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156 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 46, NO. 1, JANUARY 2018

Development of a 0.6-MV Ultracompact

Magnetic Core Pulsed Transformer for

High-Power Applications

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,

transformers.

I. INTRODUCTION

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: laurent.pecastaing@univ-pau.fr).

B. M. Novac is with the Wolfson School of Mechanical, Electrical and Man-

ufacturing Engineering, Loughborough University, Loughborough LE11 3TU,

U.K. (e-mail: b.m.novac@lboro.ac.uk).

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 [1]–[5]

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 [6], [7]. Related to the

wideband threats, simple short duration oscillating power

systems [8] 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 [9] or

an air-core Tesla transformer [10]. The present arrangement,

however, (described in [11]), 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 [12] will

all be discussed. Finally, experimental results are compared

with software predictions.

II. MOUNA ELECTROMAGNETIC SOURCE AND THE

REQUIREMENTS IMPOSED ON THE

PULSED TRANSFORMER

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) [11].

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

energy transfer.

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

when [13]

Cp=n2Cs(1)

with the corresponding maximum output voltage Vs

given by

Vs=nVp.(2)

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 [14] simulations

were used to obtain the optimum value of the transmission line

capacitance Cline as 80 pF [13] 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 [11] 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

shorter.

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

CORE CHARACTERISTICS

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

z

r

r

z

Secondary winding

Primary winding

Cylindrical winding

Conical winding

Fig. 3. Winding strategies for the secondary winding.

Primary winding

Secondary

windings

Magnetic circuit

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

tpeak =πLpCpn2Cs

Cp+n2Cs.(3)

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 [16] 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

lowered.

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 [17], 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

necessary.

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 [18]

FBD =480t−1

3

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 [19].

The magnetic circuit is made of Metglas 2605SA1 [20].

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 [15], 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:

T

2

0

VS(t)dt =NS·B·S(5)

where Tis the period and f=1/Tis the corresponding

frequency of the output voltage impulse. The cross section

can be straightforwardly estimated from

T

2

0

VSmax

21−cos 2π

Ttdt =VSmaxT

4.(6)

For VSmax =600 kV, T/2 =500 ns, NS=60, and

B=1.56 T, the cross section Sis obtained as

S=VSmaxT

4NSB≈1600 mm2.(7)

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

thickness c/2.

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

Din_prim =c√2+2e(8)

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

2≈55.5mm.(9)

The height hin Fig. 5, valid for both the primary and the

secondary windings, can be estimated as

h≈R2

int_core −R2

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

estimated as

p=h2+(Rout_sec −Rout_prim)2

n≈1.3mm.(11)

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

Lc=2Rout_core −c

4tan−1⎛

⎝Rout_core −c

42−c

42

c/4⎞

⎠

+2Rout_core −c

42−c

42.(12)

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

Mc=Lc·S·ρ(13)

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 [21] for an

accurate estimation of the magnetic core power density losses

Pwat a sinusoidal resonant frequency f (deﬁned above) as

Pw=kfαˆ

Bβ(14)

where ˆ

B=Bsat. Using the values for the coefﬁcients as

provided in [22]: 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

Ej=Pw·tpeak ·Mc(15)

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 [23]

Wmagnetic =1

2lσI2

p(16)

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 [24]. In such condi-

tions, it is reasonable to consider a constant magnetic ﬁeld H

generated in the space between the two windings [16]. With

this assumption, the total energy stored is calculated as

Wmagnetic =μ0|H|2

2Vol =μ0NpIp

h2

2Vol (17)

for which the corresponding leakage self-inductance can be

estimated as

lσ=μ0N2

p

h2Vol (18)

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 [25] 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 [26]: 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

Welectric =1

2Cpsn2V2

p=1

2ε0εrVol

E2dv(19)

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

Dps(z)=Rout_sec −Rout_prim

hz(20)

Vps(z)=n

hVpz.(21)

As a consequence the electric ﬁeld is practically constant

Eps(z)=nVp

Rout_sec −Rout_prim =Emax.(22)

In these conditions, the calculation is straightforward

1

2n2V2

pCps =1

2ε0εrRout_sec

Rout_prim

rdr 2π

0

dθh

0

E2

ps(z)dz (23)

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

is double.

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

angle α≈π/2.

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

calculated as

Dsc(z)≈R2

in_core−(z−h)2−Rout_sec−Rout_prim

hz−Rout_prim

(25)

Vsc(z)=n

hVpz.(26)

Using (25) and (26), it is easy to determine the axial variation

of the electric ﬁeld:

Esc(z)≈

n

hVpz

R2

in_core−(z−h)2−Rout_sec−Rout_prim

hz−Rout_prim

.

(27)

In these conditions, Csc is obtained by numerically solving the

equation

αCsc =ε0εr1Rin_core

Rout_sec rdr 0dθh

0E2

sc(z)dz

n2V2

p≈6pF.(28)

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

estimate.

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

winding;

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

PRACTICAL REALIZATION

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

tpeak(X)=πLp−Lσ

X+Lσ·Cpn2Cs

Cp+n2Cs(29)

trise(X)=0.295 ×2πLp−Lσ

X+Lσ·Cpn2Cs

Cp+n2Cs

(30)

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 [15],

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

Imax(X)=

Cpn2Cs

Cp+n2Cs

Lp−Lσ

X+LσVp.(31)

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 [15]. 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

transformer.

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

windings.

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

sixty turns;

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

transformer.

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 [27] 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 [28]. 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 [27]. 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

and simulated.

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.

X. SUMMARY

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

ACKNOWLEDGMENT

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

transient probes.

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

transformers.

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,

in 2006.

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.