What are transfer functions and how do you find them?

[ionlylooklazy]

i've always been a little confused on transfer functions, could someone offer me some tips/hints please?

if I have this circuit shown,

a transfer function is the ratio of the input to the output?
can it be the ratio of the currents, or must it be the voltages, also, in this circuit, would the input be considered across the capacitor?

 

[berkeman]

The transfer function is generally the ratio of an output divided by an input. You can have Vo/Vi transfer functions (the most often used), but you can also have any mix of Io, Vo divided by Ii or Vi.

In your circuit, Io/Ii, Io/Vi and Vo/Ii would each have some meaning for non-DC input signals. But since Vi = Vo, Vo/Vi == 1.

To calculate each of the transfer functions, just write the KCL or KVL equations for each node and solve for the transfer function ratio of interest.