Closed-form and technology independent phase noise relation for LC oscillators

Abstract

Purpose

The purpose of this paper is to find a closed relation for the phase noise of LC oscillators.

Design/methodology/approach

The governing equation of oscillators is generally a stochastic nonlinear differential equation. In this paper, a closed relation for the phase noise of LC oscillators was obtained by approximating the I–V characteristic of the oscillator with third-degree polynomials and analyzing its differential equation.

Findings

This relation expresses phase noise directly in terms of circuit parameters, including the sizes of the transistors and the bias. Next, for evaluation, the phase noise of the cross-coupled oscillator without tail current was calculated with the proposed model. In this approach, the obtained equations are expressed independently of technology by combining the obtained phase noise relation and g_m/I_D method.

Originality/value

A technology-independent method using the g_m/I_D method and the closed relationship is provided to calculate phase noise.

Citation

Moradnezhad, M. and Miar-Naimi, H. (2023), "Closed-form and technology independent phase noise relation for LC oscillators", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 42 No. 3, pp. 804-823. https://doi.org/10.1108/COMPEL-10-2022-0356