If we are given a frequency response curve made up of the amplitude (magnitude) and phase (angle) responses, is it possible to design an electronic network with a transfer function identical to the given ones?

I have been thinking about this. An idea which occurred to me was that if we could design a network with constant amplitude and a specific phase response, and also another with a specific amplitude response and zero phase response, the problem would be solved. However, I still haven't found a way around the sub-problems.

Is it possible to design such a network? It could be passive or active.

  • \$\begingroup\$ Related:Minimum phase systems \$\endgroup\$
    – The Photon
    Apr 8 '19 at 17:27
  • \$\begingroup\$ Need to be more specific, is it possible questions are a matter of opinion and off topic. You'll get better answers if your specific. \$\endgroup\$
    – Voltage Spike
    Apr 8 '19 at 18:21
  • \$\begingroup\$ Or maybe the OP is asking more about a algorithmic methodology for turning a curve into a circuit without trial and error or iterations? \$\endgroup\$
    – DKNguyen
    Apr 8 '19 at 18:25
  • \$\begingroup\$ This problem is very dependent of the bandwidth on which you want to fit the tranfert function : 10% is very different from 3 decades. \$\endgroup\$
    – andre314
    Apr 8 '19 at 19:19

Arbitrary response could require arbitrarily complex circuitry. For example, look at how difficult it is to build a pink noise filter.

So the answer to your question is that it is possible to approximate a given response to within a certain tolerance, but there's no guarantee that you can produce it exactly.


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