Frequency-Limited Reduction of RLCK Circuits via Second-Order Balanced Truncation

Second-order formulation using susceptance elements has become very effective in modeling on-chip inductive couplings. Several prior works have proposed model order reduction techniques for RLCK circuits, mostly based on balanced truncation (BT) and moment matching, providing reduced-order models (ROMs) that can be simulated over the whole frequency range. However, in most applications, the ROMs are simulated only at specific frequency windows, which means that established methods usually provide models that may become unnecessarily large to achieve approximation over all frequencies. In this paper, we present a second-order frequency-limited approach for RLCK circuits, which may be combined with efficient low-rank Lyapunov solvers, leading to ROMs which are either smaller or exhibit better accuracy compared to an established second-order BT method. Experimental results on interconnect bus structures demonstrate the advantages of the proposed method.