Formula for self-resonant frequency of Archimedean spiral coils

A simple empirical formula is proposed to calculate the self-resonant frequency of Archimedean spiral coils made of circular wire. A spiral coil can be considered as a deformed straight wire with some specific structural parameters. Each structural parameter is assumed to affect the self-resonant frequency. Two spiral coils, one that resonates near 13.56 MHz and one that resonates near 6.78 MHz, were fabricated to test the proposed formula. The average per cent error between the measured result and the calculated result was 2.66%. The proposed formula will be helpful in the design of Archimedean spiral coils for wireless power transfer.