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Iron core loss in transient excitation mode

# Iron core loss in transient excitation mode

This is an example of the iron losses calculation in transient magnetic simulation performed with QuickField software.

**Problem Type:**

Plane problem of transient magnetics.

**Geometry:**

All dimensions are in millimeters

**Given:**

Core type: E19/8/5-3C81 (by Ferroxcube)

Magnetic permeability of MnZn ferrite *μ*=2700

Primary winding:

Number of turns - 80

Waveform - periodic rectangular wave

Frequency - 20 kHz

Voltage magnitude - 40 V

**Task:**

Calculate core loss.

**Solution:**

According to Dartmouth university report^{1} published by Dr. Sullivan and Dr. Harris for rectangular waves it is possible to use Steinmetz-like equation (referred as equation (8) in this report):

*P*_{v}[W/m^{3}] = max(*k*_{1}·*f*^{α1}·*B*^{β1}, *k*_{2}·*f*^{α2}·*B*^{β2}),

with material-dependent parameters, which for the E-core E19/8/5-3C81 from Ferroxcube are:

*k*_{1} = 18.02, α1 = 1.23, β1 = 2.45

*k*_{2} = 0.000350, α2 = 2.10, β2 = 2.33.

Following this approach, to estimate the losses at a square wave excitation, we need to run Transient Magnetic analysis with a square wave source, and at the moment when the fluxes are at their maximums integrate the volume losses across the parts of our interest.

This may be easily implemented using Microsoft Excel and QuickField.

**Results:**

Magnetic flux density distribution at t = 2.5 ms (maximal values).

Total core loss is 19 mW.

*Reference: ^{1} Testing Core Loss for Rectangular Waveforms, Phase II Final Report, 21 September 2011 by Charles R. Sullivan and John H.Harris; Thayer School of Engineering at Dartmouth.

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