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Back-EMF Report

The BackElectromotiveForceReport returns the back-electromotive force induced in a coil by the time-varying magnetic field:

\[ \mathcal{EMF} = \int_{\Omega_c} \frac{\partial \mathbf{A}}{\partial t} \cdot \boldsymbol{\tau} \, d\Omega, \]

where \(\boldsymbol{\tau}\) is the unit current density of the coil and \(\Omega_c\) its volume. For a time-harmonic simulation the same integral is evaluated with \(\partial_t \to j\omega\) and the report returns a complex value.

Usage

The coil is referenced by its zero-based index in the order it was added to the ExcitationCoilModel:

from mufem.electromagnetics.coil import BackElectromotiveForceReport

back_emf_report = BackElectromotiveForceReport(
    name="Back EMF",
    coil_index=0,
)

back_emf = back_emf_report.evaluate()
print(f"Back EMF: {back_emf}")

When to use this

  • Synchronous-machine analysis — open-circuit back-EMF waveform characterises the rotor magnet flux and winding pitch.
  • Generator design — output-voltage estimate before connecting any load.
  • Inductor / transformer studies — separating the induced voltage from the resistive drop in a voltage-driven coil.
  • Cogging / harmonic-content analysis — Fourier-decompose the back-EMF vs. rotor position to assess winding quality.