An Effective Design Formula for Single-Layer Printed Spiral Coils with the Maximum Quality Factor (Q-Factor) in the Megahertz Frequency Range

This paper presents a design formula for a printed spiral coil to ensure the maximum quality factor (Q-factor). The formula is composed of a pattern’s metal thickness, single pattern width, total pattern width, and turn number, and is effective in the megahertz (MHz) frequency range. During the formula’s design, the resistance, self-inductance, and Q-factor are calculated according to the ratio of each pattern’s width and total pattern width and the turn number for different metal thicknesses, frequencies, and total pattern widths using a volume filament model (VFM). With a given turn number and metal thickness, the optimal ratio of individual and total pattern widths can be determined to ensure the maximum Q-factor. To verify the formula, some optimal coils were fabricated, and the calculations and measurements were shown to have good agreement. Furthermore, the optimized coils were shown to have higher coupling efficiency than the coils without optimal dimensions.