A general hierarchical circuit modeling and simulation algorithm

This paper proposes a new hierarchical circuit modeling and simulation technique in s-domain for linear analog and interconnect circuits. The new method is based on a graph-based symbolic hierarchical circuit decomposition scheme. It can derive the exact or approximate admittances in the reduced circuit matrix and compute the circuit characteristics in rational function forms for very large linear analog and interconnect circuits. We show that the exact symbolic expressions of a circuit can be obtained by finding the cancellation-free expressions from the same circuit with hierarchical definitions. Some theoretical results are characterized for the presence and conditions of cancellations in the symbolic expressions from the subcircuit reduction. A novel decancellation strategy based on a graph-based hierarchical decomposition process is proposed and canceling terms are removed both symbolically and numerically to obtain the order-reduced circuit models. The proposed method can be used for modeling and simulation of any passive or active linear circuit, which makes our method very attractive for modeling both analog circuits and resistance-capacitance-inductance interconnect circuits in both frequency and time domain. An example RC circuit is illustrated and experimental results with some large analog and interconnects circuits are presented to validate the proposed method. Our experimental results also show that subcircuit (multiple-node) reduction scheme in general is better than one-node reduction methods such as Y-Δ transformation in terms of CPU time and memory usage.