This work presents a procedural method for analytically computing losses in solid conductor air-core coils. The approach was developed for the coaxial subset of air-core coil systems in which hoop-turn, axisymmetric assumptions can be made. It encapsulates loss generally associated with magnetic diffusion, including that induced by rotating magnetic fields from multi-phase current sources, without computing the complex eddy current distribution in a conductor cross-section. Each turn in the system is replaced with an infinitesimally thin circular current loop and is independently excited according to a peak current and phase. Field contributions are summed up at each loop center, with the inclusion of phase to calculate the major and minor components of the resultant magnetic field at each turn. Well established analytic formulae are then used to compute loss accordingly. The approach is significantly faster than 2D axisymmetric finite element analysis (FEA) and greatly improves approximations for losses in isolated coils.

This paper introduces a semi-analytical method of predicting AC loss in commercial Litz wires. Simple finite-element simulations are used to compute the resultant proximity fields in a coil system of arbitrary geometry. The approach addresses non-ideal Litz wire construction by applying a surrogate skin effect model to inform and distribute the current over the cross-section into segmented layers. This simplifies the finite-element problem into a two-dimensional, DC simulation with a low number of mesh elements. Analytical solutions are then used to compute frequency-dependent loss due to skin and proximity effect. The method is demonstrated using two 14 AWG equivalent Litz wires with very different constructions and is validated with experimental results from several coil configurations. Finally, an appeal is made to commercial Litz wire manufacturers to provide an empirical “fabrication factor” specification that would allow consumers to predict the performance of a conductor in their application.