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DOMAIN SIZE: Why should(n't) you make large AIRBOX & extend TERMINALS #13

The Problem

This was a request to help with inductance analysis.

The inductor was made of solid wire and was non-symmetric. Increasing the terminal length almost doubles the inductance. Is this some issue with the tool or setup?

As we will find out, it had a purely physical explanation, and both solutions were accurate, while the difference was attributed to long terminals.

Relation between Computational Domain size and the Magnetic Field

The magnetic field in the air physically occupies infinite space. Thus, it has no borders.

However, pure FEM implementation requires a finite domain for computation. We need a so-called closure condition that would approximate infinite space outside the computational domain with some external boundary condition.

There are multiple strategies employed in different tools:

  • The Open Boundary condition in FEMM. It uses an analytical solution of the magnetic vector potential to approximate the field on the boundary as if that would take an infinite space. Typically, it requires a round domain and magnetic field source placed in the center.
  • Infinite Elements in COMSOL - applies semi-finite coordinate stretching.
  • Balloon boundary condition in ANNSS Wellmax D2 - very little info about these boundary conditions, so that we can assume a black-box magic.
  • Setting magnetic vector potential to 0 - this is the simplest and most often used closure condition for the magnetic field. It is as if we say - as we take the domain size alrge enough, we can assume that the magnetic field will be 0 on the external boundary. If we consider a magnetic dipole the the magnetic field amplitude decays as 1/R^3

The Terminal story

Conservation of charge is the answer. The current, a flow of charges, cannot start and end nowhere, otherwise we break conservation law that are written into equations that FEM solves. If so, the problem will simply not converge, there will be no solution.