How can I calculate the transfer function of this bandpass filter characteristic with Butterworth approximation?

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  • \$A_{max}\$ = 0,9 dB
  • \$A_{min}\$ = 6,5 dB
  • \$\omega\$3 = 100
  • \$\omega\$1 = 300
  • \$\omega\$2 = 1100
  • \$\omega\$4 = 3300

Which steps do I have to take and what are some good resources for learning these kinds of filter design problems?


Volki, be aware that the design will be rather involved. Here is a short summary of the main steps (active filter design):

  1. Based on the given values (center frequency, bandwidth, midband gain, attenuation values) you must use existing formulas for the bandpass-lowpass transformation. As a result, you have corresponding lowpass requirements and you can calculate the corresponding lowpass order (n=2,3,..).

  2. Applying again corresponding equations you can transform the lowpss poles back to the bandpass poles.

  3. Now you have two alternatives for pole allocation (depending on the required filter order):

    • Series connection of active lowpass and highpass sections
    • Active bandpass stage (or series connection of several stages).

For passive topologies, you must rely on filter catalogues. In any case - I strongly recommend to make use from filter design programs which are available. For example:

Passive: AADE;
Active: Filter Free, FilterLab, FilterPro

  • \$\begingroup\$ A first look on the given data has shown that a second-order bandpass can meet the requirements. \$\endgroup\$ – LvW Aug 8 '14 at 15:17

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