Rigorous Q Factor Formulation and Characterization for Nonlinear Oscillators

TL;DR

This paper introduces a rigorous, universally applicable definition of the Q factor for nonlinear oscillators, enabling accurate amplitude stability assessment across various oscillator types.

Contribution

It proposes a new, rigorous Q factor formulation for nonlinear oscillators, extending beyond traditional linear or specific topology limitations.

Findings

The new Q definition can be computed numerically from oscillator equations.

Application to various oscillator types confirms its effectiveness.

The formulation enhances oscillator characterization techniques.

Abstract

In this paper, we discuss the definition of Q factor for nonlinear oscillators. While available definitions of Q are often limited to linear resonators or oscillators with specific topologies, our definition is applicable to any oscillator as a figure of merit for its amplitude stability. It can be formulated rigorously and computed numerically from oscillator equations. With this definition, we calculate and analyze the Q factors of several oscillators of different types. The results confirm that the proposed Q formulation is a useful addition to the characterization techniques for oscillators.