I have a project on filtering out frequency above 2.5 KHz. The filter should be low pass butterworth. I am confused here as there are two cutoff frequencies I need to use. 1st cutoff freq. 1KHz and 2nd cutoff freq. 5KHz.

The passband is 5 amd I/p voltage is 0-5 V.

If any one can provide me some idea about this filter design? And what kind of configuration should I use?

  • 1
    \$\begingroup\$ "Passband is 5"? "Filtering out frequency above 2.5kHz"? These seem contradictory - also what is the "order" of the filter? It seems like you may be asking for a fourth order design given the two cut-offs you mention. Input voltage is irrelevant in the main. Why Butterworth specifically? Is it homework? \$\endgroup\$
    – Andy aka
    Commented Jul 31, 2013 at 7:36
  • \$\begingroup\$ yes it is home work...passband gain is 5 \$\endgroup\$
    – Dark lord
    Commented Jul 31, 2013 at 8:03
  • \$\begingroup\$ The question is like this " Design an active low pass Butterworth filter with 1st cutoff 1 KHz and 2nd cuoff 5KHz. Passband Gain = 5 " \$\endgroup\$
    – Dark lord
    Commented Jul 31, 2013 at 8:16
  • \$\begingroup\$ As Andy says, you could cascade two second order Butterworth filters (1 kHz and 5 kHz) and you would end up with a fourth-order filter with a cutoff frequency of 2.236 kHz but it would not have a Butterworth response. \$\endgroup\$
    – MikeJ-UK
    Commented Jul 31, 2013 at 9:19
  • \$\begingroup\$ Give a try to AWR Filter Design Tool. \$\endgroup\$
    – AKR
    Commented Jul 31, 2013 at 15:44

2 Answers 2


Question: Is it possible that the required corner frequency (3 dB) is 1 kHz and the stopband frequency (with a certain required damping specification) is given with 5 kHz ? Please note that it is NOT possible to "filter out" a frequency of 2.5 kHz. You only can provide a certain degree of damping - unless you design a filter with a passband zero at 2.5 kHz. However, this has no Butterworth response.

The filter order necesary to meet your requirements is determined by the stop band attenuation, which is not given up to now.

As an example: A Butterworth low pass of 4th order can be realized as a series connection of two active lowpass stages with the same 3dB cut-off frequency (1 kHz) but with two different Qp values (Qp: pole Q).


A second order low-pass filter with two real, negative and distinct poles (corner frequencies) shows an overdamped response (no overshoot). Damping ratio > 1 (or Q < 0.5). Attenuation 20 dB/decade above the first pole and 40 dB/decade above second pole. Remember that, in general, "cut-off frequency"should not be confused with "corner frequency". Just for first order systems or Butterworth responses.

  • \$\begingroup\$ Regarding "corner" and "cut-off": Yes I agree to the above comment. In any case it is better to speak about the "passband edge" and to mention the respective damping. \$\endgroup\$
    – LvW
    Commented May 22, 2014 at 7:00

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