Page 194 - Analog and Digital Filter Design

Bandpass Filters 1 9 1
-

required, R2 must be in circuit. Resistors R1 and R2 form a potential divider,
and their parallel resistance replaces R1' in the equations given. The following
equations use R1' to determine R1 and R2:

2. R1'
R1=-
GRR
2. R1'
R2=- (condition: GRR < 2)
~-GRR
GR
The revised gain at resonance GRR can be found from the equation GRR = -.
Go
In the DABP case the resonant frequency gain is always equal to 2, by default
due to internal feedback. Hence GR = 2 and this can be used to find Go, given
the overall filter center frequencyf, and the pole characteristicsf, and Q.

Because the gain of each DABP stage at resonance is equal to 2, the gain at the
filter center frequency may be less than unity. In this case, a separate amplifier
stage may be needed if a unity gain bandpass filter is required.

This circuit has independent adjustment of resonant frequency and Q" The
parallel combination of Rl and R2 adjust the Q at resonance. Resistor R3
determines the resonant frequency.

Denormalizing DABP Active Filter Designs

As discussed earlier in this chapter, the resistor values used should all be in
the range 1 kQ to IOOkQ where possible. This will prevent overloading of the
op-amp's output and reduce noise pickup.

Consider a DABP filter stage design that uses the poles found earlier in this
chapter for a bandpass filter with a passband from 9 rad/s to 11 rad/s. The first
pair of poles were found to be (r= 0.9239 and m = 0.3827.

From before, Q =
W = Qm + 4- = 1.039375