A Study of Marginal Oscillator Behavior

In a magnetic resonance spectrometer, a marginal oscillator is used as a transducer to convert a minute change in the tank coil resistance into a change in the amplitude of oscillation. Thus one can define a conversion gain as the ratio of the fractional change in the amplitude of oscillation to the fractional change in the tank coil resistance. Since the change in the tank coil resistance is made periodic at a low frequency to facilitate phase-sensitive detection, a study of the transient behavior of the oscillator becomes important. In this paper, the conversion gain, bandwidth, and noise associated with the oscillator are studied as functions of the circuit parameters, utilizing a piecewise linear characteristic for the active device. Unlike the studies carried out by other authors making use of a polynomial expansion for the nonlinear characteristic, the piecewise linear characteristic has been chosen because it is more amenable to synthesis. The sensitivity of the amplitude of oscillation to the variation of the characteristics of the active device has also been evaluated, and the relationship between the stability requirement of the device characteristics and the conversion gain has been established.