Resonance in a coupled circuit

[temujin]

Dear Forum,

My question is to the circuit drawing I have attached. (representing a simplified rfid system, with "Circuit 1 being the tranceiver antenna, "Load" being a transponder and "Circuit 2" represents an additional circuit between)
...
For optimal performance the circuit should resonate at a given frequency. When calculating the needed capacitance in circuit 1, do I have to consider the mutual inductance between L1 and L2 ? (For now I assume the coupling factor between L3 and L4 is small compared to the coupling factor between L1 and L2.)

$$Z_{1}=R+\frac{1}{j\omega C_{1}}+j\omega L_{1}-j\omega M$$

And that the needed capacitance is simply such that it cancels out the inductive reactance given by $$j\omega L_{1}$$ and $$jwM$$.
Am I on the right track?
If I am, I assume that the capacitor C2 must be found the same way?


best regards
eirik

 

[anorlunda]

ping @berkeman

 

[berkeman]

First, use different values for the two "M" mutual coupling coefficients. Call them M1 and M2. Second, I would prefer to use SPICE to help with optimizing this circuit -- the multiple resonances cause complications. Lastly, be sure to model the source and load complex impedances well -- they will interact with the whole system.