Time-Domain Analysis of Rectangular Power-Ground Structures With Relaxation

The rectangular power-ground structure is thoroughly analyzed in time domain. The time-dependent electric-field distribution within the power-ground structure is expanded in ray-like constituents that propagate via the reflections against circuit's periphery. Their relation to the classical eigenfunction expansion is demonstrated. It is shown that the ray-type expansion is always exact in any finite time window of observation and can be readily generalized to account for dissipation and relaxation mechanisms. Obtained results concerning a dispersive dielectric described through finite conductivity and Debije relaxation models are discussed and validated on a number of illustrative examples.