Impedance of an infinitely large parallel-plane pair and its applications in engineering modeling

In this paper, a closed-form expression for the impedance of an infinitely large parallel plane pair is presented. It is applicable to practical printed circuit board (PCB) design problems where there are multiple shorting vias around the signal vias of interest. With the presence of multiple shorting vias, reflections from the plane pair edges can be neglected since the shorting vias prevent the electromagnetic energy from leaking away from the local cavity around the signal vias. The self and transfer impedance expressions can be obtained using the expansion of cylindrical waves. The impedances calculated from both the rectangular cavity model and the infinitely large plane pair model for several design examples are compared to demonstrate the effectiveness of the infinite plane pair approximation.