Inductance and resistance calculations for isolated conductors

Various analytical and numerical calculation methods for computing the high-frequency and low-frequency inductance and resistance of isolated conductors are reviewed. The high-frequency estimates are obtained using conformal mapping theory. In both cases, a uniformly distributed return current at an arbitrary radius is assumed. Formulae are presented for the inductance of a strip conductor of zero thickness. The inductance is computed both for DC and for AC infinite conductivity. For regular polygons the conformal mapping is defined by a power series, whereas finite element analysis is used to compute the DC inductance. Conformal mapping theory is used to obtain estimates of the resistance and inductance of a rectangular conductor when the skin depth is small compared to the thickness of the conductor. A method is then presented for calculating the resistance when the skin depth exceeds the thickness of the conductor but remains small in relation to the width of the conductor. Finite element analysis is used to confirm that one of the two resistance estimates always gives a reasonable estimate of the resistance