156 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 46, NO. 1, JANUARY 2018
Development of a 0.6-MV Ultracompact
Magnetic Core Pulsed Transformer for
Laurent Pécastaing ,Senior Member, IEEE, Marc Rivaletto, Antoine Silvestre de Ferron,
Romain Pecquois, and Bucur M. Novac ,Senior Member, IEEE
Abstract— The generation of high-power electromagnetic
waves is one of the major applications in the ﬁeld of high-
intensity pulsed power. The conventional structure of a pulsed
power generator contains a primary energy source and a load
separated by a power-ampliﬁcation system. The latter performs
time compression of the slow input energy pulse and delivers a
high-intensity power output to the load. Usually, either a Marx
generator or a Tesla transformer is used as a power ampliﬁer.
In the present case, a system termed “module oscillant utilisant
une nouvelle architecture” (MOUNA) uses an innovative and very
compact resonant pulsed transformer to drive a dipole antenna.
This paper describes the ultracompact multiprimary winding
pulsed transformer developed in common by the Université de
Pau and Hi Pulse Company that can generate voltage pulses of up
to 0.6 MV, with a rise time of less than 270 ns. The transformer
design has four primary windings, with two secondary windings
in parallel, and a Metglas 2605SA1 amorphous iron magnetic core
with an innovative biconic geometry used to optimize the leakage
inductance. The overall unit has a weight of 6 kg and a volume of
only 3.4 L, and this paper presents in detail its design procedure,
with each of the main characteristics being separately analyzed.
In particular, simple but accurate analytical calculations of both
the leakage inductance and the stray capacitance between the
primary and secondary windings are presented and successfully
compared with CST-based results. Phenomena such as the core
losses and saturation induction are also analyzed. The resonant
power-ampliﬁer output characteristics are experimentally studied
when attached to a compact capacitive load, coupled to a
capacitive voltage probe developed jointly with Loughborough
University. Finally, an LTspice-based model of the power ampli-
ﬁer is introduced and its predictions are compared with results
obtained from a thorough experimental study.
Index Terms—High voltage techniques, pulse power systems,
FOR the last few years, the intentional electromagnetic
interference (IEMI) has been developed as a new threat
Manuscript received March 10, 2017; revised October 16, 2017; accepted
November 19, 2017. Date of publication December 22, 2017; date of
current version January 8, 2018. This work was supported by Direction
Générale de l’Armement, the French Ministry for Defense, under Contract
N◦07.34.027. The review of this paper was arranged by Senior Editor
W. Jiang. (Corresponding author: Laurent Pécastaing.)
L. Pécastaing, M. Rivaletto, A. S. de Ferron, and R. Pecquois are with the
Laboratoire SIAME, Université de Pau et des Pays de l’Adour, 64000 Pau,
France (e-mail: email@example.com).
B. M. Novac is with the Wolfson School of Mechanical, Electrical and Man-
ufacturing Engineering, Loughborough University, Loughborough LE11 3TU,
U.K. (e-mail: firstname.lastname@example.org).
Color versions of one or more of the ﬁgures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identiﬁer 10.1109/TPS.2017.2781620
to electronic systems. The aim of the novel directed energy
weapons based on high-power microwave technology –
is to try to interact with today’s modern increasingly complex
combination of software and hardware electronics. Basically,
there are two types of IEMI threats having either narrowband
or wideband waveforms. Whereas the narrowband waveform
threats (in the domain of a few and up to tens of gigahertz)
use vacuum technology sources, the wideband and ultra-
wideband waveform threats (in the domain of a few hundreds
of megahertz and up to a few gigahertz) are based on high-
power fast switching technologies , . Related to the
wideband threats, simple short duration oscillating power
systems  are very useful tools to investigate the suscepti-
bility of electronic systems using unprotected wiring (ethernet
cables and/or power cords). The conventional design of such
a type of directed energy weapon consists of a primary energy
source and an antenna, separated by a power-ampliﬁcation
system that forward the conditioned energy impulse from
the source to the antenna, such as a Marx generator  or
an air-core Tesla transformer . The present arrangement,
however, (described in ), uses an innovative ultracompact
0.6-MV resonant magnetic core transformer which allows an
important volume saving when compared with similar pulsed
power generator topologies previously described in the open
literature. The aim of this paper is to present in detail the
development of the resonant magnetic core pulsed transformer.
The design procedure, the calculations of leakage inductance
and stray capacitances, and an LTspice-based study  will
all be discussed. Finally, experimental results are compared
with software predictions.
II. MOUNA ELECTROMAGNETIC SOURCE AND THE
REQUIREMENTS IMPOSED ON THE
The study of the novel ultracompact 0.6-MV resonant
magnetic core transformer described in the following was part
of a much larger project related to the design, manufacturing,
and testing of an autonomous and compact electromagnetic
pulse source termed module oscillant utilisant une nouvelle
architecture (MOUNA) .
Fig. 1 presents a schematic of the overall MOUNA system
housed inside a dipole antenna having a length of about 1 m,
a diameter of about 22 cm, and corresponding to a volume
of about 38 L. The MOUNA energy source is based on
0093-3813 © 2017 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.
PÉCASTAING et al.: DEVELOPMENT OF A 0.6-MV ULTRACOMPACT MAGNETIC CORE PULSED TRANSFORMER 157
Fig. 1. MOUNA electromagnetic source. Arrangement of main components
inside the dipole antenna (top). Overall view of the metallic dipole antenna
in which all components are integrated, with the dark volume on the far right
side being an oil reservoir (bottom).
Fig. 2. MOUNA simpliﬁed circuit highlighting the principle of resonant
a magnetic core pulsed transformer powered by a battery-
charged HV dc/dc converter charging a capacitor Cpto an
initial voltage Vp. The capacitor is mounted in the pri-
mary winding circuit discharged using a triggered closing
switch Sw. Fig. 2 presents the equivalent electrical scheme of
the MOUNA circuit, highlighting the resonant energy transfer
principle. When the switch closes, the energy stored in the
capacitor is transferred to an oil-ﬁlled output transmission
line (having a capacitance included in the overall load equiv-
alent capacitance Csof Fig. 2) via the high-voltage pulsed
transformer, having a winding ratio nand a total primary
winding circuit self-inductance Lp, which includes a leakage
self-inductance Lσ. The output transmission line has a peaking
switch operated under oil and mounted at its input and a dipole
antenna connected at its output. When the transmission line
is crowbarred by the peaking switch, the remaining circuit
is equivalent to a damped oscillator; the energy of which is
radiated by the dipole antenna.
For a resonant transformer, the transfer is optimal
with the corresponding maximum output voltage Vs
The transformer load capacitance Csincludes the capacitance
of the transmission line Cline, the capacitance between primary
and secondary windings Cps, the capacitance between the
secondary winding and the magnetic core Csc, and other stray
capacitances that will be detailed later.
As the antenna includes all components, its size is ﬁxed
by the overall volume constraints of the MOUNA project.
In such conditions CST Microwave Studio  simulations
were used to obtain the optimum value of the transmission line
capacitance Cline as 80 pF  for which, at a 600-kV charg-
ing voltage, the maximum amount of energy is transferred
(coupled) to the dipole antenna. This essential result is actually
imposing both limits and requirements to the design of the
entire transformer-based pulsed power generator. The pulsed
transformer is required therefore to amplify the initial voltage
of 10–600 kV and be capable to charge an 80-pF capacitive
load. At the same time, the transformer has to minimize its
volume, but still preserve its electrical integrity under very
high electric ﬁeld stress.
The same type of CST simulations  showed that the
closure time of the peaking switch has an inﬂuence on the
antenna radiation gain and it was found that this time can be
reduced if the time to peak, also termed transfer time, of the
output voltage signal generated by the transformer is made
Taking into account all the results obtained during the
preliminary study of the MOUNA source, it was decided
that the main electrical performance required from the pulsed
transformer is the generation on Csof a voltage impulse
of 0.6 MV with a transfer time less than 500 ns. As an
immediate consequence and according to (2), because the
charging voltage Vpof the primary capacitance Cpis limited
by the dc/dc converter to 10 kV, the transformer winding ratio
nmust be 60. If the primary winding is chosen to be a single-
turn coil (i.e., Np=1), the secondary winding will have a
number of turns Ns=n.
III. PULSED TRANSFORMER DESIGN PROCEDURE,
ITS GEOMETRY,AND THE MAGNETIC
The procedure to design of the transformer is detailed in
the following. The starting point is to fulﬁll the required
electrical parameters Vp,Vs,Cline,andtpeak (deﬁned in the
following). The need for a certain magnetic core saturation
characteristic Bsat and a particular magnetic core geometry
are both clearly explained in the following. The required
dimensions of the magnetic core, i.e., its inner core radius
(Rin_core), cross section (S), and height (h), are roughly esti-
mated. These values were used to help in choosing a particular
magnetic core from the manufacturer’s catalog. Once the
precise geometry of the core is thus established, including
its square-shaped core section, the next steps are to calculate
the transformer stray elements: its leakage inductance (Lσ)
and both transformer capacitances: primary to secondary (Cps)
and secondary to core (Csc). First, simple techniques are
established to estimate analytically these essential parameters,
followed by their benchmarking against very precise, but
time consuming, calculations using a state-of-the-art software
package (CST). Finally, an optimization process is described
that helps to improve the transformer characteristics that are
158 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 46, NO. 1, JANUARY 2018
Fig. 3. Winding strategies for the secondary winding.
Fig. 4. Sectional view of the transformer geometry.
then used with a circuit solver (LTSpice) to simulate the ﬁnal
electrical performance of the pulsed transformer.
The transfer time (or time to peak, 0%–100%) of the
transformer output voltage can be expressed as
As easily noticed the transfer time depends on Lpwhich
includes, apart from the leakage self-inductance Lσ,other
parasitic self-inductances related to wires, capacitors, switches,
connections, etc. The leakage self-inductance depends mainly
on the volume between the primary and the secondary wind-
ings  and therefore this volume must be kept as low as pos-
sible. A conical form for the secondary winding (see Fig. 3),
in contrast to the standard cylindrical winding, maintains the
electric ﬁeld (approximated as the ratio of voltage by radius)
at a relatively constant value along the z-axis and therefore can
better accommodate the high-voltage insulation requirements.
As a consequence, the volume is reduced and interestingly,
as demonstrated later, the leakage inductance value is also
Fig. 4 shows the transformer magnetic circuit consisting
of two separate D-shaped circuits designed to ﬁt inside the
200-mm-diameter cylindrical volume required by MOUNA.
In the transformer center the magnetic core, which is made
from the two D pieces touching, has an overall square cross
section S. Due to mechanical requirements for inserting the
windings and the biconical electrical insulation, each circuit
is broken into two parts and the assembly is compressed
by a conductive clam collar. The secondary consists of two
conical windings, connected in parallel for halving the leakage
inductance and although this feature results in an increased
parasitic capacitance, it will be later proved that this design
reduces the transfer time.
As both the transformer and the crowbar peaking switch
operate under oil, tests were performed to experimentally
determine the oil pulsed electrical ﬁeld breakdown for con-
ditions close to the present application. The oil chosen is a
high-quality transformer oil-type Mobilect 39 , produced
by the Mobil Company, and the tests consisted of applying
voltage impulses with a time to peak of 500 ns to the oil-
ﬁlled peaking switch. For obtaining the required performance
at 0.6 MV, a gap distance of about 4 mm was found to be
For conditions inside the transformer, the electric ﬁeld
FBD (in kV/cm) for which there is a 50% probability of
electric breakdown, depends on the area under electric stress A
(in cm2) and the effective stress time teff (in microsecond) by
the expression 
eff A−0.073 (4)
valid for uniform ﬁeld conﬁgurations. For the speciﬁc working
conditions the FBD is estimated around 1000 kV/cm, a value
very close to 1100 kV/cm determined experimentally .
The magnetic circuit is made of Metglas 2605SA1 .
The advantages of using this material are: low losses, a good
behavior at high frequency, and a large value for the saturation
induction Bsat of 1.56 T. This material, with characteristics
provided in , is commonly used in power transformers and
coils operated at high frequency. The magnetic circuit must
be designed with a cross section large enough not to allow
saturation during the energy transfer. In the case of resonant
transfer, the variation of the magnetic induction B=Bsat
during tpeak =T/2 is related to the integral of the output
voltage by the following equation:
where Tis the period and f=1/Tis the corresponding
frequency of the output voltage impulse. The cross section
can be straightforwardly estimated from
For VSmax =600 kV, T/2 =500 ns, NS=60, and
B=1.56 T, the cross section Sis obtained as
As a consequence, as the central magnetic material has a
square cross section, the side of the square is c=40 mm,
and therefore each D-shaped piece in Fig. 4 has a
The circular single-turn primary winding, made from a
0.5-mm-thick copper foil, has to be mounted as close as
PÉCASTAING et al.: DEVELOPMENT OF A 0.6-MV ULTRACOMPACT MAGNETIC CORE PULSED TRANSFORMER 159
Fig. 5. Deﬁnition of the main transformer dimensions.
possible to the magnetic circuit. The minimum inner diameter
Din_prim of the primary winding can be calculated as
where eis the thickness of the cylindrical primary winding
dielectric mandrel. The dielectric material used to mechani-
cally hold the winding and provide insulation to the magnetic
core is made of polyoxymethylene (POM). The dc dielectric
strength of POM is in excess of 20 kV/mm and therefore a
1-mm-thickness is sufﬁcient but, to ensure sufﬁcient mechan-
ical strength, its thickness has been chosen 2 mm. In these
conditions and using (8) Din_prim is about 60.5 mm.
Each secondary winding is wound on a conical-shaped
mandrel. The dielectric strength of the oil is close to the
dielectric strength of the material used to manufacture the
mandrel and the electric ﬁeld can be considered as homoge-
neous. In such a case, the best solution is to position the last
turn of the secondary winding (which is raised at the highest
voltage) at an equal distance from both the magnetic circuit
and the primary winding.
To meet this requirement and in reference to Fig. 5, for
Rin_core =80 mm and Rout_prim =31 mm, it is necessary that
Rout_sec =Rin_core +Rout_prim
The height hin Fig. 5, valid for both the primary and the
secondary windings, can be estimated as
out_prim ≈74 mm.(10)
Once the conical mandrel is deﬁned, in order to wind the
60 turns for each of the two parallel-mounted secondary
windings, it is necessary the pitch pto be less than a value
The selected wire is a single strand of copper with an insu-
lating sheath made of Teﬂon. Its outer diameter is 1.25 mm
and the diameter of the conductor of 0.65 mm (AWG 22). The
main advantages of a Teﬂon sheath are very good dielectric
properties but even more importantly its good resistance to
Fig. 6. 3-D drawing of the two, parallel-mounted, secondary windings.
mineral oil attack. As the transformer is operated at a fre-
quency f of about 1 MHz, the skin effect plays a signiﬁcant
role, but these losses are negligible when compared with the
magnetic core losses and therefore the use of Litz wires would
not bring an improvement. The resultant secondary winding
design is presented in Fig. 6.
The average magnetic path LC of the two D-shaped circuits
can be calculated as
In (12), Rout_core =100 mm is the outer radius of the
magnetic core and the resultant Lcis estimated as 442 mm.
The magnetic core mass MCcan also be estimated as
and, for the magnetic material density ρ=7.18 g/cm3,
the results are MC≈5.1 kg.
To have an idea of the energy efﬁciency of the magnetic core
transformer, we use the Steinmetz empirical law  for an
accurate estimation of the magnetic core power density losses
Pwat a sinusoidal resonant frequency f (deﬁned above) as
B=Bsat. Using the values for the coefﬁcients as
provided in : k=6, α=1.51, and β=1.74, the result
is obtained as Pw≈445 kW/kg. During a pulse, the energy
Ejlost in the magnetic core can be calculated as
with the result, Ej≈1 J, representing only 2.5% of the total
initial stored energy in the primary winding capacitance.
IV. LEAKAGE INDUCTANCE CALCULATION
As already indicated, the transformer total leakage induc-
tance Lσis one of the parameters which inﬂuences the
rise time of the transformer and therefore it is essential to
minimize its value. For convenience, an analytical calculation
of leakage inductance gives in most cases an acceptable
160 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 46, NO. 1, JANUARY 2018
Fig. 7. CST EM Studio simulation of transformer magnetic ﬁeld intensity.
estimate to be used in the design of transformers. For one
of the two identical and parallel-mounted secondary windings
of the transformer, the leakage inductance Lσis related to the
total energy Wmagnetic stored by an imperfect ﬂux coupling
in the nonmagnetic regions between primary and secondary
windings. This energy can be estimated as 
where Ipis the primary current. For the present design, both
the primary and the secondary windings represent only thin
layers, occupying small volumes compared with the volume
between primary and secondary windings . In such condi-
tions, it is reasonable to consider a constant magnetic ﬁeld H
generated in the space between the two windings . With
this assumption, the total energy stored is calculated as
for which the corresponding leakage self-inductance can be
where Vol is the dielectric volume between the coils, measured
as 290 cm3. For the dimensions calculated previously and
Np=1, the estimated leakage self-inductance is about 67 nH,
in good agreement with measurements performed with a
HIOKI IM3536 LCR bridge at 1 MHz providing values
between 64 and 66 nH. We note that the leakage inductance
value for a cylindrical winding strategy for this transformer
(Fig. 3) is about 113 nH making obvious that the conical
winding strategy is advantageous, allowing a 41% reduction
of this unwanted parameter. As the transformer has two
secondary windings mounted in parallel, its total leakage self-
inductance was approximated as Lσ≈33 nH. Estimates were
also obtained for the self-inductance of the primary capacitor
as about 67 nH and for all electrical connections including
the closing switch as about 50 nH, allowing the total self-
inductance of the primary winding circuit Lpto be estimated
as 150 nH.
A study made using CST EM Studio  conﬁrmed all
these simple estimates. The results in Fig. 7 show that, apart
from a slight ﬁeld enhancement just visible near the primary
windings, the intensity of the magnetic ﬁeld is indeed constant
in the material between the primary and secondary windings,
as assumed above (with a value around 160 kA/m). In addition,
CST EM Studio evaluates the total magnetic energy stored in
this space at about 9 J, a value that validates the above estimate
of the total leakage inductance Lσ.
V. CAPACITANCES CALCULATION
In high-frequency transformers, there are four different
types of capacitance : capacitance between the turns in a
winding, capacitance between the layers of a winding, capac-
itance between windings, and stray capacitance between the
windings and the magnetic core. In the present case, the ﬁrst
two can be neglected with respect to the last two. In what
follows the most important capacitance, that one between the
primary and secondary windings will be evaluated, followed
by an estimate of the stray capacitance of the secondary
winding to core.
In analogy with the technique used to estimate the leakage
inductance, the primary–secondary capacitance Cps will be
calculated using the electric energy Welectric stored between
the two windings
where ε0is the permittivity of free space, εr=3.7 the relative
permittivity of the POM, and −→
Eis the electric ﬁeld vector
generated between windings.
The primary coil is mounted very close to the beginning
of the secondary coil, so that Rout_prim ≈Rin_sec.The
distance Dps between the two coils and the electrical potential
between them, they both vary linearly with axial distance z
As a consequence the electric ﬁeld is practically constant
Rout_sec −Rout_prim =Emax.(22)
In these conditions, the calculation is straightforward
Cps =πε0εrh(Rout_sec +Rout_prim)
Rout_sec −Rout_prim ≈30 pF.(24)
This value corresponds to only one of the two identical sec-
ondary windings. As the two secondary windings are mounted
in parallel, the transformer primary to secondary capacitance
A CST EM Studio simulation of the transformer provided
for one winding an admittance of 195 μSat1MHz,which
corresponds to 31 pF, in excellent agreement with the simple
analytical estimate of (24).
The stray capacitance Csc between the secondary winding
and the external core can also be analytically estimated.
PÉCASTAING et al.: DEVELOPMENT OF A 0.6-MV ULTRACOMPACT MAGNETIC CORE PULSED TRANSFORMER 161
Fig. 8. Top view of one-half of the transformer. The gray area represents
the magnetic core, while the semicircle represents the secondary winding. For
simplicity of calculus, to obtain a rough estimate of the capacitance between
the secondary winding and the magnetic core (C), the surface area of the
capacitor “plates” is approximated by a segment of the semicircle having an
In order to simplify the calculus of capacitance in cylindrical
coordinates, the two surfaces of the capacitor Csc are chosen
somehow arbitrary as being segments of a semicircle of angle
α≈90° (as in Fig. 8). Therefore, the distance Dsc and the
voltage between the secondary winding and the core Vsc are
Using (25) and (26), it is easy to determine the axial variation
of the electric ﬁeld:
In these conditions, Csc is obtained by numerically solving the
Rout_sec rdr 0dθh
Note that in (28) εr1=2.25 is the relative permittivity of the
oil in which the transformer is immersed. As above, because
the transformer is composed of two secondary windings in
parallel, the total secondary-core capacitance is multiplied by
two. The same CST Microwave Studio simulation provided a
value of 6.5 pF, again in excellent agreement with the simple
The above calculations highlight the fact that the stray
capacitances cannot be neglected with respect to Cline,and
this obviously affects the energy transfer efﬁciency. There are
also other stray capacitances between the following:
1) the secondary winding and the structure in which the
transformer is enclosed (the antenna strand);
2) the secondary winding and the spark gaps of the primary
3) the secondary winding and the output spark gap;
4) the two secondary windings.
Fig. 9. Variation of the time to peak and of the rise time with the number
of primary windings.
But unfortunately these cannot be estimated by simple analyt-
ical calculations. Using CST modeling, however, these were
evaluated at a total of about 50 pF.
All the above analysis shows that the total capacitive output
load of the transformer has a value of
Cs=Cline +2Cps +2Csc +50 pF ≈200 pF.
VI. DESIGN OPTIMIZATION AND
Based on the calculated value for Csand the requirement
for an optimal resonant transfer (1), the value for the corre-
sponding primary capacitance Cp=n2Csis about 720 nF.
This value is too large because it will increase the transformer
transfer time [time to peak, (3)] to about 725 ns, which in turn
will induce core saturation during the rise time of the input
voltage. Two solutions are possible:
1) increase the cross section of the magnetic circuit;
2) decrease the self-inductance of the primary circuit so
that the transfer time remains less than 500 ns.
Increasing the magnetic circuit will result in an increase of
transformer’s mass and a decrease in the volume available
for the windings, while the isolation constraints and the stray
capacitances will also increase. The solution therefore consists
in reducing the transfer time by decreasing the primary self-
inductance using several windings mounted in parallel. In case
of a number Xof parallel-mounted primary circuits, the time
to peak and the rise time are
and Fig. 9 presents the dependence of these time character-
istics on the number of parallel-mounted primary windings.
This solution brings as a bonus the advantage of reducing the
current switched by each synchronized primary spark gap ,
thus enabling a higher pulse repetition frequency (PRF) oper-
ation to be envisaged. The total current ﬂowing in the primary
162 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 46, NO. 1, JANUARY 2018
Fig. 10. Variation with the number of primary windings of the (a) total
primary current and (b) current in each winding.
Fig. 11. 3-D CAD views of (a) four single-turn primary windings and
(b) their POM mandrel.
circuit can be determined from
The only drawback of operating Xparallel circuits is the need
for synchronization between the Xspark gaps. A compromise
has to be found between the difﬁculty of mechanical realiza-
tion, the current switched by each spark gap and the time to
peak of the transformer output voltage. A reasonable choice is
to have four parallel primary circuits that allows reducing the
overall self-inductance of the primary circuit (Lp)to62nH
and, as required, brings the theoretical time to peak to 469 ns,
i.e., less than the required 500 ns. A small-size Marx generator
is used to synchronize the four switches . At the same
time, this design limits the current switched by each primary
spark gap to only 6.2 kA and thus reduces the erosion of the
electrodes of the spark gaps, allowing a higher PRF operation
of the overall MOUNA system.
Unfortunately, for practical reasons related to component
availability, only capacitors having a capacitance of 200 nF,
a stray self-inductance of 64 nH and capable of delivering
a current of about 10 kA were available to be used as
power sources in each winding circuit. Because of this the
total primary capacitance is raised to 800 nF, i.e., larger
than the 720 nF requested by (1), and such conditions
the efﬁciency of the energy transfer is slightly reduced but
the higher capacitance allows the generation of a larger
output voltage. The time to peak and the rise time are
482 and 285 ns, respectively, while the maximum primary
current is 25 kA.
The single-turn primary windings loops are each made from
a 0.5-mm-thick, 20-mm-wide copper sheet [Fig. 11(a)]. For
optimizing the magnetic coupling, it immediately follows that
the dimensions of the single-turn should be as close to the
magnetic core as allowed by the required insulating properties
Fig. 12. Final 3-D CAD design. (a) Transformer exploded. (b) Overall view.
Fig. 13. Photograph of the completed resonant magnetic core pulsed
Fig. 14. LTspice pulse generator simulation scheme.
of the mandrel. A POM support is used both as a mandrel and
as a primary winding-magnetic circuit insulator [Fig. 11(b)]
and transformer Nomex paper is used to insulate the individual
To conclude, the theoretical analysis of the resonant trans-
former and the optimization procedure provides the following
ﬁnal design characteristics:
1) four single-turn, parallel-mounted primary windings;
2) two parallel-mounted secondary windings each having
3) total primary capacitance: 800 nF (four parallel-mounted
primary capacitors each of 200 nF);
4) total secondary capacitance: 200 pF;
5) output voltage rise time: 285 ns;
6) output voltage time to peak: 482 ns (less than 500 ns
required to avoid saturation);
7) total primary current: 25 kA;
8) total secondary current: 417 A.
Fig. 12 shows the ﬁnal 3-D CAD drawings, and Fig. 13
presents a photograph of the assembled magnetic core pulsed
VII. LTSPICE MODELING
The numerical simulation of the resonant pulsed transformer
was carried out using the LTspice free software (Fig. 14),
PÉCASTAING et al.: DEVELOPMENT OF A 0.6-MV ULTRACOMPACT MAGNETIC CORE PULSED TRANSFORMER 163
Fig. 15. Hysteresis cycle for Metglas 2605SA1.
Fig. 16. LTSpice results. (a) Transformer output voltage. (b) Magnetic ﬂux
density inside magnetic core.
having as load a capacitor simulating the antenna, with a
specially developed voltage probe  mounted in parallel.
The resistance of one secondary winding is about 0.85
for a dc current, but raises to 2.33 for a pulsed current
injected at the transformer’s resonant frequency. This last
value, divided by 2 to take into account the parallel coupling
of the two secondary windings, was used in numerical simula-
tions. The results show the resistance lowers the peak voltage
value by only 0.05%. It is therefore reasonable to be neglected
from the electrical equivalent circuit.
The model for the hysteresis cycle of the transformer core
magnetic material is adopted from . The magnetic model is
deﬁning the hysteresis cycle of the material using only three
parameters, Hc,Br,andBsat, which, respectively, represent
the coercive magnetic ﬁeld, the remanent, and the saturation
magnetic ﬂux density. For the Metglas 2605SA1 the values
are: Hc=4A/m,Br=1.2T,andBsat =1.56 T, and
the theoretical hysteresis cycle thus obtained is very close
to the real curve obtained from the manufacturer (Fig. 15).
Fig. 16 presents theoretical predictions: the transformer output
peak is predicted to be 0.6 MV with a rise time of 268 ns
with the core magnetic induction reaching the saturation value
just before the end of the resonant transfer. Therefore, this
unwanted phenomenon has a small inﬂuence on the amplitude
of the output voltage.
VIII. EXPERIMENTAL RESULTS
The transformer was tested having the same ultracompact
arrangement as when mounted inside the dipole antenna, with
a polymer skeleton holding the various elements together
(Fig. 17). The term “ultracompact arrangement” is for the fact
that components are coupled with the shortest possible con-
nections. The pulsed transformer-based generator was tested
in a steel tank ﬁlled with oil (Mobilect 39) and degassed
Fig. 17. Ultracompact arrangement of the pulsed transformer-based generator.
Fig. 18. (a) Electrical scheme of the test. (b) Photograph of the real
experimental arrangement without oil.
under vacuum. The antenna is simulated by a capacitive load
of 80 pF, and the measurement of the output voltage is carried
out using a homemade fast 0.6-MV voltage probe described
in . The electrical circuit and the overall experimental
arrangement are both shown in Fig. 18.
One of the challenges of the MOUNA project is the genera-
tion of signals of short duration (500 ns) and very high voltage
(0.6 MV) in a very limited volume (less than 4 L). As the
tests described here are carried out without the output peaking
spark gap switch, the very high voltage output signal has a
duration approaching 5 μs, with multiple voltage inversions
making the electrical stress conditions much more demanding
than those encountered during operation with the transformer-
based generator placed inside the MOUNA assembly. This
issue required a very careful monitoring of the degassed oil.
A. Results Obtained in Single-Shot Mode
Fig. 19 presents the measured time history of the output
voltage for input voltages with a constant rise time around
265 ns in the range between 5 and 10 kV. At 0.6 MV, the trans-
former still operated normally but unfortunately an electrical
breakdown was noticed inside the 80-pF capacitor simulating
the Cline capacitance. As shown in Fig. 20, the output voltage
increases linearly as a function of the input voltage up to
0.5 MV. For higher voltages, as predicted by the LTSpice
model, the magnetic core begins to saturate before the end
of the energy transfer. It is possible, at least theoretically,
to overcome this saturation by premagnetizing the magnetic
circuit with a dc voltage of opposite polarity to the input
voltage, in order to cover the entire amplitude of the hysteresis
cycle of the magnetic material. To date this solution has not
164 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 46, NO. 1, JANUARY 2018
Fig. 19. Time variation of transformer output voltage for input voltages in
the range of 5–10 kV.
Fig. 20. Variation of the transformer output peak voltages for an input voltage
in the range of 4.5–10 kV.
Fig. 21. Record of a burst of 100 voltage impulses at a PRF of 20 Hz
(vertical sensitivity 50 kV/div and time interval 160 ns/div).
been tested, because it would at best increase the peak voltage
by a few percentages, while adding a demanding complexity
to the compact system.
B. Results Obtained in Repetitive Mode
It is well known that the high-intensity electric stress
issue becomes much more demanding in a high PRF mode
and therefore it was necessary to limit the time duration
the dielectrics are stressed by performing the tests under
conditions closer to those of the MOUNA prototype. In order
to do this, a pressurized gas spark gap was installed to crowbar
the output voltage impulse on a 50-resistor, when the
output voltage impulse reached a value close to its peak. It is
important to note that the crowbar also eliminates the dan-
gerous polarity reversal. Fig. 21 presents data obtained from
a burst of 100 pulses at a PRF of 20 Hz. After crowbarring,
the measurement is unfortunately not very accurate, because
Fig. 22. Typical pulsed transformer output voltages, for 9-kV input, measured
the frequency of the resulting oscillations is higher than the
50-MHz bandwidth limit of the 0.6-MV probe.
The reproducibility of the output pulses generated by the
transformer is very good, showing no sign of magnetic core
saturation. The PRF was limited by the power of the capacitor
chargers, but the tests nevertheless allowed assessing the
reliability of the oil degassing, an important issue related to
maintenance operation of the overall MOUNA prototype.
IX. COMPARISON BETWEEN EXPERIMENTAL DATA
AND THEORETICAL PREDICTIONS
Fig. 22 compares the experimental results for an initial
charging voltage of 9 kV with predictions made using the
LTspice modeling. The small differences noticed after 1 μsare
due to the imperfect modeling of the magnetic core losses, but
this issue is not important for the present project as it happens
after the peak voltage is reached and when most of the energy
is already transferred to the antenna. The peak output voltage
impulse is 560 kV, with a rise time of 265 ns and a time to
peak of 440 ns, well inside the values of parameters required
by the MOUNA project.
This paper presented the study, characterization, and the
practical implementation of a high-voltage, magnetic core,
resonant pulsed transformer. For ﬁnal testing operations, a
0.6-MV voltage probe and a capacitive load were also nec-
essary to be designed, manufactured, and calibrated which in
itself they were the subject of an extensive supplementary
study. The pulsed transformer, which occupies an overall
volume of less than 3.5 L, generates voltage impulses with
a peak up to 0.6-MV amplitude with a rise time of 265 ns
on a load of 92 pF. (The capacitive load has 80 pF, with a
supplementary 12 pF introduced by the high-voltage probe).
Calculation of the various parasitic inductive and capacitive
elements made possible the development of an LTspice model
for the transformer and therefore to very accurately predict
and control the most important experimental results.
Finally, a very important lesson for the community was
learned: the simple analytical estimates presented in this paper
can be trusted when designing magnetic core pulsed transform-
ers with the consequence that complex numerical studies using
expensive software like CST are not really required!
PÉCASTAING et al.: DEVELOPMENT OF A 0.6-MV ULTRACOMPACT MAGNETIC CORE PULSED TRANSFORMER 165
The authors would like to thank L. Caramelle,
J.-M. Duband, S. Roche, and F. Girard from Hi Pulse
Company, Pont de Pany, France, for their dedicated work and
the useful discussions along the research program.
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Laurent Pécastaing (M’13–SM’17) received
the Ph.D. and Research Directorship Habilitation
degrees in electrical engineering from the Université
de Pau et des Pays de l’Adour (UPPA), Pau, France,
in 2001 and 2010, respectively.
Since 2016, he has been a Full Professor with the
SIAME Laboratory, UPPA, where he is currently
the Head of the Electrical Engineering Team. He
is also the Director of the Common Laboratory,
CEA, Le Barp, France, and CEA, Gramat, France,
and UPPA. He has authored more 130 refereed
papers and conference contributions. His current research interests include
high-power microwave sources, compact pulsed power devices, and ultrafast
Dr. Pécastaing is the Chairman of the next Euro-Asian Pulsed Power
Conference –BEAMS conference to be held in France in 2020.
Marc Rivaletto received the bachelor’s degree from
the Supelec Electrical Engineering School, Gif-sur-
Yvette, France, in 1984, and the Ph.D. degree in
electrical engineering from Pau University, Pau,
France, in 1997.
He is currently a Lecturer with Pau University
and with the SIAME Laboratory, Université de Pau
et des Pays de l’Adour, Pau. His current research
interests include high-power microwave sources, and
compact pulsed power devices including pulse form-
ing lines, compact Marx generators, or resonant
Antoine Silvestre de Ferron received the Ph.D.
degree in electrical engineering from the Université
de Pau et des Pays de l’Adour (UPPA), Pau, France,
From 2006 to 2008, he was a Researcher with
the Atomic Energy Comission (CEA), Le Barp,
France—a French-government-funded technological
research organization. He is currently an Engineer
with the Laboratoire SIAME, UPPA. His current
research interests include high pulsed power genera-
tion for military and civil applications and combined
high-voltage transient probes.
166 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 46, NO. 1, JANUARY 2018
Romain Pecquois received the M.Sc. and Ph.D.
degrees in electrical engineering from the Université
de Pau et des Pays de l’Adour, Pau, France, in 2009
and 2012, respectively.
From 2012 to 2014, he was a Researcher with
the Commissariat à l’Energie Atomique, Le Barp,
France, with a focus on ﬂash X-ray radiography
machines and solid-state modulators. He is currently
in charge of research and development with I-Cube
Research, Toulouse, France, focusing on civilian
commercial applications of pulsed power.
Bucur M. Novac (M’06–SM’08) received the M.Sc.
and Ph.D. degrees from the University of Bucharest,
Bucharest, Romania, in 1977 and 1989, respectively.
In 1998, he joined the Loughborough Univer-
sity, Loughborough, U.K., where he is currently
a Professor of pulsed power. He is currently a
Chartered Engineer and a fellow of The Institution
of Engineering and Technology, Stevenage, U.K.
He has co-authored two books on explosive pulsed
power and has authored over 200 refereed papers
and conference contributions. His current research
interests include compact and repetitive high-power systems, explosively and
electromagnetically driven magnetic ﬂux compression generators and their
applications, electromagnetic launchers, ultrafast magnetooptic and electroop-
tic sensors, and 2-D modeling of pulsed-power systems.
Prof. Novac is a Voting Member of the Pulsed Power Science and Technol-
ogy Committee in the IEEE Nuclear and Plasma Science Society. He is also a
member of the International Steering Committees for both the MEGAGAUSS
Conferences and Euro-Asian Pulsed Power Conferences, and the organizing
committee for the IEEE International Power Modulator and High Voltage
Conference. He is the Co-Chairman of the U.K. Pulsed Power Symposium.