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An accurate mathematical model has been developed in order to describe electrical and geometrical factors affecting operation and DC transfer characteristics of the self-oscillating fluxgate current sensor. The mathematical description of the sensor circuit is based on a continuous function that approximates magnetization curve of the used transformer core. The circuit differential equation based on the adopted transformer model is analytically solved offering a fundamental basis for understanding factors that affect the operation of the sensor. All principle parameters affecting sensor operation are clearly demonstrated by using the proposed model, and good agreements with laboratory measurements has been obtained.