Study on the Inductance Calculation Methods of Spiral Coils at High Frequency Conditions

In this paper, a deep analysis of modelling and simulation is conducted to calculate a fairly precise value of inductance of a coil at high-frequency using industry standard ANSYS Maxwell simulation tool and MATLAB. Two different approaches to the simulation of inductance calculation are presented. The calculation of self-inductance in the first approach is computed by assigning the high-frequency components as a variable, which is used for sweeping analysis, which makes the analysis simpler and achieves the purpose of this research. Results proved that the self-inductance of a coil falls off with the frequency. Furthermore, an optimization algorithm is carried out in the second approach to design a coil, based on a specific inductance value at high-frequency when transient current flows through it. Introduction The distribution of low-frequency current through the wires of a coil is commensurate over the cross sections of the wires. However, with increasing the frequency, the current density becomes major at the surface of the wire which means that this uniform density current does not dominate any longer. The theory of this distribution in straight wires has been thoroughly worked out by Lord Rayleigh and by Stefan and showed that the effect of increasing frequency is to diminish self-inductance [1]. However, some references have shown a set of inductance calculation results for different shaped conductors [2-4]. Reference [5] gives correction factors to account for high-frequency operation and calculates inductance of different types of wire loops. Furthermore, reference [6] calculates high-frequency effects in inductors and covers skin and proximity effect. Since many references calculate inductance of different types of shaped conductors, this study attempts not only to calculate the inductance, but also to find methods which could firstly calculate the inductance of any model especially when it is complicated, and secondly find an approach which could be used to design a coil based on a specific inductance value. This paper discusses the methods whose purpose is to calculate self-inductance at high frequency during the transient occurrence. In this paper, different two methods to calculate a fairly precise value of inductance of a coil are presented: First method takes into account the effects of high-frequency fields with all the geometrical parameters of a coil by ANSYS Maxwell software based on reference [1] which explains clearly the influence of frequency upon the self-inductance of coils. The second method depends on a mathematical calculation to find the best design of a coil by determining a specific value of inductance, a number of turns, high-frequency value, and current peak value during the transient occurrence as input parameters for GUI of MATLAB software, thus the dimensions of the designed coil are calculated. This method gives the designed coil of a specific inductance value, but in the first method, a specific model is imported to ANSYS software for inductance calculation when a high-frequency current flows through it. This paper is organized as follows, Section 2 presents the calculation theory, Section 3 presents the methods used to perform the simulations and analysis, and Section 4 presents the conclusions of the study.