Phase noise analysis of sinusoidal oscillators based on forced-oscillation model

This paper analyzes output voltage on the assumption of short-term coherency for two types of sinusoidal oscillator circuit including a noise source. The output voltage for a negative-resistance oscillator is formulated as a differential equation of forced oscillation in time domain. The solution represents a superposition of a free running oscillation voltage and an output noise voltage. The expression of the power ratio results in an equation with the active Q which coincides approximately with the Leeson´s equation. The output noise voltage is also obtained for a FET oscillator from circuit analysis in frequency domain. Applying the active Q, the output voltage is confirmed to give an output noise power in the same fashion as the Leeson´s spectrum model.