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

16.8.4 Op Amp Selection
Active Filter Design Techniques
Practical Design Hints
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 PEAK
A 0
0
A OL
40 dB‘
Figure 16–53. Open-Loop Gain (A OL) and Filter Response (A)
f P
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:
fT 100·Gain·fc
2) Second-order filter (Q < 1):
f T 100·Gain·fc·k i
with
3) Second-order filter (Q > 1):
fT 100·Gain· fc
2
Qi 0.5
ai 2
Qi 0.25
f T
f / Hz
k i f ci
fc
For example, a fifth-order, 10-kHz, Tschebyscheff low-pass filter with 3-dB passband ripple
and a dc gain of A0 = 2 has its worst case Q in the third filter section. With Q3 = 8.82
and a3 = 0.1172, the op amp needs to have a unity-gain bandwidth of:
fT 100·2·
10 kHz 8.82
0.1172
2 0.5
8.822 17 MHz
0.25
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:
16-53