Nonlinear parametric excitation of even harmonics in a resonant circuit

The present work analyzes a parametric mechanism for exciting even harmonics in a series resonant circuit with a reactive nonlinearity having an odd characteristic. A fifth-degree polynomial is used to describe the current-flux relation in the nonlinear inductance. The equations of motion in such a circuit are developed, and it is shown that the excitation of even harmonics takes place in the first Mathieu zone. The amplitude-frequency characteristics of the second harmonic are determined by a graphical method. Theoretical results are compared with experimental data obtained for excitation of the second harmonic in a circuit containing a nonlinear inductance in the form of a coil with a ferrite core.