# Does every transfer function in a circuit have its own resonant frequency?

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?

• 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.
– Syed
Dec 12, 2021 at 4:50
• 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.
– jonk
Dec 12, 2021 at 5:31
• 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.
– Syed
Dec 12, 2021 at 5:37
• There are 6 different configurations of series RLC circuits and, all have different transfer functions. So, decide on two to make comparisons. Dec 12, 2021 at 7:09
• 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. Dec 12, 2021 at 7:16