New phase-noise model for crystal oscillators: application to the Clapp oscillator

Abstract

Leeson's is the basic model for predicting oscillator noise. A mathematical analysis of this "heuristic" model has been proposed. Both models do not detail the relative importance of the amplifier transfer function associated to its own noise with regard to that of the resonator. In this paper, an improved version of those previous models is presented. The phase noise generated by the amplifier and the one generated by the resonator are differentiated without considering their origins, such as the conversion of amplitude modulation noise into phase modulation noise. The power spectral densities of phase noise at various points of the oscillator loop are calculated from their respective correlation functions. As a consequence, the influence of the inner amplifier and resonator noises on the resulting oscillator noise is predictable. The model is especially attractive to the makers of widely used quartz oscillators. The resulting oscillator noise is easily obtained from the oscillator open-loop noise. An example of the phase-noise modeling of the Clapp quartz crystal oscillator is simulated and discussed.

A Low Phase Noise Crystal Oscillator with a Fast Start-Up Bandgap Reference for WLAN Applications

“…The output phase noise of reference clock sources is now considered a limiting factor for circuit and system performance in several applications, such as satellite communications and radar systems [27,28]. To achieve low phase noise in a crystal oscillator, several measures need to be taken to reduce noise contributions from various sources, such as the amplifier flicker noise, resonator flicker noise, resistor thermal noise, power supply noise, and nonlinear effects of the crystal [29][30][31]. In the future, researchers can focus on developing crystal oscillators with ultra-low phase noise [32,33], minimal frequency and temperature drift [34,35], fast start-up [36,37], and ultra-low power consumption [38,39], in order to cater to various application scenarios.…”

Analysis and design of low phase noise crystal oscillators

“…In the many theories and models of phase noise research [1][2][3][4][5][6][7][8][9][10], Leeson model is the most classic and convenient to use. In this paper, the methods to reduce phase noise of crystal oscillators are presented and feasibility of these methods is analyzed based on Leeson model.…”