Developing new model order reduction algorithms to enhance the efficiency of large-scale electrical and electronic circuit simulation: Mixed Balanced Truncation and Riccati–Lyapunov Mixed Balanced Truncation

Abstract

This paper investigates model order reduction (MOR) techniques for simulating large-scale electrical and electronic systems, aiming to reduce computational cost and optimize performance while preserving essential physical properties. In particular, two novel reduction algorithms—Mixed Balanced Truncation (MBT) and Riccati–Lyapunov Mixed Balanced Truncation (MRLBT)—are developed to improve efficiency compared to standard Balanced Truncation (BT) and Positive Real Balanced Truncation (PRBT) methods. Both the MBT and MRLBT algorithms maintain the stability and passivity of the original system. The paper details the implementation steps of the algorithms and compares their performance on RLC circuits through simulations that include error analysis as well as time- and frequency-domain response evaluations. The results indicate that MBT strikes a balance between accuracy and computational cost, with reduction errors positioned between those of BT and PRBT, while MRLBT achieves the best overall performance and meets the model reduction requirements most effectively among the four methods considered.