I am interested in how you would approach finding the transfer function of a circuit that involves a linear transformer. For example, the circuit below

^{simulate this circuit – Schematic created using CircuitLab}

If I wanted to find the transfer function of $$ \frac{Vout}{Vin}$$

I would first combine the RHS of the circuit, C1, C2 and R2 into an equivalent impedance. However, I'm not sure if I should use S-domain or Phasor as the source is AC 120RMS.

Then, assuming the transformer as a gain of 1, the mutual inductance would be: $$ M = 1*\sqrt{L1*L2} = 0.01 $$

From here I'm not quite sure what to do. I know the mutual inductance would create a induced voltage on each side of the transformer but I am unsure how to determine this (or use it in circuit analysis)

Note this is a circuit I made up so apologies if the values don't make sense or resemble anything that would occur in real life. I am just trying to understand how to tackle a transfer function problem that involves a ideal transformer.

I am interested in how you would approach finding the transfer function of a circuit that involves a linear transformer. For example, the circuit below

^{simulate this circuit – Schematic created using CircuitLab}

If I wanted to find the transfer function of $$ \frac{Vout}{Vin}$$

I would first combine the RHS of the circuit, C1, C2 and R2 into an equivalent impedance. However, I'm not sure if I should use S-domain or Phasor as the source is AC 120RMS.

Then, assuming the transformer as a gain of 1, the mutual inductance would be: $$ M = 1*\sqrt{L1*L2} = 0.01 $$

From here I'm not quite sure what to do. I know the mutual inductance would create a induced voltage on each side of the transformer but I am unsure how to determine this (or use it in circuit analysis)

Note this is a circuit I made up so apologies if the values don't make sense or resemble anything that would occur in real life. I am just trying to understand how to tackle a transfer function problem that involves a ideal transformer.