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

High-Pass Filter Design
16-22
|A| — Gain — dB
10
0
–10
–20
A0
A∞
Lowpass Highpass
–30
0.1 1
Frequency — Ω
10
Figure 16–24. Developing The Gain Response of a High-Pass Filter
The general transfer function of a high-pass filter is then:
A(s)
A
i 1 a i
s b i
s 2
with A ∞ being the passband gain.
(16–4)
Since Equation 16–4 represents a cascade of second-order high-pass filters, the transfer
function of a single stage is:
A i (s)
A
1 a i
s b i
s 2
(16–5)
With b=0 for all first-order filters, the transfer function of a first-order filter simplifies to:
A(s) A 0
1 a i
s
(16–6)