LS404
6/11
APPLICATION INFORMATION: Active low-pass filter
BUTTERWORTH
The Butterworth is a "maximally flat" amplitude re-
sponse filter (figure 10) Butterworth filters are
used for filtering signals in data acquisition sys-
tems to prevent aliasing errors in samples-data
applications and for general purpose low-pass fil-
tering.
The cut-off frequency Fc, is the frequency at which
the amplitude response is down 3dB. The attenu-
ation rate beyond the cutoff frequency is n6 dB per
octave of frequency where n is the order (number
of poles) of the filter.
Other characteristics :
❑ Flattest possible amplitude response
❑ Excellent gain accuracy at low frequency
end of passband
BESSEL
The Bessel is a type of “linear phase” filter. Be-
cause of their linear phase characteristics, these
filters approximate a constant time delay over a
limited frequency range. Bessel filters pass tran-
sient waveforms with a minimum of distortion.
They are also used to provide time delays for low
pass filtering of modulated waveforms and as a
“running average” type filter.
The maximum phase shift is radians where
n is the order (number of poles) of the filter. The
cut-off frequency fc, is defined as the frequency at
which the phase shift is one half of this value.
For accurate delay, the cut-off frequency should
be twice the maximum signal frequency.
The following table can be used to obtain the -3dB
frequency of the filter.
Other characteristics :
❑ Selectivity not as great as Chebyschev or
Butterworth
❑ Very little overshoot response to step inputs
❑ Fast rise time
CHEBYSCHEV
Chebyschev filters have greater selectivity than ei-
ther Bessel ro Butterworth at the expense of ripple
in the passband (figure 11).
Chebyschev filters are normally designed with
peak-to-peak ripple values from 0.2dB to 2dB.
Increased ripple in the passband allows increased
attenuation above the cut-off frequency.
The cut-off frequency is defined as the frequency
at which the amplitude response passes through
the specificed maximum ripple band and enters
the stop band.
Other characteristics :
❑ Greater selectivity
❑ Very non-linear phase response
❑ High overshoot response to step inputs
The table below shows the typical overshoot and setting time response of the low pass filters to a step
input.
Design of 2nd order active low pass filter (Sallen and Key configuration unity gain op-amp)
n
π–
2
-----------
2 Pole 4 Pole 6 Pole 8 Pole
-3dB Frequency 0.77fc 0.67fc 0.57fc 0.50fc
Number of Poles
Peak
Overshoot
Settling Time (% of final value)
% Overshoot ±1% ±0.1% ±0.01%
Butterworth
2
4
6
8
4
11
14
14
1.1Fc sec.
1.7/fc
2.4/fc
3.1/fc
1.7Fc sec.
2.8/fc
3.9S/fc
5.1/fc
1.9Fc sec.
3.8/fc
5.0S/fc
7.1/fc
Bessel
2
4
6
8
0.4
0.8
0.6
0.1
0.8/fc
1.0/fc
1.3/fc
1.6/fc
1.4/fc
1.8/fc
2.1/fc
2.3/fc
1.7/fc
2.4/fc
2.7/fc
3.2/fc
Chebyschev (ripple ±0.25dB)
2
4
6
8
11
18
21
23
1.1/fc
3.0/fc
5.9/fc
8.4/fc
1.6/fc
5.4/fc
10.4/fc
16.4/fc
-
-
-
-
Chebyschev (ripple ±1dB)
2
4
6
8
21
28
32
34
1.6/fc
4.8/fc
8.2/fc
11.6/fc
2.7/fc
8.4/fc
16.3/fc
24.8/fc
-
-
-
