Abstract :
The Phase-Locked Oscillator (PLO), also known as a parametron, was proposed almost simultaneously in 1954 by Von Neuman and Goto as a digital device [1], [2]. Since that time, much developmental of effort has been placed on parametrons utilizing ferrite cores and magnetic films. A comprehensive presentation of the use and application of the PLO can be found in the technical literature [3]-[8]. This paper is concerned with the mathematical analysis of the magnetic film PLO which is described by a nonlinear Mathieu equation. Although there are many analyses of the PLO, they all fall short of yielding a closed-form solution which quantitatively and explicitly relates circuit and film parameters to actual operation [2],[3],[7]-[12]. By establishing such a relationship, solutions for the transient response with limiting characteristics, operating frequency, and steady-state operation have been obtained.
