An Accurate and Efficient Hybrid Method for the Calculation of the Equivalent Capacitance of an Arbitrary-Shaped Coil

In this paper, we present a novel hybrid method to efficiently and accurately calculate the equivalent capacitance of an arbitraryshaped coil with a circular cross section by using finite-element method in 3-D. To avoid the high mesh and computing effort, a parallel-electrode capacitor as the basic cell is used to approximate the circular wire. According to the published analytical formulas, an equivalent relative permittivity for the basic cell can be obtained to ensure the accuracy of the presented method. Since the formulas are derived under different physical insights, the optimal equivalent relative permittivity ε equi for different winding methods of the coil has been determined. Finally, the accuracy and the efficiency of the presented method are validated by numerical results.