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.

A new moment computation technique for general lumped R(L)C interconnect circuits with multiple resistor loops is proposed. Using the concept of tearing, a lumped R(L)C network can be partitioned into a spanning tree and several resistor links. The contributions of network moments from each tree and the corresponding links can be determined independently. By combining the conventional moment computation algorithms and the reduced ordered binary decision diagram (ROBDD), the proposed method can compute system moments efficiently. Experimental results have demonstrate that the proposed method can indeed obtain accurate moments and is more efficient than the conventional approach.

A new indirect approach for designing low-order linear-phase IIR filters is presented in this paper. Given an FIR filter, we utilize a new Krylov subspace projection method, called the rational Arnoldi method with adaptive orders, to synthesize an approximated IIR filter with small orders. The synthesized IIR filter can truly reflect essential dynamical features of the original FIR filter and indeed satisfies the design specifications. Also, from simulation results, it can be observed that the linear-phase property in the passband is stilled retained. This indirect approach is accomplished using the state-space realization of FIR filters, multi-point Pade approximations, the Arnoldi algorithm, and an intelligent scheme to select expansion points in the frequency domain. Such methods are quite efficient in terms of computational complexity. Fundamental developments of the proposed method will be discussed in details. Numerical results will demonstrate the accuracy and the efficiency of this two-step indirect method.

A method is proposed to compute moments of distributed coupled RLC interconnects. Both uniform line models and non-uniform line models will be developed. Considering both self inductances and mutual inductances in multi-conductors, recursive moment computations formulae of lumped coupled RLC interconnects are extended to those of distributed coupled RLC interconnects. By using the moment computation technique in conjunction with the projection-based order reduction method, the inductive crosstalk noise waveform can be accurately and efficiently estimated. Fundamental developments of the proposed approach will be described. Simulation results demonstrate the improved accuracy of the proposed method over the traditional lumped methods.

A novel method is presented to compute moments of high-speed VLSI interconnects, which are modeled as coupled RLC trees. Recursive formulae of moments of coupled RC trees are extended to those for coupled RLC trees by considering both self inductances and mutual inductances. Analytical formulae for voltage moments at each node are derived explicitly. The formulae can be efficiently used for estimating delay and crosstalk noise. The inductive crosstalk noise waveform can be accurately and efficiently estimated using the moment computation technique in conjunction with the projection-based order reduction method. Fundamental aspects of the proposed approach are described in details. Experimental results show the increased accuracy of the proposed method over that of the traditional ones.

Projection-based model reductions become a necessity for efficient interconnect modeling and simulations. In order to choose the order of the reduced system that can really reflect the essential dynamics of the original interconnect, the residual error of the transfer function can be considered as a stopping criteria to terminate the Arnoldi iteration process. Analytical expressions of this residual error are derived in detail. Furthermore, it can be found that the approximate transfer function can also be expressed as the original interconnect model with some additive perturbations. The perturbation matrix only involves resultant vectors at the previous step of the Arnoldi algorithm. These error information will provide a guideline for the order selection scheme used in the Krylov subspace model-order algorithm.