Experimental Testing and Analytical Solution by Means of Lambert W-Function of Inductor Air Gap Length

In this paper the exact analytical closed form solutions for inductor air gap length have been presented. To be specific, in a mathematical sense, the dependence between the air gap length, inductance and other constructional parameters of inductor is nonlinear, i.e. transcendental. In this paper that nonlinear equation is solved in two manners - by using the Lagrange inversion theorem of the Lambert W function or by using its asymptotic formula and by using Special Trans Functions Theory. The numerical results obtained by using these methods, are mutually compared in terms of the calculation error. In order to prove the validity of the mathematical dependence between the inductance, air gap length, and the other constructional parameters, two inductors have been created. The measured results of inductance and air gap length are compared with the corresponding results obtained by the calculations. Very good agreement is shown between the measured and the calculated value of both the air gap length and the inductance value.