Optimization of a small planar spiral coil on a magnetic substrate for quality factor using volume filament model

In this paper, the optimization of a small planar circular spiral coil on a magnetic substrate for a higher quality factor (Q-factor) is presented. By proposing a volume filament model, inductance and ohmic resistance, including the skin and proximity effects of the coil on the magnetic substrate, are calculated. For verification, a printed planar spiral coil with 9 mm radius, 0.15 mm thickness, and 0.2 mm width on a magnetic substrate with μ_r = 100 is optimized for a maximum Q-factor at 6.78 MHz.