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Low-Pass Filter Design
The general transfer function changes to:
A(s)
A 0
1 c RC 3 A0 s (c RC) 2 s 2 A 0
1 R 4
with
R 3
The coefficient comparison with Equation 16–2 yields:
a 1
c RC 3 A0
b 1
c RC 2
Given C and solving for R and A 0 results in:
R b 1
2f c C
and
A 0
3 a 1
b 3 1 Q
1
Thus, A 0 depends solely on the pole quality Q and vice versa; Q, and with it the filter type,
is determined by the gain setting of A 0 :
Q 1
3 A 0
The circuit in Figure 16–18 allows the filter type to be changed through the various resistor
ratios R 4 /R 3 .
C
V IN
R
R
C
V OUT
R 3
R 4
Figure 16–18.
Adjustable Second-Order Low-Pass Filter
Table 16–1 lists the coefficients of a second-order filter for each filter type and gives the
resistor ratios that adjust the Q.
Table 16–1.
Second-Order FIlter Coefficients
SECOND-ORDER BESSEL BUTTERWORTH 3-dB TSCHEBYSCHEFF
a 1 1.3617 1.4142 1.065
b 1 0.618 1 1.9305
Q 0.58 0.71 1.3
R 4 /R 3 0.268 0.568 0.234
Active Filter Design Techniques
16-17