Ferrite Toroid Core Circuit Analysis

An analysis of the terminal characteristics of thin ferrite toroid cores under arbitrary drive and load conditions is presented. The analysis is founded only on the following two experimentally confirmed conditions: 1) the time required for a complete reversal of flux under unloaded conditions is inversely proportional to the magnitude of a step-driving field which is in excess of the critical field required to initiate flux change; 2) the open circuit voltage-time output waveforms caused by step driving currents are identical when normalized with respect to amplitude and time. The normalized output voltage waveform f'(x) is used to develop a terminal characteristic equation. It is shown that f'(x) may be obtained by using a nonideal step-input current. Utilizing a modified Gaussian equation to represent f'(x), equations are developed to allow the prediction of core response to arbitrary input waveforms, using 4 parameters easily obtained from voltage response vs NI step-drive plots, and f(x), which is the integral of the normalized expression for the open circuit voltage f'(x), and is proportional to the flux switched in the core. The equations are expanded to include a load circuit and to test the validity of the expressions developed. Theoretical and experimental results are compared for a core loaded with series RL and RLC circuits with both ramp and step-drive currents. Agreement is shown to be good, even though the core used was not particularly thin.