Timeline for Synthesizing an impedance given by transfer function (poles/zeros) using a passive network
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| Jun 7, 2022 at 5:23 | answer | added | user69795 | timeline score: 0 | |
| Jun 7, 2022 at 0:15 | history | edited | divB | CC BY-SA 4.0 |
Clarify I am NOT talking about voltage transfer functions
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| Jun 6, 2022 at 8:20 | comment | added | divB | Everyone, this might be a misunderstanding, I am not talking about a voltage transfer function but the output impedance of a circuit for which I want to draw an equivalent circuit. Yes, the expression must be positive real. As I wrote, the example comes from a VRM output impedance. I left out the output cap (for simplicity and in the hope to just add it afterwards in parallel which might be a over-simplification due to feedback) but we can add that cap if it makes things easier. My question is general and not tied to these exact numbers. | |
| Jun 6, 2022 at 3:42 | comment | added | user69795 | I think you want to synthesize a passive network that has a driving point impedance given by the Laplace expression. This is more complicated than you might think. You can check if it is possible at all by seeing if the expression is POSITIVE REAL. If it is not, a passive impedance cannot be synthesized, although active devices can be used. A simple process exists to realize any passive impedance, but uses ideal transformers. Realizing a general RLC impedance without transformers is more complicated. Are you doing this for simulation? | |
| Jun 6, 2022 at 3:40 | answer | added | user4574 | timeline score: 1 | |
| Jun 6, 2022 at 2:50 | comment | added | user4574 | I am not sure about passive, but assuming the roots are real you can certainly make something using resistors, capacitors op-amps. First use partial fraction expansion to expand the denominator. The inverse Laplace transforms of each of these fractions (assuming real roots) is just a decaying exponential, which can be made from an RC network. Summing of each RC network output can be done with an op-amp. I used this exact approach years ago to turn a passive RC network into an FPGA digital filter years ago and it worked great. | |
| Jun 4, 2022 at 21:03 | comment | added | Verbal Kint | @jonk, with pleasure! I did sweat on some of these circuits to exercise the FACTs : ) | |
| Jun 4, 2022 at 19:49 | answer | added | jonk | timeline score: 4 | |
| Jun 4, 2022 at 19:40 | comment | added | jonk | @VerbalKint Thanks for the 'gains' paper! | |
| Jun 4, 2022 at 13:40 | comment | added | Verbal Kint | Yes, a nice read after the lawn has been mown : ) Peaky \$RC\$ networks are fun to analyze (the circuit of page 273 is one of the examples I treated) but not sure what they could be useful for... | |
| Jun 4, 2022 at 13:17 | comment | added | a concerned citizen | @VerbalKint That's a nice Saturday afternoon read. :-) I still wouldn't use it to save my life, but maybe the neighbour's... | |
| Jun 4, 2022 at 13:04 | comment | added | Verbal Kint | @aconcernedcitizen, you might be interested by this paper also : ) | |
| Jun 4, 2022 at 11:47 | comment | added | a concerned citizen | It seems @jonk's hints go unnoticed, sorry for spoiling. Passive "amplification" is, usually, not found in full biquads, only in very high Q filters, or some very clever, but unpractical circuits, and even then for a very limited bandwidth (in fact, the higher the Q, the narrower the BW), or the lower the Q the lower the "gain". And your high freq gain is flat and impossibly high (~100 GHz!!). Where does this tf come from? | |
| Jun 4, 2022 at 8:34 | answer | added | Verbal Kint | timeline score: 2 | |
| Jun 4, 2022 at 6:16 | history | edited | divB | CC BY-SA 4.0 |
added 1 character in body
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| Jun 4, 2022 at 6:12 | comment | added | divB | $$Z_1=s20u, Z_2=s100n+0.33, Z_{eq}=\frac{1}{\frac{1}{Z_1}+\frac{1}{Z_2}}$$ | |
| Jun 4, 2022 at 5:41 | comment | added | jonk | Show me a trial and error rlc example that comes close. I'm interested. | |
| Jun 4, 2022 at 5:35 | comment | added | divB | Thank you! I edited my question and added some background. I don’t see why this should not be possible with passive only elements. I can synthesize this transfer function fairly well by just trial and error using parallel RLC with parasitic elements. But this is cumbersome and I want to do this automatically. And I’d like to do it for higher orders. I just added my current numbers to avoid “this is an XY problem question” | |
| Jun 4, 2022 at 5:35 | history | edited | divB | CC BY-SA 4.0 |
added 217 characters in body
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| Jun 4, 2022 at 1:54 | comment | added | jonk | Just breaking down your transfer function, I find:$$8.5405\:\text{k}\cdot\frac{s^2}{s^2+2\zeta\,\omega_{_0}s+\omega_{_0}^{\:2}}+288.83\:\text{m}\cdot\frac{2\zeta\,\omega_{_0}s}{s^2+2\zeta\,\omega_{_0}s+\omega_{_0}^{\:2}}+45.331\:\mu\frac{\omega_{_0}^{\:2}}{s^2+2\zeta\,\omega_{_0}s+\omega_{_0}^{\:2}}\\\\\text{where: }\omega_{_0}\approx 36.76\:\text{M}\frac{\text{rad}}{\text{s}}\text{ and }\zeta\approx 1180.73$$I may be a little curious about how one of those gain figures is to be passively achieved. | |
| Jun 4, 2022 at 1:20 | comment | added | jonk | I'm just reading your writing and it's not clear to me, yet. What passive topology do you see as a way of achieving a 2nd order for both \$N_s\$ and for \$D_s\$? Could you please use the schematic editor and draw it out? Just to be clear, I mean. | |
| Jun 4, 2022 at 0:33 | history | asked | divB | CC BY-SA 4.0 |