A method of calculating inductances based on first principles is presented, which has the advantage over the more popular simulators in that fundamental formulas are explicitly used so that a deeper understanding of the inductance calculation is obtained with no need for explicit discretization of the inductor. It also has the advantage over the traditional method of formulas or table lookups in that it can be used for a wider range of configurations. It relies on the use of fast computers with a sophisticated mathematical computing language such as Mathematica to perform the required integration numerically so that the researcher can focus on the physics of the inductance calculation and not on the numerical integration. Introduction Inductors are used to provide filtering or energy storage within many types of electrical systems. They are often coiled conductors whose time changing currents induce voltages either in the conductor itself or nearby conductors. They are used extensively in analog circuitry and are an essential component of every electric utility power grid.
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For most of the twentieth century, calculating inductances was done mainly through the use of formulas or look-up tables, because the inductance calculation which contains an integrable singularity had been intractable. For the past thirty years or so, simulation tools such as FastHenry,, and Ansys Maxwell, have been used to calculate inductances. However, while FastHenty is open-sourced, the cost of Ansys Maxwell or other tools may be beyond the user's means. Also, for these tools, the user is unlikely to be familiar with their algorithms, so the researcher is less likely to develop an understanding of the fundamentals of inductance calculations; moreover an additional discretization of the inductor may be needed. Now, with the use of modern high speed computers that use sophisticated mathematical computing languages, the numerical integration is tractable and so inductances can now be computed using first principles, using a multi-functional computational program that may already be available to the user. With this method, the workings of the numerical integration are performed by the computational program, and so there is no need for the user to become an expert in sophisticated numerical integration techniques or in methods for discretizing the geometry.