B.J. Mulvaney

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.

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.

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 methods for speeding up computation of Newton updates in harmonic balance

A new adaptive approach to solving large-dimension harmonic balance (HB) problems in RF circuit simulation is presented. The method is based on adjusting the order of the equation system according to the degree of nonlinearity of each node in the circuit. A block-diagonal preconditioner is used to construct an algorithm for order reduction during the iterative HB process.

Evaluation of Oscillator Phase and Frequency Transfer Functions

A general expression for the phase transfer functions of an oscillator for frequencies close to the harmonics of the oscillator fundamental is derived. Numerical testing and comparison with some known results are performed.

Injection locking conditions under small periodic excitations

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.

Circuit distortion analysis based on the simplified Newton's method

A new computational technique for distortion analysis of nonlinear circuits is presented. The new technique is applicable to the same class of circuits, namely, weakly nonlinear and time-varying circuits, as the periodic Volterra series. However, unlike the Volterra series, it does not require the computation of the second and third derivatives of device models. The new method is computationally efficient compared with a complete multitone nonlinear steady-state analysis such as harmonic balance. Moreover, the new technique naturally allows computing and characterizing the contributions of individual circuit components to the overall circuit distortion. This paper presents the theory of the new technique, a discussion of the numerical aspects, and numerical results.

A numerical technique for time domain noise analysis of oscillators

A new numerical technique for time domain noise analysis of oscillators is proposed. This technique is based on the linear periodically time varying model, with an equivalent transformation of the linear system. This transformation produces a nonsingular matrix when the frequency offset is zero, which avoids numerical errors at small offset frequencies. Examples are given to demonstrate the efficiency of the new approach.

Frequency adjusting numerical technique for oscillator simulation

The special-purpose numerical continuation procedure for oscillator simulation is presented. The procedure allows to extend the convergence region and supports automatic guess of starting frequency point for continuation process.