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.