An analytical method taking account of saturation and hysteresis for evaluating the iron loss in solid-iron cores subjected to an alternating field

An attempt is made to obtain an analytical solution for the field distribution inside solid magnetic cores subjected to an alternating magnetic field when the range of operation of the magnetizing force is limited to the first portion (up to the knee) of the B/H curve that can be approximated to the form B = ¿(H ¿ ¿H3), ¿ being small. As a first stage, an analytical method is developed for the solution of the partial differential equation of the form ¿2H/¿x2 = ¿/¿ ¿/¿t(H ¿ ¿H3) H being a function of x and t. Based on this method, expressions for the field distribution, eddy-current loss and overall power factor are deduced. Furthermore, the above analysis is modified to take account of the presence of hysteresis. It is claimed that the method gives a clear picture of the saturation phenomenon and offers an explanation for the increases in loss and power factor that accompany saturation. The analysis is applied to the specific case of a mild-steel toroid and verified against the test results.