IEEE Power Electronics Magazine - March 2020 - 37

Different "Types" of Transformers
All N-winding magnetic structures based on electromagnetic induction
may be modeled in the same way. Nevertheless, it is common to see
them referred to by their intended application-flyback transformers,
forward transformers, current transformers, Rogowski coils, voltage
transformers, common-mode chokes, coupled inductors, sense windings
(on inductors), gate-drive transformers, low-/medium-/high-frequency
transformers, autotransformers, pulse transformers, variacs, and so
on. This varied terminology sometimes gives the impression that
there is a great variety of physical principles at work, which is not
the case. It is important to emphasize that the varied transformer
nomenclature refers to a variety of use cases (and hence design
goals), not to any distinction in magnetic physics. (While there are
electromagnetic components, such as circulators, that incorporate
other physical principles, nearly all magnetic components used
by power electronics engineers operate based on Faraday's law of
electromagnetic induction.) It does not matter what terminology is
used; the approaches in this article apply to all such magnetic devices.
For example, a forward transformer is so called because it has been
optimized for use in a forward converter, where all of the inductances
in the T model are considered parasitic. It is therefore often designed
with no core gap and tight coupling between the windings to yield
large-magnetizing (L C) and small-leakage inductances (L A, L B). By
contrast, the magnetizing inductance (L C) in a flyback converter is
not parasitic; it plays a direct role in the intended operation of the
converter and is expected to store a substantial amount of energy. A
flyback transformer is therefore designed with a gap in the core.

is obeyed, as noted), which can actually be useful in circuit design [14].
In the more common case where N is selected as the
physical turns ratio of the transformer, the inductances
have physical meaning, namely as the primary-side leakage inductance L A = L l1 (representing flux that only
couples the primary), the primary-referred magnetizing
inductance L C = L n1 (representing flux that couples both
windings), and the primary-referred secondary-side leakage inductance L B = N 2 L l2 (representing flux that only
couples the secondary; more typically L B is reflected to
the secondary side, forming the secondary-side leakage
inductance L l2 = L B /N 2 ). Strictly speaking, the above
description only applies when flux linking any turn of a
given winding links all of the turns of that winding, such
that there is no flux leakage among turns. Otherwise, it
is merely an approximate physical understanding. Flux
leakage within a winding is one reason, along with various
numerical and measurement issues, that "physical" leakage inductances are sometimes concluded to be negative
from experiments.
Turning to the Pi model of the transformer, we can likewise see that there are four possible parameters, which
can be selectively narrowed to three parameters to realize a necessary-and-sufficient model for any two-port

Other good examples include instrumentation transformers. A
current transformer is typically designed with a single-turn primary
and a small resistive burden on the secondary. In this case, the user
assumes that nearly all of the primary current flows through the ideal
transformer in the T model. A corresponding current flows through
the burden resistor to create a sense voltage, which is proportional
to and in phase with the sensed current. The magnetizing inductance
(L C) and secondary leakage inductance (L B) are therefore considered
parasitic, and current transformer designs seek to maximize L C and
minimize L B . By contrast, a Rogowski coil is also used to sense current,
but a well-designed Rogowski coil is meant to be used with a highimpedance secondary load with all of the primary current flowing
through the magnetizing inductance (L C). The magnetizing inductance
is not parasitic in this case and is carefully optimized to create a
large signal while inserting a small impedance on the sensed system.
Thus, while current transformers are typically designed with highpermeability magnetic cores, Rogowski coils often use no core at all.
Further examples abound, including transformers that intentionally
use leakage inductance (for example, in dual-active-bridge converters)
and transformers that intentionally use both leakage and magnetizing
inductance (such as in LLC resonant converters). Nevertheless,
the same physics, analysis, characterization, and intuition apply
equally well to all cases. Therefore, while there is value in specific
nomenclature, it is useful to appreciate the unity of the principles that
underlie all such magnetic devices and the ability to model them in
the same way.

N1 : N2

N1 : N2
Pi

n: 1

Cantilever

FIG 2 Three common circuit structures for modeling two-winding transformers. These models can be made mathematically
equivalent to each other and to the inductance matrix.

March 2020

z IEEE POWER ELECTRONICS MAGAZINE

IEEE Power Electronics Magazine - March 2020

Table of Contents for the Digital Edition of IEEE Power Electronics Magazine - March 2020