On Evaluation of Inductance, DC Resistance, and Capacitance of Coaxial Inductors at Low Frequencies

A priori evaluations of inductance, stray capacitance, and dc resistance are important aspects in optimizations of inductors. In this paper, analytical formulas of the inductance (self and mutual), dc resistance (solid and litz wires), and the stray capacitances of coaxial inductors were derived for both hexagonal and orthogonal windings. Possible imperfections that occurred during the fabrication process were accounted by the inclusion of axial and azimuth filling factors into the formulations. The formulas presented here were validated using several coaxial coils with rectangular cross sections as reported in the literature and double tested by measurements. Discrepancies between estimated and measured values were less than 1%. The advantage of the present formulation is that optimization efforts are addressed at the earliest stages possible of inductor conception and construction.