In recent years, order-reduction techniques based on Krylov subspaces have become the methods of choice for generating macromodels of large multi-port RLC circuits. A widely-used method of this type is PRIMA. Its main features are provably passive reduced-order models and a moment-matching property. On the other hand, PRIMA does not preserve other structures, such as reciprocity or the block structure of the circuit matrices, inherent to RLC circuits, which makes it harder to synthesize the PRIMA models as actual circuits. Moreover, the PRIMA models match only half as many moments as optimal, but non-passive, moment-matching techniques such as SyMPVL. In this paper, we propose the reduction technique SPRIM that overcomes these disadvantages of PRIMA. In particular, SPRIM generates provably passive and reciprocal macromodels of multi-port RLC circuits, and the SPRIM models match twice as many moments as the corresponding PRIMA models obtained with identical computational work. Numerical results are reported that illustrate the higher accuracy of SPRIM vs. PRIMA.

This paper studies a projection technique based on block Krylov subspaces for the computation of reduced-order models of multiport RLC circuits.We show that these models are always passive, yet they still match at least half as many moments as the corresponding reduced-order models based on matrix-Padé approximation.For RC, RL, and LC circuits, the reduced-order models obtained by projection and matrix-Padé approximation are identical.For general RLC circuits, we show how the projection technique can easily be incorporated into the SyMPVL algorithm to obtain passive reduced-order models, in addition to the high-accuracy matrix-Padé approximations that characterize SyMPVL, at essentially no extra computational costs.Connections between SyMPVL and the recently proposed reduced-order modeling algorithm PRIMA are also discussed.Numerical results for interconnect simulation problems are reported.

This paper introduces SyMPVL, an algorithm for the approximation of the symmetric multi-port transfer function of an RLC circuit. The algorithm employs a symmetric block-Lanczos algorithm to reduce the original circuit matrices to a pair of typically much smaller, banded, symmetric matrices. These matrices determine a matrix-Pade approximation of the multi-port transfer function, and can serve as a reduced-order model of the original circuit. They can be "stamped" directly into the Jacobian matrix of a SPICE-type circuit simulator, or can be used to synthesize an equivalent smaller circuit. We also prove stability and passivity of the reduced-order models in the RL, RC, and LC special cases, and report numerical results for SyMPVL applied to example circuits.

This paper introduces a new circuit noise analysis and modeling method. The noise analysis method computes an analytic expression of frequency, in rational form, which represents the Pade approximation of the noise power spectral density. The approximation can be carried out efficiently, to the required accuracy, using a variant of the PVL or MPVL algorithms. The new method is significantly more efficient than traditional methods for noise computation, at numerous frequency points. In addition, it allows for a compact and cascadable modeling of noise that can be used in system level simulations.

This paper discusses the analysis of large linear electrical networks consisting of passive components, such as resistors, capacitors, inductors, and transformers. Such networks admit a symmetric formulation of their circuit equations. We introduce SyPVL, an efficient and numerically stable algorithm for the computation of reduced-order models of large, linear, passive networks. SyPVL represents the specialization of the more general PVL algorithm, to symmetric problems. Besides the gain in efficiency over PVL, SyPVL also preserves the symmetry of the problem, and, as a consequence, can often guarantee the stability of the resulting reduced-order models. Moreover, these reduced-order models can be synthesized as actual physical circuits, thus facilitating compatibility with existing analysis tools. The application of SyPVL is illustrated with two interconnect-analysis examples.

The quasi-minimal residual (QMR) algorithm is a Krylov-subspace method for the iterative solution of large non-Hermitian linear systems. QMR is based on the look-ahead Lanczos algorithm that, by itself, can also be used to obtain approximate eigenvalues of large non-Hermitian matrices. QMRPACK is a software package with Fortran 77 implementations of the QMR algorithm and variants thereof, and of the three-term and coupled two-term look-ahead Lanczos algorithms. In this article, we discuss some of the features of the algorithms in the package, with emphasis on the issues related to using the codes. We describe in some detail two routines from the package, one for the solution of linear systems and the other for the computation of eigenvalue approximations. We present some numerical examples from applications where QMRPACK was used.

A method for the e�cient computation of accu� rate reduced�order models of large linear circuits is de� scribed. The method � called MPVL � employs a novel block Lanczos algorithm to compute matrix Pad�e ap� proximations of matrix�valued network transfer func� tions. The reduced�order models � computed to the re� quired level of accuracy � are used tospeed up the anal� ysis of circuits containing large linear blocks. The lin� ear blocks are replaced by their reduced�order models� and the resulting smaller circuit can be analyzed with general�purpose simulators � with signi�cant savings in simulation time and � practically � no loss of accuracy. 1

In this paper, we introduce PVL, an algorithm for computing the Pade approximation of Laplace-domain transfer functions of large linear networks via a Lanczos process. The PVL algorithm has significantly superior numerical stability, while retaining the same efficiency as algorithms that compute the Pade approximation directly through moment matching, such as AWE and its derivatives. As a consequence, it produces more accurate and higher-order approximations, and it renders unnecessary many of the heuristics that AWE and its derivatives had to employ. The algorithm also computes an error bound that permits to identify the true poles and zeros of the original network. We present results of numerical experiments with the PVL algorithm for several large examples.>