Subharmonic response of the ferroresonant circuit with coil hysteresis

A SERIES circuit consisting of a capacitance, resistance, and a saturable reactor may, because of the nonlinearity, have a markedly different response from that of the corresponding linear circuit when a periodic voltage is impressed.
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This difference manifests itself in two ways: 1. Jump phenomena occur. 2. The response may contain harmonics which are not present in the impressed voltage. The harmonics may be integral multiples or exact submultiples of the frequency of the impressed voltage. This paper deals with subharmonic response, that is the fundamental frequency of the response is an exact submultiple of the impressed frequency. Specifically, the introduction of an idealized nonlinear inductor makes possible the calculation of the effect of hysteresis in the iron on the response; it also makes possible such calculation of the effect of the impressed wave form. Various types and orders of subharmonic response are predicted and their dependence on two normalized parameters is established theoretically and experimentally.