Electronic – Is it possible for the transfer function of an RLC system to have zeros other than at the origin

The classical feedback formula (H. Black) is

Ho=Ao/(1+AoH)=1/(1/Ao+H) with Ao=open-loop gain and H=feedback function. Of course, for Ao approaching infinity we have Ho=1/H.

Example: If the feedback path consists of a resistive voltage divider R1/(R1+R2) we get the classical closed-loop gain expression for a non-inverting opamp stage Acl=1+R2/R1.

Mutual inductance (M) and coupling factor (k): -

So if you have two inductors of 10uH each coupled at 70% then M = 7uH.

This means that the 10 uH coupled inductor becomes a 100% coupled transformer with leakage inductance of 3 uH in each limb.

Because the transformer is 1:1 (in my example) you can simply electrically connect the secondary components (including the extra series 3 uH leakage inductance) across the "now" 7 uH primary. Here's what it should now look like: -

^{simulate this circuit – Schematic created using CircuitLab}

If the turns ratio wasn't 1:1 (i.e. both coupled inductors were not identical in value) then it becomes a little trickier because you have to impedance transpose the components on the secondary (including the new secondary inductor due to leakage) before you can connect them across the primary inductor.

This wiki page shows how a mutually coupled arrangement of inductors is equivalent to this: -

So if you start with L1=10 uH as per my example and have 7 uH mutual coupling you end up with a common inductor of 7 uH and two teed off inductances of 3 uH as an equivalent model.