Optimal design of a small circular wire coil for maximum Q-factor in the MHz frequency

A simple design formula of a small circular wire coil is proposed for maximum Q-factor. For the formula, the inductance and resistance of the coils are calculated at 6.78 MHz using the volume filament method (VFM) by considering skin and proximity effects. In the calculations, coil radii of 10, 20, and 30 mm are used and the wire radius ranges from 0.2 mm to 0.5 mm. The quality factors (Q-factors) of the coils are derived using these calculation results. Also from the calculation results, the optimal pitch ratio (p) and wire diameter (2r
₀
) is found to be 2.0 for the maximum Q-factor. The optimal design formula between wire radius, coil diameter, and optimal turn number is derived for maximum Q-factor. This optimal relationship is based on the rapid increase in resistance due to the proximity effect as the turn number increases. By using this relationship, a coil of maximum Q-factor can be easily designed with a given coil radius (R
_out
) and wire diameter. A coil designed with a wire radius of 0.3 mm and a coil radius of 10 mm based on the formula is fabricated and measured.