Poles and Stability of Full-Wave PEEC

Time-domain simulation of full-wave partial element equivalent circuit (PEEC) often encounters stability problems. In the past, various approaches have been proposed to determine the stability of a given model. Most of these methods, however, have low efficiency and scalability. In this article, we propose a highly efficient method to obtain a particular group of the poles of the model; such information then serves as a necessary-condition test for stability. Furthermore, the method is extended to include the effects of damping resistors. From the root locus plots of the poles, we clearly see the unstable poles moving left as damping is added in, and by the time they move into the left-half-plane, we can quantitatively determine the minimum damping level required to achieve a stable model. Simulation results are provided to verify the proposed method.