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Fundamentals of Low-Pass Filters
16.2.2 Tschebyscheff Low-Pass Filters
The Tschebyscheff low-pass filters provide an even higher gain rolloff above f C . However,
as Figure 16–6 shows, the passband gain is not monotone, but contains ripples of
constant magnitude instead. For a given filter order, the higher the passband ripples, the
higher the filter’s rolloff.
10
0
|A| — Gain — dB
–10
–20
–30
–40
–50
9th Order
2nd Order
4th Order
–60
0.01 0.1 1 10
Frequency — Ω
100
Figure 16–6. Gain Responses of Tschebyscheff Low-Pass Filters
With increasing filter order, the influence of the ripple magnitude on the filter rolloff diminishes.
Each ripple accounts for one second-order filter stage. Filters with even order numbers
generate ripples above the 0-dB line, while filters with odd order numbers create ripples
below 0 dB.
Tschebyscheff filters are often used in filter banks, where the frequency content of a signal
is of more importance than a constant amplification.
16.2.3 Bessel Low-Pass Filters
The Bessel low-pass filters have a linear phase response (Figure 16–7) over a wide frequency
range, which results in a constant group delay (Figure 16–8) in that frequency
range. Bessel low-pass filters, therefore, provide an optimum square-wave transmission
behavior. However, the passband gain of a Bessel low-pass filter is not as flat as that of
the Butterworth low-pass, and the transition from passband to stopband is by far not as
sharp as that of a Tschebyscheff low-pass filter (Figure 16–9).
Active Filter Design Techniques
16-7