firstly, the resonant frequency is determined by the frequency of the AC current flowing in the primary inducrot, The series capacitor reduces the impedance of your transmitter cct, which increases the magnetic field transmitted, and hence the power transmitted.
The secondary inductor then picks up a voltage which is dependant on the strength (and frequency of the mag field) This voltage will be at the same freq of the mag field and the primary current. The current flowing through the inductor will be at this frequency.
With no cap the current flowing through the load is determined the voltage inducedand the totalimpedance. So the bigger the inductance. The bigger the voltage induced. However the increased impedance will decrse the current flowing in the cct and hence power to the load then reduce the voltage to such a degree that the power to the load is now low, despite the high voltage being induced.
impedance matching is about optimising the inductance to maximise the current flowing in the cct.
Putting in the parallel resonant cap increases the current flowing in the load. It's hard to get to grips with how that happens, and I can't remember enough to expalin it. But it is akin to lowering the internal impedance of a bettery.
From what I remember.( I'll try to check it out tonight)
the power source for your load is the secondary inductor.
you match that impeddance to the load.
that gives you and inductance. value.
The value for the paralled capacitor is determinded by the transmission frequency.
Set your primary inductor to the same value as the secondary
Choose your primary cap to to achieve resonance at the tramnsmission freq with your primary inductor.
Loads of power to the load.
Xm is your mutual inductance, you don't tweak it really, or use it to tweak. set you inductance as above you coupling is determinaed by the size positioning and orientaion of your coile, and your mutiual inductance is a product of those.
You do need to have the same resonant freqqency on both sides as both sides operate at the same frequency.