Resonant Circuits with Time-Varying Parameters

With renewed interest in the superregenerator and similar circuits there has developed a need for a solution to the differential equation of a resonant circuit with time-varying parameters. An approximate solution is presented along with a criterion of error which determines the limits of accuracy of the solution. This error criterion shows that the solution may be applied to most communications problems with high accuracy. The method and ease of manipulation of the solution are demonstrated by application of the mathematics to the constant-parameter case. If direct manipulation of the formulas is not feasible, it may be easily applied to graphical analysis.