Efficient Analysis of Power/Ground Planes Loaded With Dielectric Rods and Decoupling Capacitors by Extended Generalized Multiple Scattering Method

Generalized multiple scattering (GMS) method, previously proposed for signal integrity analysis of vias, is now extended to power integrity analysis of power/ground planes loaded with circular dielectric rods and decoupling capacitors. The transition matrices of the rods and decoupling capacitors are derived from boundary value problems and equivalent circuits, respectively. The transition matrices are then regarded as loads to the radial scattering matrix obtained by the GMS method. Therefore, a parallel-plate impedance matrix, which characterizes the power integrity performance, can be obtained. To understand physically different noise suppression mechanisms in power/ground planes with dielectric rods or photonic crystals, the field distributions in power/ground planes are derived in more detail. It is found that there are three kinds of resonances: one due to the cavity formed by the plane pair, one due to the cavity formed by surrounding dielectric rods, and one caused by the individual dielectric rod itself. The accuracy and efficiency of the extended GMS method are verified by comparing with a commercial full-wave solver.