Effective Coupling Coefficient of Directly Coupled Resonant Networks

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Original poster: "Mccauley, Daniel H" <daniel.h.mccauley-at-lmco-dot-com> 


In a directly coupled double-resonant circuit, Antonio stated there is
an equivalent coupling coefficient which is
similar to that of the magnetic coupling in a transformer based
double-resonant circuit.

In this version, k = SQRT (L1/(L1+L2))

I was wondering if someone (Antonio?) could expand in more detail the
role and its derivation within a directly
coupled system.  For example, how could I at least mathematically derive
this coefficient when doing so for 6th order and higher directly coupled
resonant systems.

Any help appreciated.
Thanks

Dan