SAPOR: Second-order arnoldi method for passive order reduction of RCS circuits

The recently-introduced susceptance element exhibits many prominent features in modeling the on-chip magnetic couplings. For an RCS circuit, it is better to be formulated as a second-order system. Therefore, corresponding MOR (model-order reduction) techniques for second-order systems are desired to efficiently deal with the ever-increasing circuit scale and to preserve essential model properties. In this paper, we first review the existing MOR methods for RCS circuits, such as ENOR and SMOR, and discuss several key issues related to numerical stability and accuracy of the methods. Then, a novel technique, SAPOR (Second-order Arnoldi method for Passive Order Reduction), is proposed to effectively address these issues. Based on an implementation of a generalized second-order Arnoldi method, SAPOR is numerically stable and efficient. Meanwhile, the reduced-order system also guarantees passivity.