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

All-Pass Filter Design
16.7.1 First-Order All-Pass Filter
16-44
Figure 16–43 shows a first-order all-pass filter with a gain of +1 at low frequencies and
a gain of –1 at high frequencies. Therefore, the magnitude of the gain is 1, while the phase
changes from 0° to –180°.
V IN
Figure 16–43. First-Order All-Pass
R 1
R 1
R C
The transfer function of the circuit above is:
A(s)
1 RCc·s
1 RCc·s
V OUT
The coefficient comparison with Equation 16–23 (b 1=1), results in:
a i RC·2fc
To design a first-order all-pass, specify f C and C and then solve for R:
R a i
2fc·C
(16–31)
(16–32)
Inserting Equation 16–31 into 16–30 and substituting ωC with Equation 16–27 provides
the maximum group delay of a first-order all-pass filter:
t (16–33)
gr0 2RC
16.7.2 Second-Order All-Pass Filter
Figure 16–44 shows that one possible design for a second-order all-pass filter is to subtract
the output voltage of a second-order band-pass filter from its input voltage.
C
V IN
Figure 16–44. Second-Order All-Pass Filter
R 1
C
R 2
R 3
R
R
V OUT