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When I studied the resonant frequency of an RLC circuit in series and parallel, there was the definition that I read in books that the imaginary part of the total impedance of the circuit has to be equal to zero and the frequency where that happens is the resonant frequency. I'm fine with that, but there can be multiple transfer functions in a circuit depending on what output signal you choose, so for every transfer function there is 1 or more frequency values that generates the maximum value (amplitude) of the function. So is there 1 (or more) resonant frequency for every specific transfer function? Or are those values not resonant frequencies?

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  • \$\begingroup\$ If your circuit doesn't have switches (with which the config can be altered) or other non-linearities that can change mode of operation, then it will have one transfer function. \$\endgroup\$
    – Syed
    Dec 12, 2021 at 4:50
  • \$\begingroup\$ Alexis, I believe that if you work out the transfer function (per conditions mentioned by @Syed) then there may be multiple roots to where the imaginary portion of the characteristic function is zero. (Though, clearly, those cases where the frequency is negative can be ignored.) You can see one discussion along these lines here, though it doesn't discuss a more complex situation with a sufficiently high order of the imaginary part to make this point better. I am tired tonight, though. So I may not be at my best right now. \$\endgroup\$
    – jonk
    Dec 12, 2021 at 5:31
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    \$\begingroup\$ To get a more concrete answer, please load a circuit diagram. By definition, a TF requires an input and an output: for every such pair there will be exactly one TF. The shape of this TF will depend on the circuit. \$\endgroup\$
    – Syed
    Dec 12, 2021 at 5:37
  • \$\begingroup\$ There are 6 different configurations of series RLC circuits and, all have different transfer functions. So, decide on two to make comparisons. \$\endgroup\$
    – Andy aka
    Dec 12, 2021 at 7:09
  • \$\begingroup\$ Add to this the three types of resonance (natural, amplitude peaking and zero phase shift) and you can see that providing a general answer is asking too much so, please apply more focus. \$\endgroup\$
    – Andy aka
    Dec 12, 2021 at 7:16

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Yes, the resonants frequencies of a circuit made of whatever bunch of RLC are intrinsic to the circuit.

But there are two subtelties :

  1. The stimulus and the measurment should not change the circuit. If the stimulus is a low impedance source (a voltage generator) then you can only apply it by insertion in a wire of the circuit you have cut. If it is a hight impedance source (current generator), then apply it simply to a pair of existent nodes. In the special case of a serie LC, you measure the resonant frequency by applying a current between the extremeties, but it turns out that can also find the same frequency by applying a voltage source and measure the current : This is a specificity to the LC circuit alone. If you do that with a more complex circuit, then consider that you have changed the circuit : it isn't the same circuit !

  2. For a more complex circuit, you have N several resonant frequencies. If you make a measure somewhere at a point P, it can happen that the contribution of a resonance is 0 at this point P (mathematicaly, one says the residu of the complex function pole is 0). Take for example a circuit made of two independent LC (I mean non coupled). In real life this is not a problem because it's evident.

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