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High-Pass Filter Design
10
A 0
A ∞
|A| — Gain — dB
0
–10
Lowpass
Highpass
–20
–30
0.1 1 10
Frequency — Ω
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
(16–4)
with A ∞ being the passband gain.
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)
16-22