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

Abstract

PurposeThe purpose of this paper is to find a closed relation for the phase noise of LC oscillators.Design/methodology/approachThe 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.FindingsThis 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 gm/ID method.Originality/valueA technology-independent method using the gm/ID method and the closed relationship is provided to calculate phase noise.