Resonance in a coupled circuit

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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.)

[tex]Z_{1}=R+\frac{1}{j\omega C_{1}}+j\omega L_{1}-j\omega M[/tex]

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


best regards
eirik
 

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berkeman
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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.
 

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