Lucent Technologies Inc.

Robert C Melville

David Esley Long

Peter Feldmann

Jaijeet S Roychowdhury

Venugopal Gopinathan

Peter R Kinget

Two or more equal amplitude periodic output signals which are mutually shifted in phase by an integer fraction of 360 degrees, such as 90&deg;, are generated by injection locking a ring type oscillator circuit arrangement with a periodic low phase noise signal source. More particularly, a first ring oscillator is injection locked by a low phase noise signal source, one having a noise characteristic which meets the GSM radio standard of at least &minus;132 dBc/Hz at a 3 MHz offset. An identical second ring oscillator is then driven with the output of the first ring oscillator. In one circuit configuration, an even numbered, e.g., a four stage ring oscillator is injection locked to a low-phase noise oscillator having a predetermined noise specification which is application specific and wherein a second even numbered stage, e.g., a four stage ring oscillator is coupled to the first ring oscillator. In a second circuit configuration, a first odd numbered, e.g., three stage ring oscillator, is injection locked to a low phase-noise oscillator and a second odd numbered, e.g., three stage ring oscillator, is injection locked to the first ring oscillator.

Injection locked multi-phase signal generator

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

Systems and methods that include a homotopy technique are employed to find a DC operating point of large-scale, transistor-based, nonlinear circuits�, allowing such circuits to be designed, tested and manufactured!. The systems and methods use arclength continuation together with a new two-phase embedding of .lambda. into equations describing the circuits. One of the systems includes: (1) a DC operating point determination circuit (or determinor) that receives parameters relating to the nonlinear circuit into a globally-convergent model thereof and embeds therein at least two arclength continuation parameters relating to driving-point and transfer characteristics of a transistor in the nonlinear circuit�, the DC operating point determination circuit capable of adjusting the arclength continuation parameters to cause the globally-convergent model to converge on a DC operating point for the nonlinear circuit! and (2) an analysis circuit, coupled to the DC operating point determination circuit, that employs the DC operating point to determine an overall response characteristic of the nonlinear circuit

Systems and methods for testing and manufacturing large-scale,

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.

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New Providence, NJ, United States of America

Robert C Melville