this is to have unity gain at the passband center frequency
GR
(fo) in each stage, then GRR = -. Suppose that Go = 10 and GR = 15. Since I
GO
want a center frequency gain of 1, not 10, the revised gain at resonance, GRR,
has to be scaled to be a tenth of GR. In this case, GRR = G, = Is = 1.5. This
Go 10
means that the stage will need a potential divider, usually at its input, to reduce
the “natural” gain of the stage from 15 to 1.5.

- -
GR
16
14

12
10
C .-
(Is 8
Q
6
4
2

0
Figure 6.10 f R
Gain versus Frequency Frequency
for a Single Stage