Simplified phase noise model for negative resistance oscillators

This paper describes a greatly simplified model for the prediction of phase noise in oscillators which use a negative resistance as the active element. It is based on a simple circuit consisting of the parallel addition of a noise current, a negative admittance/resistance and a parallel (Q limited) resonant circuit. The transfer function is calculated as a forward trans-resistance (V_OUT/I_IN) and then converted to power. The effect of limiting is incorporated by assuming that the phase noise element of the noise floor is KT/2 ie -177dBm/Hz at room temperature. The answer is the same as more complex analyses but enables a simple clear insight into the operation of oscillators. The phase noise for a given power in the resonator in the resonator appears to be lower than in feedback oscillators. The reasons for this are explained.