Abstract: A complete model numerical solver resides on an embedded processor for real time control of a system. The solver eliminates the need for custom embedded code, requiring only model equations, definition of the independent and dependent variables, parameters and input sources information as input to solve the model equations directly. Through elimination of the need for custom code, the solver speeds up the model deployment process and provides the control application sophisticated features such as Automatic Differentiation, sensitivity analysis, sparse linear algebra techniques and adaptive step size in solving the model concurrently.

Abstract: A complete model numerical solver resides on an embedded processor for real time control of a system. The solver eliminates the need for custom embedded code, requiring only model equations, definition of the independent and dependent variables, parameters and input sources information as input to solve the model equations directly. Through elimination of the need for custom code, the solver speeds up the model deployment process and provides the control application sophisticated features such as Automatic Differentiation, sensitivity analysis, sparse linear algebra techniques and adaptive step size in solving the model concurrently.

Abstract: A complete model numerical solver resides on an embedded processor for real time control of a system. The solver eliminates the need for custom embedded code, requiring only model equations, definition of the independent and dependent variables, parameters and input sources information as input to solve the model equations directly. Through elimination of the need for custom code, the solver speeds up the model deployment process and provides the control application sophisticated features such as Automatic Differentiation, sensitivity analysis, sparse linear algebra techniques and adaptive step size in solving the model concurrently.

Abstract: A complete model numerical solver resides on an embedded processor for real time control of a system. The solver eliminates the need for custom embedded code, requiring only model equations, definition of the independent and dependent variables, parameters and input sources information as input to solve the model equations directly. Through elimination of the need for custom code, the solver speeds up the model deployment process and provides the control application sophisticated features such as Automatic Differentiation, sensitivity analysis, sparse linear algebra techniques and adaptive step size in solving the model concurrently.

Abstract: Two or more equal amplitude periodic output signals which are mutually shifted in phase by an integer fraction of 360 degrees, such as 90°, 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 −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.

Abstract: 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×n sparse matrix of dense N×N blocks, such that each block is of size N2. 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×n sparse matrix which includes compressed blocks which can be represented by substantially less than N2 elements.

Abstract: 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.

Abstract: 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.

Abstract: A new class of circuit simulation methods comprises a homotopy that is constructed by employing particular models of the nonlinear elements of the circuit and by including a randomizing component in the homotopy equation. In particular, the models of the non-linear elements are passive, in the sense that they contain no negative resistors and no voltage dependent sources. Also, the models are smooth enough to at least have well-defined first and second order derivatives. One such homotopy is (1-t)(Bx+a)+tF(x)=0, where B is a randomizing matrix and a is a randomizing vector, t is the continuation parameter, x is a vector of the circuit's node voltages, and F(x) is a set of equations such that F(x)=0 describes the circuit. Another is the homotopy (1-t)(F.sub.A (x)+a)+tF.sub.B (x)+.sigma.(t)(x-a) where F.sub.B (x)=0 describes the circuit whose dc operating point is sought, F.sub.A (x)=0 describes a circuit whose dc operating point is known, and .sigma.(t) is a function that is 0 at t=0 and t=1.