Lucent Technologies Inc.

At+t Corp.

Roland Wilhelm Freund

Peter Feldmann

Zhaojun Bai

A processing unit of an analysis system comprises a processor coupled to a memory, and is configured to generate a structure-preserving reduced-order model of a circuit, device or system. The reduced-order model in one embodiment is generated by projection of input matrices characterizing the circuit, device or system onto at least one block Krylov subspace, the block Krylov subspace having a corresponding basis matrix. The projection utilizes at least one matrix that has a column range which includes a corresponding portion of the block Krylov subspace but is not itself the basis matrix of the block Krylov subspace. The processing unit generates a frequency response or other signal characterizing the circuit, device or system, based at least in part on the reduced-order model, and an associated output unit presents the generated signal in a user-perceptible format.

Method and apparatus for structure-preserving reduced-order modeling

A method and apparatus for controlling the pump powers of a broadband DWDM optical system using Raman amplification which determines pump settings that advantageously minimize the peak-to-peak ripple of the channel powers with respect to a given per-channel target. The illustrative method and apparatus first formulates a linear programming optimization problem, and then solves the formulated linear program in order to derive a new set of pump powers to be applied to the Raman amplification pumps. Illustratively, the linear program may be solved with use of any conventional linear programming solution technique, such as, for example, the simplex method.

Method and apparatus for controlling pump powers of broadband raman amplifiers used in optical transmission systems

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 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

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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New Providence, NJ, United States of America

Roland Wilhelm Freund