Page 191 - Analog and Digital Filter Design

88 Analog and Digital Filter Design

parallel combination of R1 and R2, so adjusting only one will affect more than
just the gain. This can be worked out from the design equations:

The parallel combination of R1 and R2 (R1 I1 R2) is given by:

R1.R2 R3
R1+ R2- 4Q2
R3
If R2 is omitted, R1= -
4Q’.

If the revised gain at the resonant frequency, GRR, is known (it can be calculated
from the formulae previously given in this chapter), in the section “Bandpass
Filter Midband Gain” there are equations for calculating the values of R1
and R2:

R3 R3
Rl=- and R2=
2. GRR 4Q2 - ~GRR’

If the Jilter stage’s center frequency gain Go is less than unity it will not be
possible to scale each stage’s gain using a potential divider network. Instead, the
gain produced by all the filter stages must be added together to find the overall
gain, and then one or two stages should have the gain scaling circuit added. If
all stages have a less than unity gain, a separate gain stage will have to be added
to amplify the signals and give the overall filter a gain of 1.

Denormalizing MFBP Active Filter Designs

In active filter designs, the resistor values used should all be in the range 1 kQ
to 100 kQ where possible. If resistor values are lower than 1 kQ they may load
the op-amp and cause distortion. If resistor values are much higher than
100 kQ there may be problems with noise pickup. High impedance circuits capac-
itively couple with electric fields from other circuits and these can interfere with
the wanted signal. Thermal noise may also cause problems in high impedance
circuits because noise voltage increases in proportion to the resistance.

A MFBP filter stage can be designed using the poles found earlier for a band-
pass filter with a passband from 9rads to 11 radls. The first pair of poles were
found to be CJ = 0.9239 and w = 0.3827.