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Practical Design Hints
16.8.4 Op Amp Selection
The most important op amp parameter for proper filter functionality is the unity-gain bandwidth.
In general, the open-loop gain (A OL ) should be 100 times (40 dB above) the peak
gain (Q) of a filter section to allow a maximum gain error of 1%.
|A| [dB]
A OL
A PEAK
40 dB‘
A
A 0
0
f P
f T
f / Hz
Figure 16–53.
Open-Loop Gain (A OL ) and Filter Response (A)
The following equations are good rules of thumb to determine the necessary unity-gain
bandwidth of an op amp for an individual filter section.
1) First-order filter:
f T
100·Gain·f c
2) Second-order filter (Q < 1):
f T
100·Gain·f c·k i
with
k i
f ci
f c
3) Second-order filter (Q > 1):
f T
100·Gain· fc
2
Q i 0.5
ai 2 Qi 0.25
For example, a fifth-order, 10-kHz, Tschebyscheff low-pass filter with 3-dB passband ripple
and a dc gain of A 0 = 2 has its worst case Q in the third filter section. With Q 3 = 8.82
and a 3 = 0.1172, the op amp needs to have a unity-gain bandwidth of:
f T
100·2· 10 kHz
0.1172
8.82 2 0.5
8.82 2 0.25
17 MHz
In comparison, a fifth-order unity-gain, 10-kHz, Butterworth low-pass filter has a worst
case Q of Q 3 = 1.62; a 3 = 0.618. Due to the lower Q value, f T is also lower and calculates
to only:
Active Filter Design Techniques
16-53