A Further Study of Oscillatory Circuits Having Periodically Varying Parameters

Abstract This paper presents the results of an extensive investigation of a circuit containing resistance, inductance, and a periodically varying capacitance. The problem is important in connection with: frequency modulation in radio transmitters; warble tone generation in electro-acoustics; certain systems in mechanical and acoustical engineering where the elastance or mass parameter varies periodically; and, possible other uses of the circuit in both communications and power engineering as its properties become better understood. The oscillations of this circuit may be classified as: (1) natural ; (2) spontaneous ; and (3) forced . Type (I) is the usual exponentially decaying oscillation; type (z) is an oscillation induced by the periodic capacitance variation and has either an exponentially increasing amplitude or a constant one; type (3) is the steady state current produced by an impressed a.-c. voltage. All three types of oscillations were thoroughly explored with the result that several new phenomena were observed and quantitative data were obtained for a wide range of circuit conditions. In some instances, the method used was mathematical. One result secured in this way was the development of a method for calculating the steady state current forced by an a.-c. voltage. Machine solutions were made with the M. I. T. Differential Analyzer and a series of curves of the instantaneous values of charge and current were obtained for representative circuit adjustments. An experimental investigation of the behavior of actual circuits was also made. Striking results were: the generation of electrical power in excess of one kilowatt by means of spontaneous oscillations; the discovery of the properties of quasi-resonance and of phase sensitivity in varying parameter circuits. Several applications of these circuit properties to electrical machinery are discussed.