Piecewise Semi-Analytical Formulation for the Analysis of Coupled-Oscillator Systems

TL;DR

This paper introduces a piecewise semi-analytical method for analyzing coupled oscillator systems, improving accuracy in predicting synchronization ranges and validated through simulations and measurements at GHz frequencies.

Contribution

It extends the admittance function model to a piecewise linear form, enhancing the analysis of coupled oscillators beyond previous local formulations.

Findings

Significantly improved prediction of synchronization ranges.

Good agreement with circuit-level simulations.

Accurate results validated by measurements at 5 GHz.

Abstract

A new simulation technique to obtain the synchronized steady-state solutions existing in coupled oscillator systems is presented. The technique departs from a semi-analytical formulation presented in previous works. It extends the model of the admittance function describing each individual oscillator to a piecewise linear one. This provides a global formulation of the coupled system, considering the whole characteristic of each voltage-controlled oscillator (VCO) in the array. In comparison with the previous local formulation, the new formulation significantly improves the accuracy in the prediction of the system synchronization ranges. The technique has been tested by comparison with computationally demanding circuit-level Harmonic Balance simulations in an array of Van der Pol-type oscillators and then applied to a coupled system of FET based oscillators at 5 GHz, with very good agreement with measurements.