Skin effect in the time and frequency domain—comparison of power series and Bessel function solutions

Abstract

In a time dependent solution of electromagnetic field penetration into a conductor, it turns out that the impedance power series solution diverges sharply if the ratio conductor radius to skin depth a/δ exceeds 2.7, close to the mathematical irrational number e. This problem has previously been considered to be due to the role of inversion. However, in this paper we show that the power series solution may be derived analytically from Bessel function solutions where the latter does not show the divergence problem. Experimental results are presented and we find that the logarithmic slope of the ac resistance and reactance change close to the value a/δ=e in both models. Since both models are based on the solution of a diffusion-like equation then the divergence effect at e may be expected to occur in other diffusion processes.