Accurate Analysis of RLC Trees by Laguerre Polynomials

In this paper, we propose one efficient algorithm for the transient analysis of RLC trees. Based on MNA equations, we derive the recursive formulas for the coefficients of Laguerre polynomials. Via Arnoldi algorithm, we can reduce the order of matrix directly in the time-domain instead of frequency-domain, which is often more time-consuming because inverse Laplace transformation or inverse fast Fourier transformation is needed. Furthermore, the passivity of the network reduced by our method is guaranteed because of the congruence transformations. It is shown through one example on the transient analysis of one RLC tree that the average error by our method is within 10% in comparison with results by HSPICE and our method can run faster than HSPICE.

I. INTRODUCTION

With the rapid development of VLSI technology and the complexity of VLSI circuits, interconnects are becoming one important factor for the performance of the chips and interconnect analysis is challenging CAD [1]. Conventional methods for interconnect analysis are impractical. Now, one efficient way to solve the above difficulties is model reduction. By transforming the large matrix into one smaller matrix, the response of the large network can be approximated by the response of the small network which can be calculated easily. Many algorithms have been proposed for model reduction [1]. Generally, they can be grouped into two kinds. The first is direct MMT (Moment Matching Technique) based on AWE (Asymptotic Waveform Evaluation) technique [2] and the second is implicit MMT based on Krylov subspace [3] [4] [5]. However, for the former, the passivity of the reduced network can not be guaranteed. For the latter, model reduction is completed in the frequency domain and inverse Laplace transformation or inverse fast Fourier transformation is needed to get the response in the time domain. Recently, new methods are proposed for model reduction, such as [6] and [7].