Lucent Technologies Inc.

At+t Corp.

Peter Feldmann

Roland Wilhelm Freund

David Esley Long

Robert C Melville

Jaijeet S Roychowdhury

Zhaojun Bai

Methods and apparatus for performing non-linear analysis using preconditioners to reduce the computation and storage requirements associated with processing a system of equations. A circuit, system or other device to be analyzed includes n unknown waveforms, each characterized by N coefficients in the system of equations. A Jacobian matrix representative of the system of equations is generated. The Jacobian matrix may be in the form of an n&times;n sparse matrix of dense N&times;N blocks, such that each block is of size N,. In an illustrative embodiment, a low displacement rank preconditioner is applied to the Jacobian matrix in order to provide a preconditioned linear system. The preconditioner may be in the form of an n&times;n sparse matrix which includes compressed blocks which can be represented by substantially less than N,elements. For example, the compressed blocks may each be in the form of a low displacement rank matrix corresponding to a product of two generator matrices having dimension N&times;&agr;, where &agr;<<N. The preconditioned linear system may be solved by factoring the preconditioner using a sparse lower-upper (LU) factorization or other similar sparse factorization method applied to the compressed blocks.

Low-displacement rank preconditioners for simplified non-linear analysis of circuits and other devices

A noise-computation method that determines the noise power cross-spectral density matrix of an electronic circuit or system in the form of a closed form rational expression. More specifically, the method provides a matrix-Pade approximation of the noise power cross-spectral density matrix using a numerically robust and efficient block Lanczos-type method.

Method of modeling and analyzing electronic noise using Pade

A frequency-domain analysis method computes noise power spectral densities (PSDs) in nonlinear circuits. The method uses harmonic components of the periodic time-varying PSD of cyclostationary noise, i.e., harmonic power spectral densities which are deterministic functions that describe the time-varying second-order statistics of cyclostationary noise. A block-structured matrix equation is used which relates output noise statistics to input noise statistics. By exploiting Toeplitz block structure, an efficient noise calculation method requires O(nN log N) computation time and O(nN) memory, where n is the circuit size and N is the number of significant harmonics in the circuit's steady state. The method successfully treats device noise sources with arbitrarily shaped PSDs (including thermal, shot, and flicker noises), handles noise input correlations and computes correlations between different outputs.

Method of making an integrated circuit including noise modeling and

A method and apparatus for generating and analyzing a reduced-order model of a linear circuit. The method and apparatus generates the symmetric multi-port transfer function of an RLC circuit. The invention employs a novel symmetric block-Lanczos-type procedure, termed SyMPVL for Symmetric Matrix Pade via Lanczos, to reduce original circuit matrices to a pair of banded symmetric matrices. When the circuit comprises only two of the three RLC components, the matrices are also positive definite. These matrices are typically much smaller than the original circuit matrices and determine a reduced-order model of the original multi-port transfer function of the circuit. The reduced transfer function represents a matrix-Pade approximation of the original multi-port matrix transfer function.

Apparatus and method for analyzing passive circuits using reduced-order

A method and apparatus for generating and analyzing reduced-order models of linear circuits. The method and apparatus generates a characteristic tridiagonal matrix using a look-ahead Lanczos procedure and then checks the matrix for stability and passivity. If the matrix is not stable and passive, the matrix is modified via a partial Pade via Lanczos approximation algorithm and then rechecked for passivity and stability. The process is iterated until a passive and stable model is generated. When a satisfactory matrix is generated, a Pade approximant of a transfer function of the circuit is computed and the frequency response of this circuit is generated and displayed.

Apparatus and method for analyzing circuits using reduced-order modeling

Methods and apparatus for performing frequency domain analysis using compressed matrix storage to reduce the computation and storage requirements associated with processing a system of harmonic balance equations. A nonlinear circuit, system or other device to be analyzed includes n unknown node spectra, each characterized by N spectral coefficients in the system of harmonic balance equations. A compressed version of a Jacobian matrix J representing the system of harmonic balance equations is generated by forming m sequences of length N using one or more block-diagonal matrices associated with the Jacobian matrix J, converting each of the m sequences to the frequency domain using a discrete Fourier transform, such that a set of Fourier coefficients are generated for each of the m sequences, and storing only those Fourier coefficients which exceed a threshold as the compressed version of the Jacobian matrix J. Information generated from an inverse transform of the compressed version is utilized to solve a preconditioned linear system J.sup.-1 JZ=J.sup.-1 W which is based on an approximation J of the Jacobian matrix J.

Efficient frequency domain analysis of large nonlinear analog circuits

A circuit analyzer and method are disclosed for generating and outputting a Matrix Pade via Lanczos (MPVL) approximation of a frequency response of a circuit from input circuit parameters. A processing unit has a memory for storing circuit characteristic data representing a circuit; a program for generating matrix transfer function data relating to a matrix transfer function associated with the circuit characteristic data; a processor for executing the program; and the processing unit generates the frequency response signal in response to the matrix transfer function data.

A circuit analyzer and method are disclosed for generating and outputting a Pade via Lanczos (PVL) approximation of a frequency response of a circuit from input circuit parameters. A processing unit having a processor, memory, and stored programs processes the input circuit parameters, determines a block tridiagonal matrix by an iterative look-ahead Lanczos procedure, and calculates a Pade approximant from the block tridiagonal matrix, including poles, zeros, and residues. The look-ahead Lanczos procedure employs non-singular matrices to ensure numerical stability of the iterative calculation of the components of the block tridiagonal matrix. The output is an approximation of a plurality of frequencies at which any poles and zeros of the impulse response of the circuit occur. A graphical representation of the approximated frequency response is also produced, and qualitative measurements of the accuracy of the approximated poles are provided.

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Short Hills, NJ, United States of America

Peter Feldmann