Balanced truncation with spectral shaping for RLC interconnects

This paper presents a numerically stable and efficient algorithm for model reduction of large RLC networks using a frequency-weighted balanced truncation technique. The salient features of this algorithm include guaranteed stability of the reduced transfer function as well as availability of provable frequency-weighted error bounds. Such frequency weighting is essential to provide better control over time-domain error of the reduced system. The first k largest singular values of the system are obtained using the Lanczos algorithm, and the Lyapunov equations are solved by an iterative Lyapunov equation solver. Experimental results demonstrate the higher accuracy of our technique compared to Krylov-subspace-based model reduction techniques and other truncated balanced realizations that do not use spectral shaping. Based on MATLAB simulations, the run-time of our method is only 5% more than that of PRIMA