IEEE Power Electronics Magazine - September 2023 - 19

FIG 5 Time lapse and trajectory of a magnetic domain rotation starting with aligned on the x direction and gradually rotates to
the z direction on which the external field is applied.
The complete 3D modeling
of the domain rotation,
rather than 1D or 2D, preserves
the full picture of
how the domain moves,
providing interconnecting
capability to simulate 3D
couplings with multiple
domains.
To further showcase
of
the
capability
the
model, we show that a
hysteresis loop can be
simulated (results shown
in Figure 6) by simply
introducing an anisotropy
field Hani , and that
nonlinear M-H curve and nonlinear permeability can
be readily extracted from simulation results. A constant
anisotropy field is introduced by adding constant
current sources to the ports to simulate magnetocrystalline
anisotropy that tilts the easy axis away from ˆz.
As the external excitation field Hz
increases in time,
effani=+Hz ˆ
by χ =MH
µχr =+
zz
FIG 6 Simulation results from the circuit model of a magnetic domain under an external magnetic
field H along the z direction showing (a) nonlinear permeability and flux density B versus external
field H and (b) initial magnetization curve and hysteresis loop.
which directly links a magnetic material parameter to
power electronics component behavior.
The LLG-based model has long been used in microwave
M spirals towards the direction of Hz H
and thus Mz increases. The susceptibility is extracted
/, and the relative permeability is simply
1, shown in Figure 6(a) as extracted along the
curve as Hz drops to zero after the saturation. As the
external field decreases and reverses, M moves away
from the
z ˆ direction as it precesses around the total
effective field, giving rise to hysteresis. By reversing the
external field twice, the full hysteresis loop is captured,
as shown in Figure 6(b). These results demonstrate for
the first time that the micro-dynamics in magnetic materials
can be represented and simulated in circuit solvers,
applications [16], and was more recently implemented with
equivalent circuits. Compared to power electronics applications,
microwave applications have a simpler scenario to
address, where a strong dc field in one direction biases all
domains near saturation thus the high-frequency field driving
M to precess at a small angle can be treated as a small
signal. Therefore, the nonlinear resistors Rx2 and Ry2 as
well as the 1:1 transformer Zm in Figure 4 can be ignored.
As an example, the frequency-selective limiter (FSL) is a
waveguide loaded with a piece of magnetic material that
utilizes the nonlinear insertion loss in magnetics to attenuate
input signals at different amplitudes [17]. The circuit
model has been proven effective to predict the nonlinear
losses and time delays for the filtering performance as
demonstrated in [17] and [18].
September 2023 z IEEE POWER ELECTRONICS MAGAZINE 19

IEEE Power Electronics Magazine - September 2023

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