4078 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO.

8, AUGUST 2014

Flux Balancing of Isolation Transformers

and Application of “The Magnetic Ear” for
Closed-Loop Volt–Second Compensation
Gabriel Ortiz, Member, IEEE, Lukas F¨assler, Johann Walter Kolar, Fellow, IEEE, and Oscar Apeldoorn

Abstract—Semiconductor switches possess nonideal behavior

which, in case of isolated dc–dc converters, can generate dc-voltage
components which are then applied to the isolation transformer.
This dc-voltage component is translated into a dc flux density com-
ponent in the transformer core, increasing the risk of driving the
core into saturation. In this paper, a novel noninvasive flux den-
sity measurement principle, called “The Magnetic Ear,” based on
sharing of magnetic path between the main and an auxiliary core
is proposed. The active compensation of the transformer’s dc mag-
netization level using this transducer is experimentally verified.
Additionally, a classification of the previously reported magnetic
flux measurement and balancing concepts is performed.
Index Terms—Magnetic analysis, magnetic cores, magnetic (a)
transducers, magnetic variables measurement, measurement,
transducers.

I. INTRODUCTION
SOLATED and/or high step-up dc–dc converters are built
I with arrangements of semiconductor switches which pro-
vide ac excitation to a transformer. Phenomena such as un-
matched turn-on/turn-off times, semiconductor forward voltage (b)
drop, gate driving signal delays, insufficient pulse width modu-
lation (PWM) resolution, or pulsating load, among others, can
cause differences in the positive and negative volts–seconds
applied to the transformer [1]. This results in a dc-voltage com-
ponent at the transformer terminals, which causes an undesired
(c)
dc magnetic flux density component in the transformer core.
In order to show the relation between this voltage and mag- Fig. 1. (a) MEGACube transformer [2], [3] optimized for efficiency. (b) DAB
netic flux density dc components, consider the circuit presented converter with simplified transformer model. (c) Equivalent model of the con-
in Fig. 1(b), where a dual active bridge (DAB) dc–dc converter verter with independent dc and ac voltage sources and reflected secondary side.
topology is shown. The primary and secondary bridges apply
voltages vp (t) and vs (t) to the transformer, respectively. The 
primary side. Here, the resistances Rp,T and Rs,T represent
dc and the ac components of these voltages can be separated 
the winding resistances Rp,s and Rs,s plus the semiconductors’
into independent voltage sources, building the circuit depicted equivalent on-state resistances of the primary and secondary
in Fig. 1(c), where the secondary side has been reflected to the side switches, respectively.
In steady state, the dc part of the magnetizing current Im ,dc
of the transformer is given by
Manuscript received July 18, 2013; revised November 14, 2013; accepted 
 Vp,dc Vs,dc
November 25, 2013. Date of current version March 26, 2014. Recommended Im ,dc = Ip,dc − Is,dc = −  . (1)
for publication by Associate Editor S. K. Mazumder. Rp,T Rs,T
G. Ortiz, L. Fässler, and J. W. Kolar are with the Power Electronic Systems
Laboratory, ETH Zurich, 8092 Zurich, Switzerland (e-mail: ortiz@lem.ee. The dc magnetic flux density is then determined by the char-
ethz.ch; faessler@lem.ee.ethz.ch; kolar@lem.ee.ethz.ch).
O. Apeldoorn is with the Power Electronics and Medium Voltage
acteristics of the winding and core through
Drives, ABB Switzerland Ltd., CH-5300 Turgi, Switzerland (e-mail: oscar.  

apeldoorn@ch.abb.com). Im ,dc · Np Vp,dc Vs,dc Np
Color versions of one or more of the figures in this paper are available online Bdc = · μ0 μ̄r = −  · · μ0 μ̄r
at http://ieeexplore.ieee.org.
lm Rp,T Rs,T lm
Digital Object Identifier 10.1109/TPEL.2013.2294551 (2)

0885-8993 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications standards/publications/rights/index.html for more information.
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ORTIZ et al.: FLUX BALANCING OF ISOLATION TRANSFORMERS AND APPLICATION OF “THE MAGNETIC EAR” 4079

Fig. 2. Classification of previously proposed flux balancing concepts. The two main areas are flux measurement and flux feedback control. The proposed
measurement concept, “The Magnetic Ear,” is highlighted within this classification.

where lm is the length of the magnetic path, Np is the number

of turns in the primary side, μ0 is the permeability of air, and
μ̄r is the core’s relative permeability in the linear region of the
B–H curve.
From (2), it can be seen that the dc magnetic flux density is

limited by the equivalent series resistances, Rp,T and Rs,T , of
the circuit, which are typically kept as low as possible in order
to decrease the converter’s conduction losses. This means that (a) (b)
a small dc component in the voltage applied to the transformer
generates a large dc flux density component.
For example, taking the shell-type 166-kW/20-kHz
efficiency-optimized transformer [3] [cf. Fig. 1(a)] with suit-
able switches on the primary side, the primary side equivalent
resistance Rp,T reaches 1.7 mΩ. This design considers a Ferrite
N87 core material which is characterized by a relative perme-
ability μ̄r around 1950. In this design, a 0.0125% of relative (c)
difference in the duration of the positive and negative semicy-
cles of the primary voltage vs (t), i.e., a switching time error of Fig. 3. Previously proposed concepts for magnetic saturation prevention:
(a) Parallel magnetic path in an E-core with a gaped leg [5]. (b) Parallel magnetic
2.5 ns, would suffice to create a dc flux density component of path with external cores and reduced cross section [6]. (c) Integration of applied
Bdc = 50 mT. voltage with an RC network [7].
With this dc flux density component, the core can be easily
driven outside the linear region of the B–H curve, generating
subcategorizations are possible, as displayed in Fig. 2 and dis-
a nonlinear magnetizing current with high peak values. This
cussed in the following sections.
results in increased conduction and switching losses, causing
reduction in efficiency and higher semiconductor and trans-
former operating temperatures, compromising the converter’s A. Flux Measurement/Saturation Detection
reliability. Moreover, a dc-biased flux density waveform results The methods for recognition of the core’s flux state can be
in higher core losses [4], further compromising the converter’s classified into: 1) saturation detection; 2) dynamic flux mea-
efficiency. For these reasons, the operation of the transformer surement,; and 3) continuous flux behavior measurement. The
under balanced condition, i.e. with zero dc flux density compo- measurement method proposed in this paper lies in this last
nent, must be ensured. It is also worth to note that if a balanced class.
operation of the flux density in the core is ensured, the trans- 1) Saturation Detection: In [5], an E-core was used with an
former can be designed with low flux density overdimensioning, air-gap in one of the external legs [see Fig. 3(a)]. During the
meaning that its magnetic cross section, and therefore its vol- normal operation, the flux flows only in the ungapped leg but
ume, can be reduced, increasing the converter’s power density. as soon as this leg saturates, part of magnetic flux is forced
In order to ensure balanced flux operation, the main problems through the gapped leg, and therefore, a voltage can be induced
that must be addressed are measurement of the core’s internal in an additional winding, detecting the saturation of the main
flux status (see Section I-A) and balancing or closed-loop con- flux path. Alternatively, in [6], a slot is placed in one of the core
trol of the flux (see Section I-B). Within these two topics, other legs, as shown in Fig. 3(b) in order to reduce the cross-sectional

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4080 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014

area in this place. An additional magnetic path with a winding

is provided parallel to the slotted part of the core. As the slotted
section has a smaller area, it saturates at lower flux densities
with respect to the rest of the core, and therefore, the magnetic
flux is forced into this parallel magnetic path. This induces a
voltage in a winding indicating the impending core saturation.
With both these methods, only the saturation of the core is
detected, which may be enough in some applications. In applica-
tions which require high efficiency, however, this is not enough
since the flux density in the core can still be biased without
being saturated, and therefore, the core losses are increased. (a) (b)
Moreover, in order to implement both these methods, modifi-
cations to the magnetic components are required, increasing its
cost and complexity.
2) Dynamic Flux Measurement: This method was proposed
in [7] in order to detect flux unbalance due to variations in
the converter loading conditions. The principle is to perform
an integration of the applied voltage through an RC network (c)
or an active integrator [cf., Fig. 3(c)]. This integrated signal is
proportional to the core’s magnetic flux. Due to the requirement
of an integration, this method can only sense dynamic variations
of the flux, i.e., steady-state asymmetries will not be detected.
3) Continuous Flux Behavior Measurement: The sensing of
the flux behavior with large bandwidth and independent of the
operating conditions has been covered by several publications,
where the following main categories can be identified:
a) Magnetizing Current Measurement: The magnetizing
current im (t) indicates the status of flux density in the core. The (d)
measurement of this current through subtraction of the scaled
primary and secondary currents was proposed in [7]. Fig. 4. Continuous measurement of core’s internal flux: (a) Construction of
In [8], and later in [10], a measurement of the magnetizing the magnetizing current with an external transformer [8]. (b) Magnetic flux
measurement with the Hall sensor in magnetic path. (c) Orthogonal magnetic
current was performed by building an additional transformer fluxes [9].
with the same turns ratio as the main transformer but with one
of the windings in the inverted orientation [cf., Fig. 4(a)]. This
transducer effectively operates as a mutual magnetic compen- linear region, voltage would be induced in the orthogonal coil
sator similar to other current sensing concepts, and is therefore only when the core is saturated.
able to sense dc components on the transformer’s magnetic flux c) Converter Current Measurement and Processing: The
density. direct measurement of the primary and/or the secondary currents
The disadvantage of this method is the requirement of iso- has also been used to balance the flux in the core. As an example,
lation on the additional transformer, which needs to be at least the dc magnetization of the core generates primary/secondary
the same as the one of the main core. Also, practical issues may currents with even numbered Fourier components. The ampli-
arise in higher power transformers where the wiring of primary tude of these components can be measured and used as feedback
and secondary sides has an increased complexity [3]. signal to balance the transformer flux, as was performed in [12].
b) Orthogonal Magnetic Fluxes: In [9], the internal core In converters with modulations which do not operate always
flux was measured by using an additional coil fed by a dc current at 50% duty cycle, only the magnetizing current is present dur-
which generates a magnetic flux orthogonal to the main flux ing the freewheeling periods. This current can be measured
[cf., Fig. 4(c)]. The orthogonality of the magnetic fluxes ensures during these intervals obtaining information about the status of
that no voltage is induced in the additional coil due to the main the core’s flux. In this case, however, high vertical resolution
flux. As the main magnetic flux density is changed, the B–H is required on the analog-to-digital converter since typically at
characteristic of the material is also changing. This material these power levels, the magnetizing current is very low com-
property change is translated into a variation of the flux in pared to the main current; thus, its detection becomes a major
the orthogonal coil, inducing a voltage in its terminals. This challenge.
principle was also proposed for microfabricated inductors [11] d) Flux Observer: In order to overcome the limitation
in order to intentionally shape the B–H loop of the magnetic of only dynamic flux measurement, the method described in
material. In this concept, modified or specially shaped cores are Section I-A2 can be complemented with a measurement of the
required in order to insert the orthogonal winding, increasing transformer current [7]. This way, an observer that reconstructs
its cost and complexity. Moreover, if the B–H loop has a large the flux density based would be feasible.

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ORTIZ et al.: FLUX BALANCING OF ISOLATION TRANSFORMERS AND APPLICATION OF “THE MAGNETIC EAR” 4081

e) Hall Sensing: The most direct way to measure the flux as with a series capacitor; thus, this is not strictly a flux balanc-
in the core would be to insert a thin hall sensor in the mag- ing method. Moreover, the inclusion of an air-gap in the core
netic flux path [13] [cf., Fig. 4(b)]. However, this requires the decreases the value of magnetizing inductance Lm , increasing
insertion of an air gap in the magnetic core, reducing the mag- the switched and conducted currents.
netizing inductance and increasing the reactive power provided In addition to the previously presented passive flux balancing
to the transformer. Moreover, the fabrication of the Hall sen- principles, the prevention of core saturation can be included
sor presents major challenges, as known from current sensor as part of the converter design process. In [1], the different
manufacturing. converter electrical parameters that influence the core saturation
f) Flux-Gate: The flux-gate principle is a well-known were clearly pointed out and used to give design considerations
concept for current measurement [14]. This measurement prin- which help avoiding it.
ciple can be adapted in order to build a flux-density transducer, 2) Active Saturation Correction: The flux measuring con-
as presented in [15] and shown in Fig. 4(d). In this concept, cepts presented in Section I-A1 can be used in order to imple-
an E-type core is utilized whereby the primary and secondary ment feedback control which only operates under impending
windings are placed around the core’s middle leg while two ad- core saturation, as was done in [5].
ditional windings are placed in one of the “I” parts of the core, 3) Active Feedback Control of the Flux: If a signal propor-
as depicted in Fig. 4(d). With this arrangement, a dc bias in the tional to the internal core flux density is available, the dc magne-
flux-density would result in a change in the inductance in the tization of the core can be actively controlled by modifying the
terminals of the auxiliary winding, thus enabling monitoring of volts–seconds applied to the transformer. The main feedback
the flux density in the core. flux control principles that have been proposed are detailed
The main disadvantage of this concept is the requirement of in [7]–[9], [13], and [19]. The feedback scheme proposed in this
full isolation between the auxiliary windings and the primary paper is revised in Section IV.
and secondary windings. Additionally, the auxiliary windings In this paper, a novel magnetic flux density transducer is in-
must be placed in the core window, therefore reducing the re- troduced and its operating principle is experimentally verified.
spective filling factor. The measured transducer signal is used to perform a closed-loop
flux balancing control, ensuring the operation of the transformer
core within safe flux density values. The proposed flux den-
B. Flux Balancing/Feedback Control sity transducer is described in Section II and the design trade-
The internal core flux can be passively or actively balanced. offs regarding this transducer are presented in Section III. In
Depending on whether the measuring principle detects core sat- Section IV, the output signal of the transducer is used in order
uration or performs a complete flux measurement, the active to perform a closed-loop compensation of the flux density in the
flux balancing principles can be subdivided into saturation cor- transformer core.
rection or continuous flux control.
1) Passive Balancing: Passive balancing refers to any bal-
ancing principle which does not actively modify the switching II. THE MAGNETIC EAR
signals of the semiconductor devices in order to keep the trans- The main requirements for a flux density transducer in MF
former flux between safe margins. The following passive flux high-power applications can be summarized as follows:
balancing principles can be pointed out: 1) Continuous monitoring: Since the MF transformer is a
a) Series Capacitor: One of the most utilized flux balanc- critical component within high-power dc–dc converters,
ing principles, due to its simplicity, is the inclusion of a capacitor it is desirable to continuously monitor the magnetization
in series to the transformer winding. The main disadvantages of state of the transformer core.
this approach are 1) increased converter volume, 2) increased 2) Isolation: The measurement concept needs to be specified
converter losses, and 3) slow dynamic response. This idea was for the same isolation level as the main transformer.
further developed in [16] where a resistor was placed in parallel 3) Noninvasive: Due to the high complexity and cost of MF
to the capacitor in order to improve low-frequency behavior. transformer technologies, it is highly desirable to real-
b) Zero-Voltage-Switching: Ensuring zero-voltage-swit- ize the design of this component independent from its
ching (ZVS) of all converter semiconductor devices partially magnetic flux-density measurement concept, i.e., a flux
compensates for mismatches in the volts–seconds applied to the measurement principle which does not interfere with the
transformer, as presented in [17] and [18]. Here, the modifi- MF transformer design is required.
cation of the current shape due to the biased operation results Accordingly, a novel magnetic flux density transducer, The
in an inherent modification of the voltage waveform during Magnetic Ear, which complies with these requirements is pro-
the switching intervals, therefore positively affecting the volts– posed and extensively studied in the following. The Magnetic
seconds applied to the transformer which partially compensates Ear’s main concept consists of a shared magnetic path between
for the biased operation. the main core (the actual transformer core) and an auxiliary core
c) Air-gap in Core’s Magnetic Path: When an air-gap is represented by the reluctance Rm in Fig. 5(a), where the trans-
included in the core’s magnetic path, the permeability of the former serves as link between the primary and secondary side
core is effectively decreased. This in turn increases the tolerable full-bridges, building a DAB configuration as already discussed
dc magnetization but does not eliminate the dc flux component in Fig. 1(b). This shared reluctance Rm changes its magnetic

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4082 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014

(a)

(a)

(b)

Fig. 6. (a) B–H loop of the transformer core shown in Fig. 1. (b) Measured
inductance from the auxiliary core’s terminals as the main core is driven through
the B–H loop.
(b)

Fig. 5. The Magnetic Ear main concept: (a) Equivalent circuit representation
with main core and auxiliary core sharing part of the magnetic path. (b) Real
implementation of the main core (EPCOS UU93/76/30 N87) and auxiliary core
(EPCOS EQ30/8 N87 with removed middle leg) and N a u x = 3.

properties, namely its relative permeability μr,m as the main

core is driven through the B–H loop. This variation results in a (a) (b)
change in the inductance Ls measured from the terminals of the
auxiliary core’s winding Ws . This variation in the inductance Fig. 7. Magnetic flux density transducer, The Magnetic Ear, geometric
is sensed by an auxiliary drive circuit which extracts the induc- definitions.
tance value of the auxiliary core, delivering a signal directly
related to the instantaneous magnetization state of the core. The III. DESIGN, DRIVE CIRCUITS, AND SAMPLING METHODS
main and auxiliary cores used to test this concept are presented
As mentioned earlier, The Magnetic Ear transducer consists
in Fig. 5(b).
of an auxiliary core with its auxiliary winding and the respec-
The B–H loop of the transformer in Fig. 1(a) is presented
tive drive circuit used to measure the inductance seen from the
in Fig. 6(a), while the measurement of the inductance for the
auxiliary winding terminals and to convert it to an analog sig-
auxiliary core arrangement shown in Fig. 5(b) is presented in
nal. Moreover, in order to implement the feedback loop which
Fig. 6(b), whereby the main and auxiliary cores are built with
performs the flux balancing in the main transformer core, the
EPCOS UU93/76/30 N87 and EPCOS EQ30/8 N87 cores, re-
sampling strategy of the aforementioned signal needs to be stud-
spectively. As can be seen, the inductance of the auxiliary core
ied. As a start, the selection of the appropriate auxiliary core
is considerably sensible to the instantaneous magnetization state
geometry (dimensions) and core material is addressed.
of the main core; thus, the instantaneous value of the auxiliary
core’s inductance can be used as measure of the magnetization
state of the main core. It should be noted that the behavior of A. Auxiliary Core Design
the auxiliary core’s inductance is depending on the shape of the The selection of the auxiliary core’s shape and magnetic prop-
main core’s B–H loop, whereby higher sensitivities are reached erties, namely its relative permeability μr,a , will directly affect
if the permeability of the main core continuously changes along the sensitivity of the auxiliary inductance Laux to changes in the
the B–H loop. In case, the core material is highly linear until main core’s permeability μr,m , i.e., changes in the magnetization
saturation is reached, e.g., in gapped cores, this sensitivity is de- state of the main core.
teriorated and only a change in the inductance can be perceived In order to analyze the impact of the auxiliary core’s geom-
once the core is driven into saturation. The details and tradeoffs etry and its magnetic properties on the measurement sensitiv-
in the transducer’s design, which is ultimately used to control ity, consider the arrangement presented in Fig. 7(a), where a
the flux in the main core, will be discussed in the following. C core is used as auxiliary core. In order to achieve a high

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ORTIZ et al.: FLUX BALANCING OF ISOLATION TRANSFORMERS AND APPLICATION OF “THE MAGNETIC EAR” 4083

sensitivity to changes in the main core’s permeability μr,m , the

total reluctance of the auxiliary core’s magnetic path must be
mainly defined by the shared reluctance Rm and not by the auxil-
iary core’s reluctance Ra , i.e., Rm  Ra . These reluctances are
defined by
la
Ra = (3)
μ0 μr,a Aa (a) (b)
lm
Rm = (4)
μ0 μr,m Am

where la , μr,a , and Aa are the magnetic path length, relative per-
meability. and cross section of the auxiliary core, respectively;
lm , μr,m , and Am are the corresponding values of the shared
magnetic path and μ0 is the permeability of air. It should be
noted that Am represents the mean core cross section of the (c) (d)
shared magnetic path since this area is not constant along lm .
Moreover, Am is tightly linked with the dimension ca of the Fig. 8. Simulation examples for different auxiliary core geometries. The sen-
sitivities, i.e., the changes ΔL a u x in auxiliary inductance value resulting for
auxiliary core, as will be shown later in this section. various values of ca and a a (cf., Fig. 7) are presented.
Considering the definitions from Fig. 7(a) and (b), the fol-
lowing observations can be made:
1) The height ha of the auxiliary core must be as small as auxiliary core’s inductance Laux to changes in the shared mag-
possible in order to reduce the length of the auxiliary core’s netic path’s reluctance Rm . Therefore, the simulation consists
magnetic path la and therefore reduce the reluctance Ra . of measuring the difference in the auxiliary core’s inductance
2) The width aa of the core cross section must be large in ΔLaux when the permeability μr,m of the main core drops by
order to increase the auxiliary core’s cross section Aa and 50% for different values of ca . Additionally, the effect of the
therefore reduce reluctance Ra . For the same reason, the auxiliary core’s permeability μr,a as well as the dimension aa in
depth of the auxiliary core da must be as close as possible this inductance variation is analyzed since these two parameters
to the depth d of the main core. were found to have the greatest influence in the transducer’s
3) The permeability μr,a of the auxiliary core must be high sensitivity.
in order to reduce the reluctance Ra . Fig. 8 shows the magnetic flux density for four exemplary sim-
4) The air gap between the auxiliary and the main core must ulations, whereby also the respective simulation parameters and
be kept as low as possible since this air gap introduces a resulting inductance variations ΔLaux are shown. In Fig. 8(a),
constant reluctance that deteriorates the sensitivity of the a comparatively small value of ca was employed, resulting in
transducer. a short shared magnetic path lm . On the other hand, Fig. 8(b)
5) The number of turns Naux of the auxiliary core only af- shows the resulting flux density distribution for a larger value of
fects the absolute value of inductance of the auxiliary core ca . When compared to Fig. 8(a), the flux lines in this figure show
but does not affect the sensitivity to changes in the main that a larger cross section Am is achieved with this value of ca ;
core’s permeability. Therefore, low number of turns are thus, no considerable gain in sensitivity is achieved (change in
suggested in order to reduce the induced voltage in the ΔLaux from 3.7% to 3.8%) in spite of the larger auxiliary core
auxiliary core winding due to the flux in the main core, as length ca . Similar effects can be seen when comparing Fig. 8(c)
will be shown in the next section. and (d), where a larger auxiliary core width aa was used.
The dimension ca of the auxiliary core has a large impact on In Fig. 8(c) and (d), the results for the same variation in ca but
the transducer’s sensitivity. For example, a small ca would result with a larger value of aa are shown. This increased value of aa
in a short magnetic path lm , and therefore, the auxiliary core’s results in a larger auxiliary inductance variation when compared
inductance would be mainly defined by the auxiliary core’s re- to Fig. 8(a) and (b) due to the larger auxiliary core cross section
luctance Ra . On the other hand, a large ca results in a large cross Aa , i.e., lower auxiliary core reluctance Ra while the shared
section Am of the shared magnetic path and therefore in a small magnetic path’s cross section Am is not significantly increased,
shared reluctance Rm , thus deteriorating the sensitivity of the as can be seen from the flux lines in the respective figures.
transducer. For this reason, the influence of this dimension on The performed parametric sweeps are summarized in Fig. 9.
the transducer sensitivity was studied by means of FEM simu- In Fig. 9(a), the effect of different auxiliary core widths aa for a
lations. In order to generalize the analysis, a per-unit system is given auxiliary core permeability (μr,a = 2.0) is presented. As
used whereby the width w of the main core is taken as base di- expected, the variation ΔLaux in auxiliary inductance increases
mension, while the relative permeability (in nonsaturated state) with increasing aa , as the auxiliary core cross section is also
μr,m of the main core is chosen as base permeability value. increased. Moreover, for each value of aa , the value of ca that
As mentioned earlier, the goal is to find the geometry of the maximizes the variation in auxiliary inductance can be found, as
auxiliary core which results in the highest sensitivity of the shown by the dashed line in Fig. 9(a). However, this optimum is

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4084 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014

(a)
(a) (b)

(b) (c)

Fig. 9. Sensitivity of auxiliary core’s inductance variation to different di- Fig. 10. Arrangement of auxiliary cores utilized to reduce the effect of the
mensions and permeability as determined by FEM simulations; (a) Constant main core’s flux on the auxiliary core inductance measurement. The auxiliary
auxiliary core permeability μ r, a = 2.0, variable width a a , and length ca . core can be placed so that its flux is (a) parallel or (b) orthogonal to the main
(b) Constant auxiliary core width a a = 0.05, variable auxiliary core perme- flux. The auxiliary core is not shown to scale.
ability μ r, a , and length ca .

not highly dependent on the core length ca , i.e., this dimension

and the core width aa can be independently selected. As a result,
independent of the core length ca , the core width aa must always
be made as large as possible.
The sensitivity of the transducer to variations in the perme-
ability μr,a of the auxiliary core is studied in Fig. 9(b) for dif-
ferent values of auxiliary core width ca . As mentioned earlier,
a higher permeability of the auxiliary core affects positively Fig. 11. Test circuit consists of a full bridge driving the transformer’s main
the sensitivity of the transducer whereby, the value of ca which core, the magnetic flux density transducer, and an external circuit utilized to
force a dc-flux component in the main core.
maximizes the sensitivity can be found for each value of auxil-
iary core relative permeability, as shown by the dashed line in
Fig. 9(b). In this case, however, the optimum value of core length
B. Auxiliary Core Placement
ca is considerably dependent on the value of relative permeabil-
ity of the auxiliary core μr,a . For example, if the main core and The auxiliary core offers a parallel magnetic path for the
the auxiliary core possess the same permeability, i.e., μr,a = 1.0, flux in the main core, and therefore, an induced voltage in the
the peak of sensitivity is encountered when the length of the aux- auxiliary core’s winding due to the main flux is encountered. In
iliary core ca is 0.45 times the width w of the main core, whereas a first step, the auxiliary core can be placed so that its magnetic
if the auxiliary core’s permeability is 2.5 times that of the main flux is orthogonal to the main flux [cf., Fig. 10(b)] as opposed
core, the maximum sensitivity is found with an auxiliary core parallel to the main flux [cf., Fig. 10(a)] in order to reduce the
whose length ca is 1.3 times the width w of the main core. coupling between the transformer’s main windings and auxiliary
The previous analyses shows that, in order to achieve the high- core’s winding. In order to further improve the decoupling from
est sensitivity in the transducer, first, the relative permeability the main core’s flux, the arrangement presented in Fig. 10(c) is
μr,a of the auxiliary core must be selected as high as possible. considered. Here, two identical auxiliary cores with windings in
Once this property is selected, the length ca of the auxiliary core opposed orientation are utilized. Nearly identical voltages are
that maximizes the sensitivity for a given main core width w can induced in the windings of these cores, but due to the opposed
be determined with help of Fig. 9(b). orientation, these induced voltages virtually cancel each other
With the rules for the selection of the auxiliary core di- out.
mensions defined, the next step in the implementation of the In order to verify the effectiveness of this compensation
transducer is the proper placement of the auxiliary core, which scheme, consider the test circuit presented in Fig. 11, which
ultimately defines the coupling of the main core’s flux with is utilized to magnetize the core to nominal flux, while the mag-
the auxiliary core’s winding. This topic is addressed in the netizing current im can be directly measured at the transformer
following. winding. The right-hand side circuit is utilized later to force a

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ORTIZ et al.: FLUX BALANCING OF ISOLATION TRANSFORMERS AND APPLICATION OF “THE MAGNETIC EAR” 4085

(a)

(b)

Fig. 12. Testing of the compensation arrangement shown in Fig. 10: (a) Ap-
plied voltage and resulting magnetizing current in transformer of Fig. 1.
(b) Induced voltage with and without compensation arrangement.

(a)
dc-flux component in the core and can be omitted for the testing
of the proposed compensation arrangement.
Fig. 12 shows the results of the compensation arrangement
testing. The full bridge in Fig. 11 is supplied with Vp = 400 V,
operated with a 20-kHz switching frequency, and 40% duty cy-
cle was used to magnetize the transformer in Fig. 1. The resulting
primary winding voltage vp (t) is shown in Fig. 12(a) together
with the corresponding magnetizing current im (t). The auxil-
iary cores were arranged as presented in Fig. 10, whereby the
voltage vaux,T (t) induced in the winding of the auxiliary core 1
vaux,1 (t) and the compensated signal are depicted in Fig. 12(b).
As can be seen, the voltage in a single auxiliary core winding
is considerable and would result in a distorted measurement of
the auxiliary core’s inductance. When compensated, the signal
vaux,T (t) features negligible induced voltage, thus, this arrange-
ment can be reliably used in order to extract the auxiliary core’s
inductance. This last task is performed by the driving circuit of (b)
the auxiliary core, as described in the next section.
It should be noted that the proposed magnetic flux density Fig. 13. Driver circuits utilized to extract the inductance value of the auxiliary
transducer can be implemented on virtually any core shape, core. (a) Interleaved bridges operated at a constant frequency and with minimum
filtering requirements. (b) Constant peak-peak, variable frequency-controlled
given its noninvasive characteristic which does not require spe- driver. The inductance value is translated into the operating frequency of the
cially shaped cores in order to be implemented. bridge.

C. Drive Circuit With the aforementioned driving circuit concept, however,

the filtering stage at the output of the driving circuit defines
In order to extract the inductance value from the auxiliary
the bandwidth of the transducer, thus, in order to improve
core, a constant amplitude high-frequency excitation voltage is
this bandwidth limitation, the driving circuit of Fig. 13(a) is
used in order to drive the auxiliary core, whereby the peak value
proposed. This circuit consists of two interleaved half-bridges
of the current through the inductor is inversely proportional to
phase-shifted by 90 ◦ driving each auxiliary core (each of these
its inductance value. This current is later rectified and filtered,
cores is then replaced by another pair of cores to compensate for
generating a low-frequency signal directly related to the value
the induced voltage, as shown in Fig. 10) with a switching fre-
of the auxiliary core’s inductance and therefore to the magneti-
quency several times higher than the main core’s excitation fre-
zation state of the main core.
quency. Each bridge forces a current through their corresponding

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4086 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014

(a)

Fig. 15. Hardware realization of The Magnetic Ear flux density transducer.

(b) The aforementioned behavior of the magnetic flux density

transducer, comprising the drive circuit from Fig. 13(a), demon-
Fig. 14. Performance of the magnetic flux density transducer for unbiased strates the utility of this measurement concept, as the output
operation. (a) Excitation voltage v p (t) applied by the test circuit and the result-
ing magnetizing current im (t). (b) Output signal of the magnetic flux density signal of the transducer is directly related to the magnetization
transducer v m (t). state of the main core. It is now the task of the digital controller
to sample the transducer output signal vm (t) in order to detect
and finally actively correct a biased magnetization state of the
main core.
auxiliary cores. Respective current transformers are used to
sense this current which, is then rectified by diode bridges.
The output diode rectifiers are connected in series, causing the D. Sampling Methods
phase shifted currents to compensate the ripple in the output sig- The output signal shown in Fig. 14(b) continuously changes
nal vm (t), reducing the amount of required output filter capaci- as the magnetization state of the main core is varying. This
tance and therefore increasing the bandwidth of the transducer. signal can be sampled at a high sampling rate, e.g., ten times
An alternative drive circuit is shown in Fig. 13(b). The main higher than the frequency of the main core excitation. A lookup
idea of this circuit is to operate the bridge at a constant peak- table implemented in the digital control platform is utilized in
to-peak current by controlling the current with a hysteresis con- order to translate the signal vm (t) into the instantaneous value
troller whereby the switching frequency of the bridge is in- of the magnetic flux density in the main core.
versely proportional to the inductance of the auxiliary core. For the purpose of operating the main core with unbiased
The switching signal at the output of the controller can be later flux density, however, sampling The Magnetic Ear’s output sig-
demodulated into an analog signal containing the information nal during the freewheeling states of the full-bridge (coinciding
about the magnetization state of the main core. with the moment when the flux density is the highest in the
The final transducer comprising two pairs of auxiliary cores main core) would suffice to obtain the dc magnetization state of
based on EPCOS EQ30/8 cores and the described drive circuit the main core. This behavior can be seen from Fig. 17, where a
was built and is shown in Fig. 15. This arrangement of cores dc component I¯m in the magnetizing current, i.e., in the main
[one pair for each auxiliary core in Fig. 13(a)] driven by the core’s flux density was induced by adjusting the duty cycles on
circuit presented in Fig. 13(a) was tested with the setup shown the test bridge [cf., Fig. 17(a)]. Fig. 17(b) shows the resulting
in Fig. 11. The resulting output signal vm (t) of the transducer is output signal vm (t) from the flux density transducer whereby
presented in Fig. 14(b). As shown in this figure, the transducer a clear difference in its peak value can be noticed during two
outputs a high signal value when the magnetizing current im (t) consecutive freewheeling intervals. Due to the biased flux den-
reaches a high value, i.e., when the flux in the main core is sity operation, the output signal vm (t) features its peak value at
entering saturation region. On the other hand, the output signal the end of the positive semicycle since it is at this point when
vm (t) stays low during the zero crossing of the magnetizing the main core’s permeability is at its minimum, i.e. the auxiliary
current, i.e., when the magnetic flux in the main core is zero. core’s inductance is at its minimum.
The slight phase-shift between the peak magnetizing current The difference between the peak values of the output signal
im (t) and the transducer’s output signal vm (t) is due to the at the end of the positive and negative semicycles is directly
output filter capacitor of the drive circuit. However, since this related to the biased magnetization state of the main core. This
signal is sampled only at the end of the freewheeling period, this means that keeping this difference at its minimum is equivalent
phase shift does not deteriorate the behavior of the closed-loop to minimizing the dc component of main core’s magnetic flux
controller, as described in Section V of this paper. density. This strategy is used in order to actively control the dc

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ORTIZ et al.: FLUX BALANCING OF ISOLATION TRANSFORMERS AND APPLICATION OF “THE MAGNETIC EAR” 4087

(a) (b)

Fig. 16. (a) Feedback/balancing scheme: the output of The Magnetic Ear, v m (t) is sampled by the ADC in the DSP board. By sampling on each switching event
of the full-bridge [part (b)], a construction of the dc-flux density in the core is obtained and used to balance the flux in the main core.

core. It should be noted that the gain from The Magnetic Ear
output to flux density is highly nonlinear since, when the core is
close to saturation, a small increase in the flux density generates
a large change in the output signal of the transducer whereas,
when the core is in linear region, the change in the output sig-
nal with respect to changes in the flux density is several times
smaller.
(a) The outputs of the look-up tables are the absolute values of
flux density in the main core at the switching instants. Therefore,
the subtraction of these two signals gives twice the value of dc
flux density component Bdc inside core. For example, in the
steady-state operation, if no dc bias is present in the core, the
output of The Magnetic Ear would be identical at the positive and
negative edges of the applied voltage vp (t). As a consequence,
the output of the look-up tables, the flux density at the switching
times, would be identical and, thus, the measured dc flux density
component would be zero.
(b) In order to control the dc flux density in the core, a standard
PI controller, CB is used [cf., Fig. 16(a)]. The output of this
Fig. 17. Performance of the magnetic flux density transducer for biased main
core operation. (a) Excitation voltage v p (t) applied by the test circuit and the controller is the additional duty cycle ΔD required to increase
resulting magnetizing current im (t) with dc component I¯m in the magnetizing or decrease the dc voltage applied to the primary winding. In the
current. (b) Output signal of the magnetic flux density transducer v m (t). PWM modulator, this signal is combined with the duty cycle D
calculated to transfer desired amount of power, which was left
component of the magnetic flux density in the core, as will be to 40% in this case.
experimentally shown in the next section. Several experiments in different testing conditions were real-
ized in order to study the dynamic performance of this feedback
loop. The first test, shown in Fig. 18(a), consists of a step re-
IV. CLOSED-LOOP OPERATION
sponse from −30 to 30 mT in the dc flux density component
The output vm (t) of The Magnetic Ear must be fed into the reference Bdc ∗. As can be seen, the feedback loop is success-
DSP controller of the full-bridge converter in order to actively fully able to regulate within 5 ms the dc component Bdc in
compensate the dc bias. In order to obtain the value of Bdc in the magnetic flux density. Considering the slow dynamics of the
the main core, the scheme shown in Fig. 16(a) was used. As can potential sources for dc components in the voltage applied to the
be seen from Fig. 16(b), different start of conversion (SOC) sig- transformer (e.g., differences in switching times, forward volt-
nals (the signals that trigger a conversion of the analog-to-digital age drops, and gate driving signal delays), this response time
converter of the DSP), i.e., SOC1 and SOC2 are generated in is considered appropriate. Fast modifications in loading condi-
the positive and negative edges of the full-bridge output voltage tions can also cause imbalances in the dc flux density compo-
vp (t). The sampled values at each of these instants are indepen- nent, as described in [16]. However, with modern digital control
dently stored and filtered by moving average filters (MAF). In platforms, this problem can be solved by introducing a middle
order to obtain the final flux density value, a look-up table is built step in the duty-cycle actualization, as described in [20]. Addi-
based on the measurements of The Magnetic Ear output and the tionally in Fig. 18(b) and (c), the voltage and current through
magnetic flux density calculated from the voltage applied to the the transformer together with the transducer’s output signal are

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4088 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014

(a) (a)

(b) (c)
(b) (c)
Fig. 18. Step response of the feedback loop comprising the proposed trans-
ducer is shown in (a). The voltage v p (t) and current im (t) on the transformer Fig. 19. Response of the feedback loop to external disturbance utilizing the
and magnetic ear output v m (t) (b) before and (c) after the dc flux-density step. proposed transducer. The voltage v p (t) and current im (t) on the transformer
and magnetic ear output v m (t) (b) before and (c) after the activation of the
compensation loop.

presented before and after the application of the reference step performed. The duty-cycle variation and the respective dc flux
in Bdc ∗. Here, the relation between the output signal vm (t) and density component value BD C(t) are presented in Fig. 20(a).
the transformer’s flux density can be clearly seen as this out- The duty cycle ramp starts at 25% and reaches 45%. The dc flux
put signal exhibits higher values at the positive voltage slopes density component stays well regulated during the duty-cycle
before the step, meaning negative dc bias on the flux density. ramp, with variations below ±1 mT. Moreover, the voltage and
On the other hand, after the step in flux-density, the higher val- current in the transformer for 25% duty cycle and 45% duty
ues in the output signal are seen at the negative voltage slopes, cycle are presented in Figs. 20(b) and (c), respectively, where
which shows that the dc flux density component has changed to the change in the voltage’s duty-cycle can be clearly seen. Ad-
a negative value. ditionally, the output signal of The magnetic ear is affected for
The second performed test consists of forcing an external dc lower duty-cycles as expected, reaching low values due to the
flux density component with the external dc source and induc- lower reached magnetization state of the core.
tor shown in Fig. 11. By adjusting the current IE , the dc flux Very often dc–dc converters are coupled with single-phase
density component Bdc,E in the main core can be adjusted. This power-factor-correction rectifiers, which inherently generate a
dc component is measured with The Magnetic Ear flux density double frequency component in the dc-link’s voltage. In order
transducer and used in the feedback loop in order to compen- to test the performance of the compensation loop under these
sate for it with the main full bridge. The result of this test is conditions, a 100-Hz voltage component was inserted in the
shown in Fig. 19(a). Here, the feedback loop is left off until t = driving bridge’s dc-link voltage, as shown in Fig. 21(b). The
6 ms, whereby before this time a forced dc component Bdc,E = response of the feedback loop presented in Fig. 21(a) shows that
40 mT can be noticed. As the dc flux density component feed- the dc flux density component Bdc (t) is kept regulated under
back loop is activated at t = 6 ms, the dc flux density component this variation in the dc-link voltage and during the ramping of
Bdc is regulated to zero after 5 ms, achieving an unbiased flux the converter’s duty cycle.
density operation. The output of the transducer before and af- These tests show the effectiveness of the proposed mag-
ter the activation of the feedback loop is shown in Figs. 11(b) netic flux density transducer and its respective drive circuit and
and (c), respectively. As can be seen, the transducer output fea- feedback scheme, ensuring the unbiased dc flux density opera-
tures an unsymmetrical behavior before the compensation loop tion of the transformer.
is activated, which implies a biased operation of the flux den-
sity. As the compensation loop is activated, the dc flux density
component is controlled to zero, which can be seen from the V. CONCLUSION
symmetrical behavior of the transducer’s output signal. Medium-frequency transformers are critical components
An additional test consists of ramping on the duty-cycle within high-power dc–dc converters. In order to maintain a high
while controlling the dc flux density component to zero was reliability of the system, the operation of these transformers

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ORTIZ et al.: FLUX BALANCING OF ISOLATION TRANSFORMERS AND APPLICATION OF “THE MAGNETIC EAR” 4089

density operation of the transformer. In order to implement this

transducer, first, a general analysis of the tradeoffs in the selec-
tion the of the auxiliary core geometry was performed, leading
to clear rules which can be utilized to appropriately select the
dimensions that best suit the main transformer dimensions. The
drive circuit utilized to extract the inductance value of the auxil-
iary core and therefore to extract the information about the mag-
netization state of the core was presented. Here, a drive circuit
(a) with large bandwidth was utilized, enabling the implementation
of a fast feedback loop, which was ultimately utilized to actively
control the dc magnetization state of the core, as demonstrated
experimentally under a variety of operating conditions.

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4090 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 8, AUGUST 2014

[18] D. Costinett, D. Seltzer, D. Maksimovic, and R. Zane, “Inherent volt- Johann Walter Kolar (S’94–M’91–SM’04–F’´10)
second balancing of magnetic devices in zero-voltage switched power received the M.Sc. and Ph.D. degree (summa cum
converters,” in Proc. Appl. Power Electron. Conf. Expo., 2013, pp. 9–15. laude/promotio sub auspiciis praesidentis rei pub-
[19] S. Han, I. Munuswamy, and D. Divan, “Preventing transformer saturation licae) from the University of Technology Vienna,
in bi-directional dual active bridge buck-boost DC-DC converters,” in Vienna, Austria.
Proc. Energy Convers. Congr. Expo., Sep. 2010, pp. 1450–1451. Since 1984, he has been working as an inde-
[20] J. Claassens and I. Hofsajer, “A flux balancer for phase shift ZVS DC- pendent international consultant in close collabora-
DC converters under transient conditions,” in Proc. Appl. Power Electron. tion with the University of Technology Vienna, in
Conf. Expo., Mar. 2006, pp. 523–527. the fields of power electronics, industrial electron-
ics, and high performance drives. He has proposed
numerous novel converter topologies and modula-
tion/control concepts, e.g., the VIENNA Rectifier, the Swiss Rectifier, and the
three-phase ac–ac Sparse Matrix Converter. He has published more than 450
scientific papers in international journals and conference proceedings, and has
filed more than 85 patents. He was appointed a Professor and the Head of the
Power Electronic Systems Laboratory at the Swiss Federal Institute of Technol-
ogy (ETH) Zurich, Zurich, on Feb. 1, 2001. The focus of his current research
is on ac–ac and ac–dc converter topologies with low effects on the mains, e.g.,
for data centers, more-electric-aircraft, and distributed renewable energy sys-
tems, and on solid-state transformers for smart microgrid systems. Further main
research areas are the realization of ultracompact and ultraefficient converter
modules employing latest power semiconductor technology (SiC and GaN), mi-
cropower electronics and/or power supplies on chip, multidomain/scale mod-
eling/simulation and multiobjective optimization, physical model-based life-
time prediction, pulsed power, and ultrahigh speed and bearingless motors.
He initiated and/or is the founder/cofounder of four spin-off companies target-
Gabriel Ortiz (M’´10) studied electronics engineer- ing ultrahigh speed drives, multidomain/level simulation, ultracompact/efficient
ing at Universidad Técnica Federico Santa Marı́a, converter systems, and pulsed power/electronic energy processing. In 2006, the
Valparaı́so, Chile, joining the power electronics group European Power Supplies Manufacturers Association awarded the Power Elec-
early on 2007. He received the M.Sc. degree in tronics Systems Laboratory of ETH Zurich as the leading academic research
December 2008, and he has been working toward institution in Power Electronics in Europe.
the Ph.D. degree at the Power Electronic Systems Dr. Kolar has been appointed as an IEEE Distinguished Lecturer by the
Laboratory, ETH Zurich, Zurich, Switzerland, since IEEE Power Electronics Society in 2011. He received the Best Transactions
February 2009. Paper Award of the IEEE Industrial Electronics Society in 2005, the Best Paper
During his Master’s thesis, he worked with recon- Award of the ICPE in 2007, the 1st Prize Paper Award of the IEEE IAS IPCC
figuration of regenerative and nonregenerative cas- in 2008, the IEEE IECON Best Paper Award of the IES PETC in 2009, the
caded multilevel converters under fault condition, IEEE PELS Transaction Prize Paper Award 2009, the Best Paper Award of the
obtaining maximum qualification in his thesis examination. The focus of his IEEE/ASME TRANSACTIONS ON MECHATRONICS 2010, the IEEE PELS Trans-
research is in solid state transformers for future smart grid implementations and actions Prize Paper Award 2010, the Best Paper 1st Prize Award at the IEEE
traction solutions. Specifically, his PhD. research deals with the modeling, op- ECCE Asia 2011, and the 1st Place IEEE IAS Society Prize Paper Award 2011
timization, and design of high-power dc–dc converters operated in the medium and the IEEE IAS EMC Paper Award 2012. Furthermore, he received the ETH
frequency range with focus on modeling of soft-switching processes in IGBTs Zurich Golden Owl Award 2011 for Excellence in Teaching. He also received
and medium-frequency transformer design, among others. an Erskine Fellowship from the University of Canterbury, New Zealand, in
2003. He is a Member of the International Steering Committees and Technical
Program Committees of numerous international conferences in the field (e.g.,
Director of the Power Quality Branch of the International Conference on Power
Conversion and Intelligent Motion). He is the founding Chairman of the IEEE
PELS Austria and Switzerland Chapter and Chairman of the Education Chap-
ter of the EPE Association. From 1997 through 2000, he has been serving as
an Associate Editor of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
and since 2001, as an Associate Editor of the IEEE TRANSACTIONS ON POWER
ELECTRONICS. Since 2002, he has also been an Associate Editor of the Journal
of Power Electronics of the Korean Institute of Power Electronics, and a member
of the Editorial Advisory Board of the IEEE TRANSACTIONS ON ELECTRICAL
AND ELECTRONIC ENGINEERING.

Oscar Apeldoorn received the M.Sc. and Ph.D. de-

grees from the Technical University Aachen, Aachen,
Germany, in 1991 and 1997, respectively.
Lukas Fässler was born in Wetzikon, Switzerland, He then worked at ABB Power Electronic and
on April 18, 1986. He studied electrical engineering MVD, Turgi, Switzerland. Until 1999, he was respon-
with a focus on power electronics, drive systems, and sible for the development of new high-power convert-
high voltage technology at the Swiss Federal Institute ers. Following this, he joined the power electronics
of Technology (ETH), Zurich, Switzerland, where he innovation and in this responsibility he developed
received the M.Sc. degree in Summer 2011. new converter concepts and power semiconductors.
After working on an ultrahigh speed spinning ball From 2001 to 2005, he was Incharge of the power
project during an internship with the company Levit- electronics development team. In parallel to his fol-
ronix, he designed and constructed a 166-kW/20-kHz lowing study for Executive Master of Business Administration at the University
NPC module as his Master’s thesis at the Power Elec- of St. Gallen Switzerland, he was responsible for the development of new high
tronic Systems Laboratory, ETH Zurich, which was power IGCTs applications and converters. After his graduation in 2007, he be-
a part of the 1-MW Megacube solid-state transformer project. Since 2012, he came Local Technology Manager in the business unit for power electronics and
has been working for the ETH spin-off company Enertronics. medium voltage drives.

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