On the Oscillations of a Circuit Having a Periodically Varying Capacitance

Abstract

A previous theoretical study of a dissipationless oscillatory circuit having a periodically varying capacity predicted the existence of several interesting types of oscillations. An experimental investigation of such a circuit was therefore made. The results of this investigation are presented in this paper. The dissipation was reduced to a minimum by means of an associated vacuum tube in a regenerative connection. An auxiliary condenser and rotating commutator produced the periodic capacity variation. The nature of the oscillations was studied by means of oscillograph and meter measurements of the currents in the several parts of the circuit and by the use of headphones. A quite good agreement with theory was found, consistent with the deviations of the experimental conditions from the theoretically postulated ones. The oscillations were generally of a complicated nonsinusoidal character, but assumed a substantially sinusoidal form for certain adjustments of the circuit. The frequency of these sinusoidal oscillations was twice that of the capacity variation. Periodic oscillations were found to occur when, approximately, α = 2ω0/n, n = 1, 2, 3, ..., where ω0is the natural angular velocity of the circuit for the mean capacity value and α is the angular velocity of the capacity variation. Failure of all oscillations for certain circuit adjustments was related to the inherent loss of energy in the switching method employed for varying the capacity. The theory had predicted certain unstable conditions for which the amplitude should increase without limit.