Sergey G. Rusakov

Simulation of high-Q oscillators

We present a new technique, based on a continuation method, for oscillator analysis using harmonic balance. With the use of Krylov subspace iterative linear solvers, harmonic balance has become a very powerful method for the analysis of general nonlinear circuits in the frequency domain. However, application of the harmonic balance method to the oscillator problem has been difficult due to the very small region of convergence. The main contribution of the paper is a robust and efficient continuation method that overcomes this problem.

Iterative solution of linear systems in harmonic balance analysis

Harmonic balance (HB) is a steady-state simulation technique of primary interest for RF and microwave circuits. Krylov subspace methods promise efficient solution of the large linear systems that arise in HB simulators. This paper deals with an experimental investigation of GMRES and QMR, two leading Krylov subspace methods as applied to the HB problem. The problem of coordinating the linear solvers accuracy with the error at the nonlinear level is also discussed.

A robust and efficient oscillator analysis technique using harmonic balance

In this paper, we present a new technique, based on a continuation method, for oscillator analysis using harmonic balance. With the use of Krylov subspace iterative linear solvers, harmonic balance has become a very powerful method for the analysis of general nonlinear circuits in the frequency domain. However, application of the harmonic balance method to the oscillator problem has been difficult. The strong dependence of the oscillator behavior on frequency, and the dependence of the frequency of oscillation on the circuit waveforms result in a very small region of convergence for harmonic balance. The main contribution of this paper is a robust and efficient continuation method to obtain global convergence.

The enchancing of efficiency of the harmonic balance analysis by adaptation of preconditioner to circuit nonlinearity

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 circuit has components being operated in a very nonlinear region. Even 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.

Analysis of oscillator injection locking by harmonic balance method

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.

Adaptive preconditioners for the simulation of extremely nonlinear circuits using harmonic balance

Krylov subspace techniques in harmonic balance simulations become increasingly ineffective when applied to strongly nonlinear circuits. This limitation is particularly important in the simulation of the nonlinear aspects of a circuit such as the 1 dB gain compression or if the circuit has components being operated in a very nonlinear region. Even if the circuit contains only a few very nonlinear components, Krylov methods using standard preconditioners can become ineffective. To overcome this problem, we present an adaptive preconditioner that dynamically exploits the properties of the harmonic balance Jacobian. With this technique we have been able to retain the advantages of Krylov methods even for strongly nonlinear circuits. Some numerical experiments illustrating the technique are presented.

New numerical technique for cyclostationary noise analysis of oscillators

A new numerical technique for cyclostationary noise analysis of oscillators is proposed. This technique is based on the transformation of the frequency conversion linear system for periodic small signal analysis. This transformation provides nonsingular matrix with zero frequency offset that allows to avoid numerical errors at small frequency offset values. The numerical examples are given to demonstrate the efficiency of the new approach.

Smoothed form of nonlinear phase macromodel for oscillators

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.

New computational technique for periodic distortion analysis of communication circuits

A new approach and technique for periodic distortion analysis is proposed. It is computationally efficient in comparison with complete nonlinear steady-state analysis. In contrast with the Volterra series approach this technique does not require high order derivatives of the device models. The numerical scheme of periodic distortion analysis is described. The technique is illustrated by examples of periodic distortion computation in nonlinear circuits using Spice-like simulator.

Approximation Approach for Timing Jitter Characterization in Circuit Simulators

A new computational concept of timing jitter is proposed that is suitable for exploitation in circuit simulators. It is based on the approximation of computed noise characteristics. To define jitter value the parameter representation is used. The desired parameters are obtained after noise simulation process in time domain by minimization of integral residual L/sub 2/-norm. The approach is illustrated by examples of jitter computation using spice-like simulator.