Extraction of Equivalent Network of Arbitrarily Shaped Power-Ground Planes With Narrow Slots Using a Novel Integral Equation Method

A novel integral equation method for efficient and accurate modeling of power-ground planes with narrow slots is provided in this paper. The equivalence principle is used to extend finite-size power-ground planes to infinite parallel planes. The discontinuities in the original power-ground planes, including the slot, via clearance, and boundary, are represented by equivalent electric and magnetic currents. Coupled integral equations are created for these equivalent currents. By making use of the modal field distribution between the power and ground planes, the complex surface integrals are reduced to simple one-dimensional line integrals. This greatly reduces the computing time while good accuracy is preserved. Thereafter, the paths of integration are discretized into many segments, which are equivalent to network ports, such that an equivalent microwave network of the power-ground planes with slots is derived through the solution of the integral equations. This equivalent network is used for power integrity analysis. By comparing the proposed method with measurement results and available full-wave methods, its accuracy and efficiency are verified.