An Accurate Model for Fast Calculating the Resonant Frequency of an Irregular Solenoid

A fast and accurate calculation of the resonant frequency of a solenoid coil is needed in many applications, e.g., wireless power transfer and magnetic resonance imaging. It helps to accelerate the design and optimization of a coil. However, the existing calculation models for the key equivalent parameters, the inductance (
$L$
) and the capacitance (
$C$
), of the solenoid coils can only provide estimations for standard tightly wound cylindrical coils, and the accuracy is not high. There are no accurate models available for calculating
$L$
,
$C$
, and the resonant frequency when a solenoid becomes irregular, e.g., when it is sparse (with a large pitch), when it has nonuniform pitches, or when it is noncylindrical. In this paper, we propose a fast and accurate model for such an irregular solenoid coil to calculate its inductance, capacitance, and, thus, the resonant frequency. The accuracy of the proposed model is tested on the solenoid coils (with large pitches, nonuniform pitches, or noncylindrical shape) by comparing the calculated results to those using commercial simulation software and the measurement results. For a sparsely wound solenoid, the proposed model provides an accurate calculation of the inductance with a maximal pitch-to-wire-diameter ratio of 40 (an error rate of 8.33% at this ratio). For a varied-pitch solenoid and a noncylindrical one, an error rate of less than 5% can be achieved for a calculation of the inductance.