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Networks of coupled LC oscillators that do not share a common ground node arestudied. Both resistive coupling and inductive coupling are considered. Fornetworks under resistive coupling, it is shown that the oscillator-couplerinterconnection has to be bilayer if the oscillator voltages are toasymptotically synchronize. Also, for bilayer architecture (when both resistiveand inductive couplers are present) a method is proposed to compute acomplex-valued effective Laplacian matrix that represents the overall coupling.It is proved that the oscillators display synchronous behavior if and only ifthe effective Laplacian has a single eigenvalue on the imaginary axis.

Synchronization of oscillators not sharing a common ground