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High-Pass Filter Design
To simplify the circuit design, it is common to choose unity-gain (α = 1), and C 1 = C 2 = C.
The transfer function of the circuit in Figure 16–28 then simplifies to:
A(s)
1
1 2
c R 1 C · 1s 1 · 1
2 c R 1 R 2 C 2 s 2
The coefficient comparison between this transfer function and Equation 16–5 yields:
A 1
a 1
2
c R 1
C
b 1
1
2 c R 1
R 2
C 2
Given C, the resistor values for R 1 and R 2 are calculated through:
R 1
1
f c Ca 1
R 2
a 1
4f c Cb 1
16.4.2.2 Multiple Feedback Topology
The MFB topology is commonly used in filters that have high Qs and require a high gain.
To simplify the computation of the circuit, capacitors C 1 and C 3 assume the same value
(C 1 = C 3 = C) as shown in Figure 16–29.
C 2
V IN
C 1
=C
C 3
=C
R 2
R 1
V OUT
Figure 16–29.
Second-Order MFB High-Pass Filter
The transfer function of the circuit in Figure 16–29 is:
C C 2
A(s)
1 2C 2 C
c R 1 C 2 C · 1s 1
· 1
c 2R
2 R 1 C 2 C s 2
Active Filter Design Techniques
16-25