Phase-noise Analysis for single and Dual-mode Colpitts Crystal Oscillators

Leeson´s model (1996) is the basic model for predicting oscillator noise. The model is easy to understand and can be very useful in identifying sources and characteristics of oscillator noise. But, its main drawback lies in the fact that the amplifier gain is assumed to remain a constant versus the frequency close to the carrier frequency. Watannake (2000) describes the phase-noise characteristics and the analysis modeling of a dual-mode Colpitts oscillator, and the one pointed the Leeson´s limit to negative resistance oscillators, but it has not presented an improved model to analysis the phase-noise in dual-mode Colpitts oscillator. Watannake used Leeson´s to identify the phase-noise in dual-mode oscillators in which the impedance characteristics of the resonator and filter are negligible. Galliou (2003) presents an improved version of those previous models. The application of which model is to the Clapp crystal oscillator in the paper. The one pointed out that the model is especially attractive to the makers of widely used quartz oscillators. In this paper, we use Galliou (2003) new phase-noise model to analyze the negative resistance oscillators, such as the conventional and dual-mode Colpitts oscillators. The open loop transfer function modules and phase curve diagram of three kinds of circuits were given, and open-loop Q of three oscillators was calculated. By comparing with their open-Q value and open-loop f^-1 noise, the relationship of close loop nearer carrier and noise floor phase noise characteristics can be indirectly reflected