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.