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

|A| — Gain — dB
10
0
–10
–20
–30
–40
–50
Butterworth
Tschebyscheff
–60
0.1 1
Frequency — Ω
10
Fundamentals of Low-Pass Filters
Bessel
Figure 16–9. Comparison of Gain Responses of Fourth-Order Low-Pass Filters
16.2.4 Quality Factor Q
The quality factor Q is an equivalent design parameter to the filter order n. Instead of designing
an n th order Tschebyscheff low-pass, the problem can be expressed as designing
a Tschebyscheff low-pass filter with a certain Q.
For band-pass filters, Q is defined as the ratio of the mid frequency, f m, to the bandwidth
at the two –3 dB points:
Q
fm
(f 2 f 1 )
For low-pass and high-pass filters, Q represents the pole quality and is defined as:
Q bi
ai High Qs can be graphically presented as the distance between the 0-dB line and the peak
point of the filter’s gain response. An example is given in Figure 16–10, which shows a
tenth-order Tschebyscheff low-pass filter and its five partial filters with their individual Qs.
Active Filter Design Techniques
16-9