A new method for treating nonlinear problems with applications to iron-cored oscillatory circuits I ¿ Subharmonics do not exist

Nonlinear circuits are now widely used in many control regulation systems or other industrial applications. Most of the solutions of such circuits have been based on either the step-by-step or successive approximation methods which do not always lead to the correct results, except in some special cases. Also, such calculations are complex so that generally the first approximation only is adopted. In this paper a new method for attacking nonlinear problems is suggested. By a certain representation of the nonlinear given relation the amount of work is greatly reduced and the calculations can even be carried out by an ordinary slide rule. According to the author´s knowledge, the solution for the case of iron-cored oscillatory circuits and similar cases when the supply frequency, current or voltage, contains considerable harmonics is obtained for the first time. With respect to hysteresis action a simplified solution is given. Experimental results are in good agreement with the theoretical solutions. Harmonics up to the fifth are the only ones used herein to represent the required results. Such representations can be carried out with any number of harmonics by similar process.