equating resonance frequency for complex rlc circuits

[vijith133]

could anyone help to derive the equation for the resonance frequency in complex rlc circuit. Pls do note that am not requesting for simple series or parallel rlc circuit. My circuit includes more than one capacitance and 2 inductors.

pls do help me out to solve this

 

[FvM]

Counter question for clarification, how do you define resonance frequency?

My suggestion for a circuit with two terminals: a local minimum or maximum of impedance, with cancellation of imaginary part. See https://www.edaboard.com/threads/132661/

Depending on the topology and component values, a complex RLC circuit will expose more than one resonance frequency.

 

[BigBoss]

Derive its transfer function and then find the poles and zeros.
They will give you an idea about resonance or frequency response of the circuit.