IEEE Power Electronics Magazine - March 2020 - 39
electric circuit. Because the identification of relevant
reluctance paths is an unconstrained choice, the final
result may be under- or overdetermined [with respect to
the M (M + 1) / 2 independent parameters for describing
port relationships] and therefore will only match reality to
the extent that the original magnetic circuit captures the
right amount of information.
Physical modeling of magnetics is most useful in
design. If we want some functionality in a circuit, we can
reverse the above process to obtain a magnetic circuit and
then synthesize an actual component. However, physical
models can be less useful in characterizing an existing
device, especially for the likely case of an under- or overdefined model. For example, consider the complicated
between the electric and magnetic domain for the same
component. Note that while we belabor the details for
completeness, in practice, the transformation is often
easily drawn by inspection.
In this example, the physical model reduced to a wellknown necessary-and-sufficient representation (the Pi
model with a physical turns ratio), but there is no guarantee that it would have. A magnetic circuit can include
reluctance paths at many levels of granularity, producing
just as many inductances in the electric equivalent circuit.
The limit of an ultrafine-grained reluctance model is similar in essence to a finite-element simulation. A magnetic
circuit could also include fewer reluctances than a necessary-and-sufficient model, resulting in a reduced-order
R1
N1 i1
+
-
R2
+
-
R3
Across = MMF (Ampere-Turn)
N2 i2
Through = Flux (Volt-second/Turn)
Dual
P3
N1 i1
P1
Differentiate
P2
N2 i2
P2
N2
Across = Flux (Volt-second/Turn)
Through = MMF (Ampere-Turn)
P3
N1
di1
dt
P1
Exchange
Roles
di2
dt
Across = dφ/dt (Volt/Turn)
Through = N di /dt (Ampere-Turn/second)
L2
N1 i1
Add
Transformers
N1 : 1
i1
N2 i2
L3
L1
L2
L1
Across = dφ/dt (Volt/Turn)
Through = MMF (Ampere-Turn)
1 : N2
L3
i2
Across = Volt
Through = Ampere
FIG 4 How magnetic circuits can be converted into electric equivalent circuits through topological duality (and vice versa).
This physical modeling approach can be used to analyze existing structures or synthesize a structure with some desired
functionality, but it is not guaranteed to have the number of independent parameters required by the inductance matrix.
March 2020
z IEEE POWER ELECTRONICS MAGAZINE
39
IEEE Power Electronics Magazine - March 2020
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