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I'm having trouble with a cascaded butterworth notch filter I'm designing and was hoping to get some insight on the summing amplifier stage at the end. I'm still a student, so my question may be a bit basic. I'm trying to get a unity gain response for the filter, but the summing amp pushes the response more positive rather than overlaying the responses.

I tried an inverting summing amplifier with 1kohm resistors to achieve a unity gain, and I've generally fiddled with the resistors as much as I can to get the response I want. That didn't work, so I tried switching to a non-inverting summing amp, thinking my response was pushed upward due to the inverting nature of the original design (seen below).

schematic

simulate this circuit – Schematic created using CircuitLab filter response cutoff frequency plot The non-inverting amp didn't work for me either. It could be because I was using bad values for the resistors in the non-inverting summing amp, so I'm looking for any insight as to what I might be doing that is causing this response to behave the way it is.

EDIT: I should add for clarity that the filter is a notch filter in the range of 77.5KHz with a B of 15KHz using a 4th-order butterworth design.

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  • \$\begingroup\$ Does each filter section individually give the response you expect? \$\endgroup\$ – Brian Drummond Dec 2 '15 at 17:24
  • \$\begingroup\$ @BrianDrummond, yes, analyzing the filter response coming out of the high pass and low pass sections is exactly what I'm hoping for. The 'OUT' node is where my filter response is giving me grief. \$\endgroup\$ – Adam Dec 2 '15 at 17:29
  • \$\begingroup\$ You haven't actually defined "doesn't work" and I'm not going to guess what you mean. Graphs of expected and actual response would help. \$\endgroup\$ – Brian Drummond Dec 2 '15 at 17:39
  • \$\begingroup\$ @BrianDrummond, see the response image above. The output of the filter doesn't follow the notch as I was hoping. Expected response is to follow the two individual portions of the notch filter. Does that help clarify? \$\endgroup\$ – Adam Dec 2 '15 at 18:17
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    \$\begingroup\$ Welcome to analog filter design. If you think its fun now, wait until you try to build it with 10% caps \$\endgroup\$ – Scott Seidman Dec 2 '15 at 20:25
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It looks like both filter sections are designed with the -3dB point at the same frequency, or very close together, so this filter is doing what it should.

In the crossover region, both sections contribute to the output, so it is higher than either alone. The slight peax at the crossover frequency would be 3dB if both signals were in phase(so they added coherently), so presumably they aren't. EDIT : apparently the small separation between -3dB points, rather than phase, accounts for this peak being less than 3dB.

For a classic design without that bulge, read up on the Linkwitz-Riley crossover, commonly used in loudspeakers where you want HPF and LPF outputs to sum to unity.

I don't know what you were expecting but if you wanted a notch you'd have to separate the -3dB frequencies, then the depth of notch will depend how far apart they are, and it won't be a deep notch.

If you wanted a deep notch, one approach is the Twin-T filter which can be made as narrow as you want.

Or start by specifying the frequency, notch width (at -3dB), and notch depth you want, and research filter design techniques to meet that specification.

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  • \$\begingroup\$ Brian, please see my edit to include the LTSpice plot showing the cutoff frequency at -3dB for the high pass branch. They are separate. Is it that the quality of this filter doesn't allow the summing amp to meet the demands of that range of frequencies? \$\endgroup\$ – Adam Dec 2 '15 at 20:01
  • \$\begingroup\$ your links are dead \$\endgroup\$ – not2qubit Apr 17 at 20:36

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