Assessment of the Current for a Non-Linear Power Inductor Including Temperature in DC-DC Converters

A method for estimating the current flowing through a non-linear power inductor operating in a DC/DC converter is proposed. The knowledge of such current, that cannot be calculated in closed form as for the linear inductor, is crucial for the design of the converter. The proposed method is based on a third-order polynomial model of the inductor, already developed by the authors; it is exploited to solve the differential equation of the inductor and to implement a flux model in a circuit simulator. The method allows the estimation of the current up to saturation, intended as the point at which the differential inductance is reduced to half of its maximum value. The current profile depends also on the inductor temperature. Based on this, the influence of core temperature on the conduction time of the power switch was determined. This study shows that the exploitation of saturation requires a proper value of the conduction time value that depends on the temperature. The theoretical analysis has been experimentally verified on a boost converter and is valid for the entire class of DC-DC converters in which the power inductor is subjected to a constant voltage for a given time. The simulations agree with the experimental data from a case study concerning conduction time and temperature.