Analytic model for describing the operation of the marzolf tunnel diode inverter

A mathematical model for the Marzolf tunnel diode inverter is described. The nonlinear elements, a square-loop magnetic core, and two tunnel diodes are handled analytically by assuming a 4-segment piecewise linear model for the core and a nonlinear resistance, paralleled by a linear capacitance, for each of the tunnel diodes. A fourth-degree polynomial approximates the nonlinear resistance. On each linear flux segment, the system of equations for the inverter are reduced to a single nonlinear second-ordered differential equation which has the form of Rayleigh´s equation. The relaxation oscillations predicted by the Rayleigh equation are in good agreement with experimental results. In particular, the model predicts : 1) the amplitude and period of the square-wave output, 2) the magnitude of the load voltage spikes which occur during switching, and 3) the shift to higher frequency operation caused by overload and/or inadequate supply voltages. Errors in 1) ranged from a few percent at no load to about 12 percent at maximum load.