# Difference between converter input impedance and transfer functions

#### SiCEngineer

Joined May 22, 2019
444
I am doing some work trying to derive the transfer function of a resonant LCC power supply. I have come across analysis online which shows the derivation of the input impedance of the converter, which I have attached.

My question is a basic one which may sound stupid, but i've not much experience in this part of the design procedure yet. The impedance equation looks a lot like a typical transfer function with some laplace terms. But, is it the same? If not, how would the transfer function be extracted so that I can design a PID controller or some sort to close the feedback loop?

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#### TeeKay6

Joined Apr 20, 2019
573
I am doing some work trying to derive the transfer function of a resonant LCC power supply. I have come across analysis online which shows the derivation of the input impedance of the converter, which I have attached.

My question is a basic one which may sound stupid, but i've not much experience in this part of the design procedure yet. The impedance equation looks a lot like a typical transfer function with some laplace terms. But, is it the same? If not, how would the transfer function be extracted so that I can design a PID controller or some sort to close the feedback loop?
In general, impedance and transfer function are two entirely separate concepts and are not related. Neither can be derived from the other.

#### Papabravo

Joined Feb 24, 2006
21,294
A transfer function is not a general purpose construct. It only applies to linear time invariant systems described by ordinary differential equations with constant coefficients. A system with any sort of non-linearity will destroy the possibility of creating or using a transfer function for analysis. At that point you can try to linearize the system about an operating point but that has limited utility. Other methods must be considered if that happens.