OSTC-FRVF: Order Determination and S-TSVD for Constrained Macromodeling of S Parameter

Macromodeling for S parameter, obtained by capturing the frequency response of multiport devices, is a crucial methodology for transient simulations. However, current methods face significant challenges in efficiency, reliability, and accuracy. FRVF will exceed the operational memory when applied to a circuit with 384 ports, and the error with an incorrect order is substantial. Algorithms like AAA and ORA may struggle to satisfy the conjugate properties and stability. To overcome these issues, this paper introduces OSTC-FRVF, a comprehensive solution that achieves acceleration, order correction, and constraint satisfaction. For accuracy, OSTC-FRVF establishes an order determination mechanism (O) to balance the relationship between accuracy and complexity. The improved peak detection method calculates the initial order, and Prony Analysis with a new termination condition adjusts the order promptly. For efficiency, to maximally utilize data redundancy to simplify the computational process, OSTC-FRVF designs a two-pronged acceleration method, S-TSVD. The innovative resonance sampling method (S) and the improved truncated singular value decomposition method (T) collaborate synergistically, which fully exploit the data characteristics to enhance the efficiency in macromodeling. For reliability, the constraints satisfaction method (C) addresses the DC preserve, D-passivity, conjugate properties, and stability to facilitate the success of transient simulations. The validity is thoroughly substantiated on circuits of diverse scales, spanning from 2 to 384 ports. OSTC-FRVF achieves an average speedup ratio of 25.69× and a maximum of 40.29 compared to FRVF. And the relative error is generally below ×1%.