Minimum loss sections of flat conductors

Abstract

Flat conductors used in a single-phase go-and-return configuration are, in general, subject to eddy-current losses due to electromagnetic coupling. There is a particular crosssectional shape, first studied by A.H.M. Arnold in 1936, which minimises the losses by producing a current distribution which is uniform across the conductor width. The present study uses the magnetic vector potential to obtain the conductor shapes, and obtains the dependence of inductance per unit length on minimum separation. Perfect current uniformity is only possible in ideal thin conductors, and results indicate that finitethickness conductors should have less curvature and a slight taper. List of symbolsA 2 Ho I J, F, b, Si, m 9 a E a CO S Z, X,-«k w, / a 1 : ( r ) JAC > J> c,fc, pp/ »^i > &i 'Pk a,D,e= magnetic vector potential = permeability of free space, An x l ( T 7 H / m = total current K = current densities = lengths of straight filament = dimensions of rectangular filaments = distances to filaments = separation of image filaments = self geometric mean distance = metal conductivity = applied electric field = angular frequency = skin depth DC = two-way impedance, inductance, resist ance = co-ordinates of filament axes = polynomial coefficients = dimensions of asymptotic geometries = linear taper rate = separation/width ratio