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Band-Pass Filter Design
In accordance with Equations 16–14 and 16–15, the mid frequencies for the partial filters
are:
f mi
10 kHz
1.036 9.653 kHz and f m2
10 kHz·1.036 10.36 kHz
The overall Q is defined as Q f m B , and for this example results in Q = 10.
Using Equation 16–16, the Q i of both filters is:
Q i
10· 1 1.036 2 ·1
1.036·1.4142 14.15
With Equation 16–17, the passband gain of the partial filters at f m1 and f m2 calculates to:
A mi
14.15
10 · 1 1.415
1
The Equations 16–16 and 16–17 show that Q i and A mi of the partial filters need to be independently
adjusted. The only circuit that accomplishes this task is the MFB band-pass filter
in Paragraph 16.5.1.2.
To design the individual second-order band-pass filters, specify C = 10 nF, and insert the
previously determined quantities for the partial filters into the resistor equations of the
MFB band-pass filter. The resistor values for both partial filters are calculated below.
Filter 1: Filter 2:
R 21
Q i
f m1 C 14.15
·9.653 kHz·10 nF 46.7 k R 22 Q i
f m2 C 14.15
43.5 k
·10.36 kHz·10 nF
R 11 R 21
2A mi
R 31 A miR 11
2Q i 2 A mi
46.7 k
2· 1.415 16.5 k R 12 R 22
2A mi
1.415·16.5 k
2·14.15 2 1.415 58.1 R 32 A miR 12
2Q 2 i A mi
43.5 k
15.4 k
2· 1.415
1.415·15.4 k
2·14.15 2 1.415 54.2
Figure 16–35 compares the gain response of a fourth-order Butterworth band-pass filter
with Q = 1 and its partial filters to the fourth-order gain of Example 16–4 with Q = 10.
Active Filter Design Techniques
16-35