# Mutual Inductance Transfer function

1. Dec 14, 2015

### JasonHathaway

1. The problem statement, all variables and given/known data
Find Io(s)/Ii(s)

2. Relevant equations
Basic KVL laws.

3. The attempt at a solution
My idea is to start from the RHS of the circuit until I get a relation between Io(s) and Ii(s).

Actually I stopped at this point, I wondered whether my approach is appropriate or not since the equations is getting longer and longer.

What do you say?

2. Dec 14, 2015

### Staff: Mentor

I think you can expect the expressions to get longer and nastier. You've got a circuit with four inductors, a mutual inductance and a capacitor, so it's going to have some complex behavior in its general solution. It would be considerably simpler if the input current was confined to being a single frequency sinewave

If it were me I'd think of "replacing" the input current and R2 with a Thevenin equivalent just to get rid of one loop, then write mesh equations and use Cramer's Rule to solve symbolically for the capacitor current (mesh 3). Then all the hairy parts will be confined to one step: the hammering out of the two 3 x 3 determinants.

3. Dec 14, 2015

### The Electrician

In the I2 loop is a resistor R2, but the resistor in parallel with the input source also looks like R2 to me. Are they really both R2?

Also, your equations so far don't include LR; I see LL but not LR.

4. Dec 15, 2015

### rude man

I would agree with gneill to change the current input to a Thevenin.
Then, you stated you want to use KVL but you used KCL instead. Stick to KVL. This is not a complicated circuit. Just two equations.
Also, use lowet case for the Laplace variable s.