An Adjoint Network Approach for RLCG Interconnect Model Order Reductions

Chia-Chi CHU  Herng-Jer LEE  Ming-Hong LAI  Wu-Shiung FENG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.2   pp.439-447
Publication Date: 2006/02/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.2.439
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Analog Circuit Techniques and Related Topics)
RLCG interconnects,  model-order reduction,  Arnoldi algorithm,  Lanczos algorithm,  adjoint network,  

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This work proposes a new method for RLCG interconnect model-order reductions in consideration with the adjoint network. Relationships between an original MNA network and its corresponding adjoint MNA network will be explored first. It will be shown that the congruence transformation matrix used in the one-sided projection can be constructed by using the bi-orthogonal bases developed from the Lanczos-type algorithms. In particular, if the multi-port driving-point impedance of RLCG interconnect circuits is the main concern, the transfer functions and system moments of the adjoint network can be directly calculated from those of the original RLCG interconnect network by exploring symmetric properties of the MNA formulation. Therefore, the cost of constructing the congruence transformation matrix can be simplified by up to 50% of the previous methods. Comparative studies among various standard methods and the proposed methods are also investigated. Experimental results on large-scale RLCG interconnect circuits will demonstrate the accuracy and the efficiency of the proposed method.