Robust and passive model order reduction for circuits containing susceptance elements

Numerous approaches have been proposed to address the overwhelming modeling problems that result from the emergence of magnetic coupling as a dominant performance factor for ICs and packaging. Firstly, model order reduction (MOR) methods have been extended to robustly capture very high frequency behaviors for large RLC systems via methods such as PRIMA with guaranteed passivity. In addition, new models of the magnetic couplings in terms of susceptance (inverse of inductance) have shown great promise for robust sparsification of otherwise intractable inductance coupling-matrix problems. However, model order reduction via PRIMA for circuits that include susceptance elements does not guarantee passivity. Moreover, susceptance elements are incompatible with the path tracing algorithms that provide the fundamental runtime efficiency of RICE. In this paper, a novel MOR algorithm, SMOR, is proposed as an extension of ENOR which exploits the matrix properties of susceptance-based circuits for runtime efficiency, and provides for a numerically stable, provably passive MOR using a new orthonormalization strategy.