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

Active Filter Design Techniques
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
cR1C · 1 s
1
c 2R1R2C The coefficient comparison between this transfer function and Equation 16–5 yields:
A 1
a 1 2
cR 1 C
b 1
1
c 2 R 1 R 2 C 2
s 2
2 · 1
Given C, the resistor values for R 1 and R 2 are calculated through:
R 1 1
R 2
fcCa1 a1 4fcCb1 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.
V IN
C 1 =C
C 2
C 3 =C
Figure 16–29. Second-Order MFB High-Pass Filter
The transfer function of the circuit in Figure 16–29 is:
A(s)
R 2
R 1
C
C2 1 2CC2 · cR1CC2 1 s 2CC2 · cR1CC2 1
s2 V OUT
16-25