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MIMO Interconnects Order Reductions by Using the Multiple Point AdaptiveOrder Rational Global Arnoldi Algorithm
ChiaChi CHU MingHong LAI WuShiung FENG
Publication
IEICE TRANSACTIONS on Electronics
Vol.E89C
No.6
pp.792802 Publication Date: 2006/06/01
Online ISSN: 17451353
DOI: 10.1093/ietele/e89c.6.792
Print ISSN: 09168516 Type of Manuscript: Special Section PAPER (Special Section on Analog Circuit and Device Technologies) Category: Keyword: rational Arnoldi algorithm, global Arnoldi algorithms, model reductions, interconnect, Krylov subspace, MIMO,
Full Text: PDF(649.3KB)>>
Summary:
We extend the adaptiveorder rational Arnoldi algorithm for multipleinputs and multipleoutputs (MIMO) interconnect model order reductions. Instead of using the standard Arnoldi algorithm for the SISO adaptiveorder reduction algorithm (AORA), we study the adaptiveorder rational global Arnoldi (AORGA) algorithm for MIMO model reductions. In this new algorithm, the input matrix is treated as a vector form. A new matrix Krylov subspace, generated by the global Arnoldi algorithm, will be developed by a Frobeniusorthonormal basis. By employing congruence transformation with the matrix Krylov subspace, the onesided projection method can be used to construct a reducedorder system. It will be shown that the system moment matching can be preserved. In addition, we also show that the transfer matrix residual error of the reduced system can be derived analytically. This error information will provide a guideline for the order selection scheme. The algorithm can also be applied to the classical multiple point MIMO Pade approximation by the rational Arnoldi algorithm for multiple expansion points. Experimental results demonstrate the feasibility and the effectiveness of the proposed method.

