"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10

The general transfer function changes to:
A(s)
A 0
1 cRC3 A 0 s (cRC) 2 s 2
The coefficient comparison with Equation 16–2 yields:
a 1 cRC3 A 0
b 1 cRC 2
Given C and solving for R and A 0 results in:
R b 1
2fcC
and
with
A0 3 a1 3
1
b Q
1
Active Filter Design Techniques
Low-Pass Filter Design
A 0 1 R 4
R 3
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.
V IN
R R
Figure 16–18. Adjustable Second-Order Low-Pass Filter
C
C
R 3
R 4
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
V OUT
a1 1.3617 1.4142 1.065
b1 0.618 1 1.9305
Q 0.58 0.71 1.3
R4/R3 0.268 0.568 0.234
16-17