Lucent Technologies Inc.

Agere Systems Inc.

Other

Jaijeet S Roychowdhury

Alper Demir

David Esley Long

Peter Feldmann

Robert C Melville

Onuttom Narayan

Amit Mehrotra

An apparatus for, and method of, modeling a time-varying system and a computer-readable storage medium containing the apparatus or the method. In one embodiment, the apparatus includes: (1) a transfer function generator that develops, for the system, a linear, time-varying transfer function of a particular order and having separate scales corresponding to time variations in the system and an input thereto and (2) an approximator, coupled to the transfer function generator, that approximates the transfer function to yield a model of an order lower than the particular order.

Apparatus and method for reduced-order modeling of time-varying systems and computer storage medium containing the same

The phase noise of an oscillator described by a known set of differential algebraic equations (DAEs) can be predicted by a) finding the steady state waveform of the oscillator, e.g., by using harmonic balance techniques or so-called &ldquo;shooting&rdquo; techniques, either of which involves developing a mathematical quantity known as the augmented Jacobian matrix; b) solving a prescribed linear system of equations that uses the augmented Jacobian matrix, the solution being called a perturbation projection vector (PPV), c) plotting a graph of the phase noise of the oscillator as a Lorentzian function of the solution of the prescribed linear system of equations. The prescribed linear system of equations which is used is the system of equations formed by setting a matrix product equal to a unit vector.

Oscillator phase noise prediction

A system for, and method of, analyzing a forced or unforced oscillator. In one embodiment the system includes: (1) a transformation circuit that transforms a frequency-modulated waveform representing an output of the oscillator into a function based on at least two time scales and (2) a numeric analyzer, associated with the transformation circuit, that warps at least one of the at least two time scales and thereafter numerically analyzes the function to determine a frequency thereof.

System and method for analyzing forced and unforced oscillators

A nonlinear analysis for characterizing phase noise and timing jitter in oscillators is disclosed. The method and apparatus utilize a nonlinear differential equation to characterize the phase error of a given oscillator. A precise stochastic characterization of timing jitter and spectral dispersion is also disclosed based on the nonlinear differential equation. Representative time and frequency domain computational techniques are disclosed for characterizing the phase noise and timing jitter of circuits. In addition, a single scalar constant, c, is utilized to describe jitter and spectral spreading in a noisy oscillator.

Method and apparatus for characterizing phase noise and timing jitter in

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

Novel algorithms for computing the responses of circuits to multi-tone excitations. The new algorithms are efficient and robust for large, strongly nonlinear circuits excited by multi-tone (quasi-periodic or envelope-modulated) signals. Hence they are particularly useful for integrated RF applications. The multivariate representation captures features produced by strong nonlinearities (such as spikes or pulses) much more compactly than traditional frequency- or time-domain representations. The new algorithms compute these functions efficiently by solving a partial differential equation ODE) in the time or mixed frequency-time domains. Frequency-domain spectra or time-domain waveforms are generated from the multivariate functions as cheap post-processing steps. Two methods, multivariate FDTD and hierarchical shooting, are purely time-domain techniques suitable for the general strongly nonlinear circuit problem. They differ in their memory and computation needs. A new mixed frequency-time method is more efficient for circuits that are moderately (but not strongly) nonlinear in one or more tones (e.g., switching mixers, switched-capacitor filters). The linear systems at the core of all three techniques are especially well suited for iterative solution. This is exploited in the methods to achieve linear growth of computation and memory with respect to circuit size. The mixed frequency-time method of this work avoids the ill-conditioning problem by computing with the slow harmonic components directly, rather than with time-domain samples at sets of points close to each other.

Method and apparatus for efficient design and analysis of integrated

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,

Systems and methods for determining one or more characteristics of a singular circuit, allowing such circuits to be efficiently designed, tested and manufactured. One of the systems includes: (1) a minimum least-squares ('MLS') determination circuit that receives parameters relating to the singular circuit into a matrix A, determines range and null spaces for the matrix A, applies an orthonormalization procedure to determine a solution x to Ax=b', where b' is an orthogonal projection of a known vector b onto the range space of the matrix A and derives an MLS solution from the solution x and (2) a simulation circuit, coupled to the MLS determination circuit, that employs the MLS solution to simulate an operation of the singular circuit and determine the characteristic therefrom.

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Murray Hill, NJ, United States of America

Jaijeet S Roychowdhury