The Effect of Background Noise on the Operation of Oscillators†

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Abstract
A method for the analysis of the effect of noise on the output of oscillators is presented. The method is based on the balance between the equivalent linearization parameters of the oscillator and the noise. The presence of the noise moves the poles of the equivalent and noise-free linear model to the left, causing the oscillator to operate as a negative resistance noise amplifier with extremely high gain and selectivity. The variations in the envelope of the noise amplifier output are strongly suppressed by the amplitude-control action of the oscillator non-linearity, the effect of the non-linearity being equivalent to gain changes of the noise amplifier which keep the output almost constant. Expressions are derived for the autocorrelation function and spectral density of the oscillator output. The model of the oscillator analysed is composed of an L—C tank circuit, an active non-linear part which presents to the tank an equivalent negative conductance, and an amplitude control mechanism controlling the amplitude by controlling the value of the negative conductance presented to the tank. The results cover oscillators with instantaneous non-linearity as well as oscillators with separate automatic amplitude control.

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