Influence of the Number of Turns of the Single-Layer Winding of the Inductive Element on the Resistance of Losses

Abstract

The paper analyzes one of the common analytical methods (Ferrer) for calculating the losses of the windings of the  inductive elements, including those operating at frequencies up to 100 kHz, and identifies the main shortcomings of this method - neglecting the influence of the geometry of the winding of the inductive element (including the number of  turns) on the amount of losses, expressed  by  the dimensionless coefficient. Theoretically, this is the reason for the appearance of an incorrect calculation result according to this method. To test the assumption, an experimental study of the impact  of the length of the single-layer winding (number of turns) on the amount of losses was performed. Single-layer windings of a fixed diameter with different conductor diameters, at different frequencies, without a core and with a ferromagnetic core were studied. It was determined that it is possible to use the considered analytical method for calculating the losses of a single-layer winding, provided that the winding is without a core, with the number of turns N ≥ 30 turns, and the obtained result is adjusted by the appropriate value (to 20.5 % depending on the frequency and diameter of the conductor). It was found out  that an increase in the diameter of the conductor leads to an increase in winding losses (this increase is 67 % when the diameter is doubled). During the study of the winding with the core, a significant increase in the value of the winding losses was found, which exceeded the calculated values by more than ten times. It was established that the probable cause of such a significant discrepancy is the effect of changing the configuration of the magnetic field lines when the ferromagnetic core is introduced into the winding, which, in its  turn, changes the shape and area of the conductive region of the conductor. It was also determined that, under these conditions, the influence of core losses on the change in winding losses is insignificant (up to 3 %) and can be neglected. The effect of the core on the configuration of the lines of force of the magnetic field and, accordingly, on the current distribution in the conductor was studied. The study was carried out for the winding without a core and with a core. Based on this, it was established that the chosen analytical method of calculation cannot be used for the calculation of single-layer windings with a core.