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

High-Pass Filter Design
16-24
To dimension the circuit, specify the corner frequency (f C), the dc gain (A ∞), and capacitor
(C 1), and then solve for R 1 and R 2:
R 1
1
2fca 1 C 1
R2 R (A 3 1) and
R2 R1 A
16.4.2 Second-Order High-Pass Filter
High-pass filters use the same two topologies as the low-pass filters: Sallen-Key and Multiple
Feedback. The only difference is that the positions of the resistors and the capacitors
have changed.
16.4.2.1 Sallen-Key Topology
The general Sallen-Key topology in Figure 16–27 allows for separate gain setting via
A 0 = 1+R 4/R 3.
Figure 16–27. General Sallen-Key High-Pass Filter
A(s)
V IN
The transfer function of the circuit in Figure 16–27 is:
1 R 2 C 1 C 2 R 1 C 2 (1)
cR 1 R 2 C 1 C 2
· 1 s
C 1
C 2
R 1
R 2
1
c 2 ·
R1R2C1C 2
1
s2 R 3
R 4
with
V OUT
1 R 4
R 3
The unity-gain topology in Figure 16–28 is usually applied in low-Q filters with high gain
accuracy.
V IN
C C
Figure 16–28. Unity-Gain Sallen-Key High-Pass Filter
R 1
R 2
V OUT