Phase noise of electrical oscillators due to multi‐Lorentzian noise sources based on the LTV model

Abstract

Using the general expression of the phase variance expressed by the linear time variant (LTV) phase noise model, phase variances due to multi‐Lorentzian and white noise sources of electrical oscillators have been extracted and phase noise expressions due to white and Flicker noises have been calculated. Despite the basic LTV model in which the expressed phase noise due to white noise is valid for offset frequencies larger than the −3 dB corner frequency of the output and it tends to infinity for small offset frequencies, in the proposed model, the extracted phase noises due to white and Flicker noises are valid for the entire spectrum and become limited for small offset frequencies. Comparison between the results of the proposed model by those of the harmonic balance technique shows the validity of the model. Also, the effects of the physical parameters of the oscillator circuit on the extracted phase noise can be observed in the expressions. The proposed model is applicable to calculate the phase noise of the oscillators with single perturbation source applied to the intended output node.