A new approach to analyze injection locking mode of oscillators under small external excitation is proposed. The proposed approach exploits existence conditions of the solution of HB linear system with degenerate matrix. The method allows one to obtain the locking range for an arbitrary oscillator circuit with an arbitrary periodic injection waveform. The approach can be easily implemented into a circuit simulator. Examples are given to confirm the correctness of the new approach.

This paper proposes an improvement to the well-known oscillator nonlinear phase macromodel based on Floquet theory. A smoothed form of the nonlinear phase macromodel is derived by eliminating highly oscillatory terms in the macromodel, resulting in a significant speed-up in transient simulation. For an LC oscillator under sinusoidal excitation the new macromodel is equivalent to the Adler model. Numerical experiments confirm a considerable decrease of computational efforts. It is further shown that the new macromodel allows one to perform phase noise analysis of locked oscillators under arbitrary periodic injection.

Injection locking of oscillators subject to small periodic excitations is derived from existence conditions of the solution of the small signal harmonic balance degenerate system. The resulting expression for the locking range can be applied to any oscillator circuit with arbitrary periodic injection waveform, and can be easily implemented into a circuit simulator. The application of the general expression to some special cases is considered, and comparison with known results is given. Theoretical results are confirmed by SPICE simulations.

A new computational technique for nonlinear distortion is presented. Unlike Volterra series this technique doesn't require computation of the second and third derivatives of device models. The approach is oriented for implementation in Spice-like simulators

A new numerical technique for periodic small signal analysis, based on the harmonic balance method, is proposed. Special-purpose numerical procedures, based on Krylov subspace methods, are developed that reduce the computational efforts of solving linear problems under frequency sweeping. Examples are given to show the efficiency of the new algorithm for computing the small signal characteristics for typical RF circuits.

The paper presents a new approach to the problem of automatic order reducing of rational transfer function (TF). The approach is directed to obtain low-order models under criterion of minimal integral square error. The developed computational scheme allows to determine reduced model of the minimal order with the given error tolerance.

Krylov subspace techniques in harmonic balance simulations become increasingly ineffective when applied to strongly nonlinear circuits.This limitation is particularly important in the simulation if the circu it has components being operated in a very nonlinear region.Ev en if the circuit contains only a few very nonlinear components, Krylov methods using standard preconditioners can become ineffective.To overcome this problem, we present two adaptive preconditioners that dynamically exploit the properties of the harmonic balance Jacobian.With these techniques we have been able to retain the advantages of Krylov methods even for strongly nonlinear circuits.Some numerical experiments illustrating the techniques are presented.

A new method for computation of timing jitter in a PLL is proposed. The computational method is based on the representation of the circuit as a linear time-varying system with modulated stationary noise models, spectral decomposition of stochastic process and decomposition of noise into orthogonal components i.e. phase and amplitude noise. The method is illustrated by examples of jitter computation in PLLs.

This paper discusses the problem of numerical stability analysis of large networks in electrical circuit simulators. It is proposed to apply a numerical technique that combines a highly efficient algorithm for fast computation of poles with reliable identification of instability. The approach is oriented toward implementation in Spice-like simulators.

A technique to accelerate harmonic balance (HB) analysis by taking into account frequency domain latency is presented. The algorithm automatically determines the individual number of harmonics for different nodes. The algorithm is based on Krylov subspace iterative techniques and provides selective estimation of residual norm under reducing dimension.

A new method for transient noise analysis of nonlinear circuits is presented. The method is based on the presentation of a circuit as a linear time-varying system with modulated stationary noise models. The equations of the method are derived and their solution is described. The expression needed to compute the complete probabilistic characterization of a circuit is presented. The method can be easily applied to noise analysis of RF circuits with periodic large-signal excitation.

A three-dimensional process simulator in which both the standard nonlinear diffusion model and a five-species kinetic model are implemented to model phosphorus diffusion in silicon is described. The reaction-diffusion equations are discretized using finite differences in space and the numerical method of lines. The resulting ordinary differential equations are solved using the system integrator LSODP. LSODP uses a backward difference formula for time integration and a Krylov projection method to solve the linear system in the inner Newton loop. Comparisons of the two diffusion models are run on several test problems. Results show that the Krylov approach works well for the mildly asymmetric system of the single species, but requires a large dimension (K/sub m/ approximately=20) subspace for the five-species model.>

PEPPER is a computer program that simulates in one dimension the ion implantation, diffusion, oxidation, epitaxy, deposition, and etch processes used in VLSI technology. The program contains an efficient Monte Carlo ion implantation algorithm that includes explicit calculation of ion channeling and damage. The key feature of the diffusion calculation is a general partial differential equation solver for rapid prototyping of physical models. The solver has been used to develop several unique diffusion models. A novel model for impurity diffusion in polysilicon treats the problem as a two-stream process, with relatively slow standard diffusion within the grain and a much more rapid component of diffusion along the grain boundaries. The two components are coupled at each point by a segregation term. Two other models for impurity diffusion in silicon include explicit calculation of the coupling of point defects with impurities. One of the point-defect models is a general and detailed formulation from a chemical kinetics viewpoint, while the other makes further assumptions to simplify the model for engineering analysis.>