Subharmonics in Circuits Containing Iron-Cored Reactors

The performance of a series circuit consisting of a resistor, a capacitor, an iron-cored inductor, and a sinusoidal impressed voltage is specified by the non linear differential equation dψ/dt + ri + L di/dt + 1/C∫i dt = E sin (t + θ) in which ψ is an odd function of i. Particular solutions of this equation, showing the effect of varying boundary conditions, are obtained by means of the differential analyzer. An approximate analytical method for determining the types of oscillations possible in this circuit is developed. Results obtained by this method are compared with differential analyzer solutions.