Stable partial inductance calculation for partial element equivalent circuit modeling

Accurate and stable analytical solutions for partial element calculation in partial element equivalent circuit (PEEC) modeling are desirable due to fast and simple usage. Conventional analytical formulae based on integral Neumann formula may give miscalculations when we compute the partial inductance of three-dimensional structures with large spacing. In this paper, a novel model-order reduction (MOR) method is presented for mutual inductance calculation in order to improve its accuracy and stability. Mutual inductances of higher order models are represented by relatively lower order models. The criteria for MOR are revealed and a code implementation routine is described. The numerical accuracy, stability and calculation cost are investigated comparing with conventional procedures. Numerical experiments show that the MOR method can guarantee numerical stability and reduce calculation complexity simultaneously, and it has advantages to be implemented in PEEC modeling for large complex electronic systems.