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I'm designing a passive filter for a power electronic circuit.

Theoretically I have obtained a transfer function of a passive filter that fits my requirement. But I don't know how to implement it practically using a RLC circuit. I searched online but most of the solutions are showing using OPAMPs. So can anyone suggest me the steps (procedures) to implement my transfer functions using RLC circuit?

My transfer functions are for instance given below.

  • 20/(4.4e-06 s + 1) or 4.5455e+06/(s + 2.2727e+05)

and

  • 9e-05 s/(1.08e-10 s^2 + 1)
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  • \$\begingroup\$ Do you know how to put them into one of the two usual standard forms? The 2nd TF will be interesting to see regardless of how it is implemented. I look forward to seeing a specific implementation suggested for it. And given only RLC, the first TF implementation will also be interesting. \$\endgroup\$ Commented Feb 6, 2023 at 7:36
  • \$\begingroup\$ Yes I know the standard form of writing first order and second order transfer functions. \$\endgroup\$ Commented Feb 6, 2023 at 7:42
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    \$\begingroup\$ Then it would be better to put them into that form here. Doing so makes a few things more obvious, too. What does the lack of an 's' term in the denominator of the 2nd TF suggest to you? What does the required gain of the 1st TF suggest to you? \$\endgroup\$ Commented Feb 6, 2023 at 7:42
  • \$\begingroup\$ 4.5455e+06/(s+2.2727e+05) for the first equation but for the second equation it will be a 3rd order equation when re-arranged. \$\endgroup\$ Commented Feb 6, 2023 at 8:00
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    \$\begingroup\$ For example, your first equation should be in the form of \$K\frac{\omega_{_0}}{s+\omega_{_0}}\$, where you specify both \$K\$ and \$\omega_{_0}\$. Your 2nd equation is of the form \$K\frac{2\zeta\,\omega_{_0}\,s}{s^2 + 2\zeta\,\omega_{_0}\,s+\omega_{_0}^2}\$ and where in this case it's pretty obvious that \$\zeta=0\$ and that \$K=\infty\$. Both of which are problems. So I'd love to see the 3rd order form of that. \$\endgroup\$ Commented Feb 6, 2023 at 8:15

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To find an RLC circuit given the Poles & Zeros of ones equations, the Pole Removal methods are used. Some 50 years ago, SYNTH2 program was used to do just that.

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