Efficient 2-D Integral Equation Approach for the Analysis of Power Bus Structures With Arbitrary Shape

A 2-D contour integral-equation method for the frequency-domain analysis of arbitrarily shaped power bus structures is presented. The numerically efficient approach allows the rapid and accurate computation of the frequency-dependent transfer parameters between an arbitrary number of ports, as required for embedding the power plane structure into network simulation. A formulation is developed for calculating the voltage distribution between the planes, as well as for determining the resulting radiated fields based on the field-equivalence principle. The method is applied for several test boards including a populated board with a surface-mount decoupling-capacitor network. The suggested approach is well confirmed by an analytical solution for the rectangular structure, by measurement and 3-D full-wave simulation results.