# How inductance is calculated

I am using Ansys electronics desktop 18.2 for a 3D transient magnetic analysis. I have a coil with current excitation and aluminum conductors near the coil that have induced Eddy currents from the coil. I would like to calculate the self inductance of the coil and the mutual inductance between the coil and aluminum.

I have tried different methods to calculate the self inductance and each method gives me a different value. When I check the box to calculate apparent inductance in the Design Settings I then see the inductance value that Ansys calculates for the self inductance of the coil. I also divide the flux linkage by the current in the coil to calculate the self inductance. The other calculation method I tried is to find the volume integral of the energy in the coil from the field calculator and divide that by the current in the coil and multiply by 2. I have not been able to find documentation on how the inductance matrix is calculating inductance so I am wondering what is the best method to find the self inductance?

I also don't know if the inductance matrix can be used to find mutual inductance between a coil and aluminum conductors. To find the mutual inductance I wanted to use the volume integral of the energy in the field calculator. However, since this calculation did not match the value generated from the inductance matrix, I am not sure if it is a valid method to calculate inductance.

If someone has knowledge of the inductance matrix calculation or suggestions to calculate inductance between conductors I would really appreciate feedback. Thank you!

## Comments

The inductance calculation in transient uses the “Frozen permeability” method, and so it does not maintain eddy effects for the inductance calculation only. Maxwell calculation process for transient inductance as defined here:

https://ansyshelp.ansys.com/Views/Secured/Electronics/v193/home.htm#../Subsystems/Maxwell/Content/InductanceComputationfor2Dand3DTransientSolutions.htm

https://ansyshelp.ansys.com/Views/Secured/Electronics/v193/home.htm#../Subsystems/Maxwell/Content/MatrixComputationSettingsforTransientSolutions.htm

An alternative in the transient solver is to use the FluxLinkage value, which is a true (unambiguous) transient quantity, and to derive an inductance value based on the transient flux-linkage and current quantities.

The other fact that may affect the inductance calculation is whether the aluminium conductors are loop inductance or not. Maxwell can only calculate loop inductance, which means the conductor shall either start and end at the boundaries or is a closed loop.