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 :

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 :

Butterworth

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 :

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

-

-

-