How we can use KVL and KCL in calculating the equations for loop and node analysis in a coupled resonator filter but in a generalized form? Any relevant information or research papers you can provide would be appreciated.
Take a look at
http://www.mathworks.com/matlabcentral/fileexchange/27244-circuit-analysis-toolbox
and
http://www.swarthmore.edu/NatSci/echeeve1/Ref/mna/MNA6.html
Coupled resonators are a wee bit too complicated to tackle with KVL and KCL alone, as the mutual interactions happen too near the resonance, and component tolerances come very much into play. And you generally have more than one solution. Instead you should concentrate your focus on some network solvers, such as SPICE. There you can decompose your circuit into lumped element network, or you can use more complex primitives such as lines and do your model that way.
I successfully modelled and implemented coupled cavity filters for 2m band in PSpice, and confirmed the validity of coupling strategy in real life. So yeah, it works.
There is a free implementation LTspice that uses most of the models in PSpice.
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