Self-resonant frequencies of air-core single-layer solenoid coils calculated by a simple method

Single-layer air-core solenoid coils are important components in many fields of electrical engineering, such as, high- frequency applications, air-core transformers, inductive sensors and wireless power transfer. The calculation of its self-resonant frequencies is of primary interest in many different situations. In these components, the validity of lumped element models is critical, since even for relatively small coils the wavelength at resonant frequency is often comparable with coil’s total length. In these situations, a more complete electromagnetic analysis and description of the coil as a helical resonator is necessary. The electromagnetic behavior of single-layer air-core coils is a well-known problem in literature; however, still there is a lack of more practical works and expressions for the self-resonant frequencies calculation. The aim of this paper was to describe in general terms the behavior of the coil at resonance, to present a practical equation for the self-resonant frequencies determination, and finally to present measurements and tests that help to clarify the analysis and prove the validity of the model.