We present theoretical foundations about error estimations of the global Krylov subspace techniques for multiple-inputs multiple-outputs (MIMO) Interconnect reductions. Analytical relationships between Lyapunov functions of the original interconnect network and those of the reduced system generated by the global Arnoldi algorithm will be developed. Under this framework, a new moment matching reduced network is proposed. Also, we will show that the reduced system can be expressed as the original network with some additive perturbations.

This paper presents a methodology based on congruent transformation for distributed interconnects described by state-space time-delays system. The proposed approach is to obtain the passive reduced order of linear time-delays system. The unified formulations are used to satisfy the passive preservation. The details of the mathematical proof and a couple of validation examples are given in this paper.

The global Lanczos algorithm for solving the RLCG interconnect circuits is presented in this paper. This algorithm is an extension of the standard Lanczos algorithm for multiple-inputs multiple-outputs (MIMO) systems. A new matrix Krylov subspace will be developed first. By employing the congruence transformation with the matrix Krylov subspace, the two-side oblique projection-based method can be used to construct a reduced-order system. It will be shown that the system moments are still matched. The error of the 2q-th order system moment will be derived analytically. Furthermore, two novel model-order reduction techniques called the multiple point global Lanczos (MPGL) method and the adaptive-order global Lanczos (AOGL) method which are both based on the multiple point moment matching are proposed. The frequency responses using the multiple point moment matching method have higher coherence to the original system than those using the single point expansion method. Finally, simulation results on frequency domain will illustrate the feasibility and the efficiency of the proposed methods.

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 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.