Null network oscillators

The paper deals with the frequency stability of a class of oscillators with two feedback paths, one containing a null network representable by a transfer function K/(1 - jb/u), and the other a frequency independent attenuator of gain δ. The latter provides the finite feedback voltage necessary to maintain oscillations at the null frequency and usually incorporates nonlinear thermal dements such as lamps or thermistors for amplitude stabilization. Such oscillators are important and interesting because 1) the overall feedback can be arranged to be degenerative at practically all but the oscillating frequency with consequent improvement in waveform, and 2) their frequency stability, which can be shown to depend inversely on δ and hence directly on the gain of the maintaining amplifier, can be made quite high. A general theory for the frequency stability of these oscillator circuits is developed and it is shown that the figure of merit of a particular null network for oscillator applications is its "sensitivity factor": -K/b. A number of illustrative examples show how the theory can be applied to determine the frequency stability of a wide variety of such circuits and for the synthesis of the optimum configuration of any particular null network for oscillator applications.