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All-Pass Filter Design
0
|A| — Gain — dB
–5
–10
Q = 10
Q = 1
Q = 0.25
–15
–20
1 10 100 1 k 10 k
Frequency — Ω
Figure 16–41.
Comparison of Q Between Passive and Active Band-Rejection Filters
16.7 All-Pass Filter Design
In comparison to the previously discussed filters, an all-pass filter has a constant gain
across the entire frequency range, and a phase response that changes linearly with frequency.
Because of these properties, all-pass filters are used in phase compensation and signal
delay circuits.
Similar to the low-pass filters, all-pass circuits of higher order consist of cascaded first-order
and second-order all-pass stages. To develop the all-pass transfer function from a
low-pass response, replace A 0 with the conjugate complex denominator.
The general transfer function of an allpass is then:
i 1 ai s b i
s 2
A(s)
i 1 ai s b i
s 2
(16–23)
with a i and b i being the coefficients of a partial filter. The all-pass coefficients are listed in
Table 16–10 of Section 16.9.
Expressing Equation 16–23 in magnitude and phase yields:
Active Filter Design Techniques
16-41