Modeling & Measurement of Mutual Coupling Resulting from via Structures Within Printed Circuit Boards

We report measurements and modeling of mutual coupling resulting from closely spaced copper plated through holes on printed circuit boards (PCB), known as vias. When the magnetic flux generated by a primary system couples with the inductance of a secondary system a 'reflected impedance' is induced in series with the primary inductance. Our investigation includes practical measurements and full-wave 3D electromagnetic (EM) modeling using transmission line matrix code (TLM) in order to establish the change in coupling and 'reflected impedance' as a function of distance between quasi resonant structures. With significant numbers of coupled vias, possible coupling permutations are large. We report models for 2, 3, and 4 via coupling, the results from which are extendable to arbitrary 3D structures.