Magnetic Inductance Report¶

The MagneticInductanceReport computes the magnetic inductance matrix of a single- or multi-coil system. The matrix characterises how time-varying currents in one coil induce voltages in the same or in other coils.

In a system with multiple coils and no eddy currents, the voltage \(V_i\) induced in coil \(i\) by time-varying currents \(I_j\) in all coils is

\[ V_i = \sum_j L_{ij} \, \frac{dI_j}{dt}, \]

where \(L_{ij}\) is the inductance matrix. The diagonal entries are the self-inductances \(L_{ii}\) (a coil's ability to store magnetic energy and oppose changes in its own current). The off-diagonals are the mutual inductances \(L_{ij}\), \(i \ne j\) (magnetic coupling between coils, the basis of transformer action).

Magnetic Energy¶

The total magnetic energy stored in the system is

\[ W = \frac{1}{2} \sum_{i,j} L_{ij} I_i I_j. \]

Usage¶

The report covers all coils you added to the ExcitationCoilModel. You do not need a coil_index argument.

import numpy as np
from mufem.electromagnetics.coil import MagneticInductanceReport

inductance_report = MagneticInductanceReport("Inductance Matrix")

inductance_matrix = inductance_report.evaluate()
print(inductance_matrix.to_numpy())

When to use this¶

Transformer characterisation — extract the leakage and magnetising inductances of multi-winding designs.
Wireless power transfer — mutual inductance between primary and secondary determines the coupling coefficient \(k = M/\sqrt{L_1 L_2}\).
Equivalent circuit extraction for system-level simulation (Spice, Modelica) of motors, contactors, and inductors.
Saturation curves — sweep the bias current and watch \(L_{ii}(I)\) collapse as the core saturates.

Available only with the Time-Domain Magnetic model. For the time-harmonic case the analogous quantity is exposed through MagneticImpedanceReport.