Modeling the Self-Capacitance of an Irregular Solenoid

Irregular solenoids, i.e., sparse solenoids, varied-pitch solenoids, and noncylindrical solenoids, has started to appear recently for specific applications, and an accurate and fast modeling of their self-capacitance is necessary to accelerate the design and optimization process of such coils. Conventional capacitance modeling methods only work for coils, which are standard tightly wound cylindrical solenoids, but fail for irregular solenoids. Full-wave electromagnetic (EM) simulators provide good accuracy, but the computation time is usually long. In this article, a fast and accurate model to calculate the self-capacitance of an irregular solenoid is proposed. A modified turn-to-turn capacitance model, which considers the capacitance in the insulation layer of a wire as well as the air capacitance between the nearest neighbouring loops and the second nearest neighbouring loops is adopted. It works for solenoids of different types (e.g., sparse, varied-pitched, and noncylindrical ones). The accuracy of the proposed model is validated by comparing the calculation results to both those obtained by using commercial full-wave simulators and experimental results. For sparse solenoids, the proposed model is always accurate for coils with either small or large pitches. For varied-pitch solenoid and noncylindrical solenoid, the error rate of the proposed model is around 10%. Computational time wise, the computation time of the proposed model is reduced by over $10^4$ times compared to that of a commercial EM simulator whereas the accuracy is comparable.