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I know I came across a 2 op-amp, 2 capacitor circuit that can be used for a single section of an Inverse Chebyshev (a.k.a. "Chebyshev Type II) or an Elliptic (Cauer) filter. It has a pair of zeros on the \$j\omega\$-axis at \$\pm j\omega_z\$, and with resonant frequency \$\omega_0<\omega_z\$ and the transfer function is:

$$ H(s) = \frac{1 + \left(\tfrac{s}{\omega_z}\right)^2 }{1+\tfrac{1}{Q}\tfrac{s}{\omega_0}+\left(\tfrac{s}{\omega_0}\right)^2} $$

I know how to brute force derive a circuit with a pair of integrators and the canonical form we learned in Linear Circuits class 4 decades ago. Such as this:

2nd-order canonical

I just thought I saw a more elegant circuit, with one less op-amp and a couple fewer resistors, that pretty much guaranteed that the zeros lie on the \$j\omega\$-axis and at a higher frequency than the resonant frequency \$\omega_0\$. Anybody know how to save a couple of parts with this? Is there a single op-amp, two-capacitor, 4-resistor circuit that can do this?

A sorta Sallen-Key with zeros.

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  • \$\begingroup\$ I'm so ashamed of myself. 4 decades ago, I would know this. But I can't remember this now. \$\endgroup\$ – robert bristow-johnson Aug 2 '18 at 7:55
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There are several one-opamp circuits with Chebyshev II or Cauer behaviour, for example:

  • double-T-feedback circuits with positive (fixed) gain,
  • Boctor-filter (based on Multi-feedback topology),
  • Scultety-structure
  • GIC-based structures

(Hint: Google for Boctor and Scultety)

For example, see here:

http://www.schematica.com/active_filter_resources/a_list_of_active_filter_circuit_topologies.html

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  • \$\begingroup\$ my goodness, what a useful link! i had never heard of schematica.com before. \$\endgroup\$ – robert bristow-johnson Aug 2 '18 at 17:23
  • \$\begingroup\$ looks to me that the Boctor might be the one. (i don't want more storage elements than the order of the filter, so the double T is less preferred.) \$\endgroup\$ – robert bristow-johnson Aug 2 '18 at 17:25
  • \$\begingroup\$ Yes - another point: Double-T is very sensitive to component tolerances (exact matching required). In this respect, GIC structures are best - however with two opamps. \$\endgroup\$ – LvW Aug 3 '18 at 7:31
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I'm wondering, will this do it?

schematic

simulate this circuit – Schematic created using CircuitLab

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  • \$\begingroup\$ doing the node-voltage method now. what an interesting trip down memory lane. \$\endgroup\$ – robert bristow-johnson Aug 2 '18 at 8:19
  • \$\begingroup\$ Why not simulate it? \$\endgroup\$ – Andy aka Aug 2 '18 at 8:19
  • \$\begingroup\$ i wanna transfer function. \$\endgroup\$ – robert bristow-johnson Aug 2 '18 at 8:20
  • \$\begingroup\$ Well you can try this circuit or that circuit and derive the TF for each and examine the TF to see if it matches or you can just mess around with a sim until you get the TF looking about right then derive it. It's your time you'll be spending. \$\endgroup\$ – Andy aka Aug 2 '18 at 8:21
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    \$\begingroup\$ This opamp circuit only has one zero, so it can't realize the transfer function in the question. \$\endgroup\$ – Sven B Aug 2 '18 at 12:30

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