IEEE Power Electronics Magazine - September 2021 - 33

is the tendency for current to flow on the outer skin of its
conductor as the frequency increases [15].
Therefore, instead of using the entire cross section, the
current is contained on the edge, increasing the losses by
resistance in the copper. The skin depth is the depth below
the surface of the conductor at which the current density
has fallen to 1/e (~ 0.368) of the surface current density.
As the frequency increases, the skin depth decreases thus
concentrating the alternative current around the outer skin.
The skin depth can be determined using equation 2:
d=
2
~n
t
(2)
Where:
t = Resistivity of the conductor material
~ = Radian frequency of the current in the conductor
n = Permeability of the conductor material
d = Skin depth
Figure 2 shows this effect with respect to a flat and
round conductor. The lower portion of the image shows the
effective conductor thickness as a function of frequency,
and at 400 kHz has increased the resistance substantially
whereas the flat conductor yields higher overall area and
thus lower resistance.
Alternative conductor structures, such as litz wire, have
also been considered given their traditional low resistance
at high frequency due to the excellent reduction in skin and
proximity effect. However, due to the high aspect ratio of
the winding window, the poor window fill factor results in a
higher effective resistance for the winding. This application
requires an average 12.5 A dc current with 20% ripple so dc
current losses will be dominant over ac current losses, further
making the flat conductor a better choice.
Core Material Selection
Core material selection needs to optimize key parameters
such as saturation magnetic flux density, power loss density
and permeability. Since the inductor stores energy in the airgap,
with unity relative permeability, the permeability of the
core directly drives inductance where a higher value yields
higher inductance per turn of the winding. The number of
turns in the winding is further bound by saturation flux density
and hysteresis losses in the core. In most high frequency
applications, the core losses play a dominant role.
Therefore, we will prefer low hysteresis losses property to
high saturation flux density.
Each material has a different thermal profile, which
affects the overall performance depending on its working
temperature as shown in Figure 3. Selecting a material
solely on the lowest power losses, highest saturation density
and optimum frequency range does not necessarily
yield the best inductor. It is rare to find a material that will
satisfy all the conditions simultaneously. In addition, material
properties are interdependent and modifying one will
impact the others. For this inductor, a manganese-zinc ferrite
(MnZn) core was chosen as it has the best compromise
at the desired frequency and over the expected operating
temperature range.
Permeability is furthermore a complex parameter and
expresses both the reactive and resistive behavior of the
core material as shown in Figure 4. Given these behaviors
are frequency dependent, it is key for this application
to select a material with optimal reactive and minimal
600
T = 25 °C
T = 100 °C
400
200
Magnetic Field Strength H(A/m)
400
200
FIG 3 Flux density as a function of magnetic field strength at
various temperatures.
µ′
µ′
µ″
Round Conductor Current
tRES
µ″
0.1
1
(kHz)
FIG 2 Current density (Red) at various frequencies for round
(lower) and flat (upper) conductors.
400
Frequency
FIG 4 Resistive and reactive components of permeability as
function of frequency for a typical ferrite material.
September 2021 z IEEE POWER ELECTRONICS MAGAZINE 33
Permeability
Flux Density B(mT)
IEEE Power Electronics Magazine - September 2021

Table of Contents for the Digital Edition of IEEE Power Electronics Magazine - September 2021
