Magnetic Impedance Report¶

The MagneticImpedanceReport computes the complex impedance matrix \(Z\) of a multi-coil system at the operating frequency of the Time-Harmonic Magnetic model. For a voltage excitation with coil currents \(\mathbf{I}\) and terminal voltages \(\mathbf{U}\), the matrix satisfies

\[ Z \, \mathbf{I} = \mathbf{U}. \]

The entries are

\[ Z_{nm} = \delta_{nm} R_n + \frac{j \omega}{I_n} \int_{V_m} \mathbf{A} \cdot \boldsymbol{\tau}_m \, dV, \]

where \(R_n\) is the DC resistance of coil \(n\), \(\mathbf{A}\) is the complex magnetic vector potential excited by a unit current in coil \(m\), and \(\boldsymbol{\tau}_m\) is the unit current density of coil \(m\). The diagonal carries both the DC resistance and the self-impedance; the off-diagonals carry the mutual coupling. The matrix is Hermitian.

Usage¶

The report covers all coils added to the ExcitationCoilModel; no coil_index argument is needed.

from mufem.electromagnetics.coil import MagneticImpedanceReport

impedance_report = MagneticImpedanceReport("Impedance Matrix")

impedance_matrix = impedance_report.evaluate()
print(impedance_matrix.to_numpy())

The returned ComplexMatrix exposes real and imaginary parts; the imaginary part divided by \(\omega\) gives the inductance matrix at the chosen frequency.

When to use this¶

AC equivalent-circuit extraction for transformers, motors, and inductors at the operating frequency.
Wireless power transfer / inductive coupling — the off-diagonal \(|Z_{ij}|\) characterises coupling between primary and secondary.
Eddy-current loss accounting — the real part of the impedance, beyond the DC resistance, captures AC losses (skin / proximity).
Resonance design — combine with external capacitance to size matching networks.

Available only with the Time-Harmonic Magnetic model. For the time-domain case the analogous quantity is MagneticInductanceReport.