Page 195 - Analog and Digital Filter Design

1 92 Analog and Digital Filter Design

fo
The frequencies are fR, = - 9.57306 and fR2 = Wfo = 10.34178.
=
w
Consider the pole with fR2 = 10.34178.
Let c = 1pF

Rl‘=Q.R= 82.928kQ.

Note that these values are less than the nominal 100 kQ maximum and greater
than the 1 kC2 minimum, so the value of C is suitable.

GR 2
Hence, GRR = - = 1 .OS32
=
Go 1.8463811
An attenuator is needed to reduce the gain at resonance from 2 to 1.0832. The
following equations use R1’ to determine R1 and R2:

The parallel combination of R1 and R2 equal the value of Rl’. Thus,
although the individual resistance values of R1 and R2 exceed the recom-
mended maximum of 100 kQ, the effective resistance into the op-amp will be
82.928 kQ.

State Variable Bandpass Filters

The state variable design can be used for all-pole responses. It has a lower sen-
sitivity to the op-amp’s gain-bandwidth product limitation, and stage Q factors
of up to 200 are possible. It does, however, need three op-amps, as shown in
Figure 6.13.