This paper presents a compact and portable highvoltage generator based on magneticcore Tesla transformer for driving an UWB high power electromagnetic source. In order to optimize the performance of the highvoltage generator, a novel openloop cylindrical magneticcore adopting the quaddivision lamination structure is proposed and manufactured. The designed highvoltage generator using the proposed magnetic core has a batterypowered operation and compact size of 280 mm × 150 mm in length and diameter, respectively. The highvoltage generator can produce a voltage pulse waveform with peak amplitude of 450 kV, a rise time of 1.5 ns, and pulse duration of 2.5 ns at the 800 V input voltage.
1. Introduction
Recently, the vulnerability of electronic devices to high power electromagnetic (HPEM) threats has been studied widely
[1]
. Ultrawideband (UWB) HPEM source capable of producing output power in the giga watts range allows real investigation of susceptibility of electronic devices as well as their protection and hardening against HPEM threats
[2]
. In the future, UWB HPEM source tends to be higher pulse repetition rate, compact and portable size for the efficient testing in a variety of conditions.
Marx generators are usually applied for the generation of highvoltage pulse power to drive the UWB HPEM source. However, besides huge and complex, it is difficult to operate under high repetition rate
[3]
. In order to circumvent these problems, a magneticcore Tesla transformer with compact structure and high coupling coefficient can be an alterative of Marx generator. The magneticcore Tesla transformer, which is Tesla transformer with openloop cylindrical magneticcore, was first proposed by Russian scientists
[4]
. The performance of the transformer is dependent on the magneticcore properties. Particularly, as the transformer become smaller, its performance degrades significantly due to the core loss and magnetic saturation which are proportional to the operation frequency. Hence, the use of low loss magneticcore is required to achieve good performance of the transformer.
So far highvoltage pulse power generator based on the magneticcore Tesla transformer has been widely developed. The most commonly known systems are SINUS and RADAN series
[5]
. However, there have been no research results for the magneticcore structure applicable to the Tesla transformer) In this paper, a novel magneticcore adopting the quaddivision lamination structure is proposed. Also, the highvoltage generator using the proposed magneticcore is designed and tested.
2. Parameters Analysis of magneticcore Tesla Transformer[6,7]
Magneticcore Tesla transformer consists of a primary circuit, a secondary circuit, and the magneticcores. The primary circuit is formed by a series of a primary winding and a capacitor. The secondary circuit is also formed by a series of the secondary winding and a coaxialtype capacitor. The magneticcores enhance the magnetic coupling between the primary and the secondary circuits. At the same time, it plays a role of the inner and the outer conductors of the coaxialtype secondary capacitor.
The structure and magnetic field distribution of the magneticcore Tesla transformer is shown in
Fig. 1
. Here
r
_{i}
and
r
_{o}
represent the outer radius of the inner magneticcore and the inner radius of the outer magneticcore, respectively. The effective crosssectional area of the inner and the outer magneticcore are marked as
A
_{e1}
and
A
_{e2}
, respectively. The
l
_{T}
is the length of the magneticcore with relative permeability
μ
_{r}
. The
l
_{K}
is the overlap length of the primary and the secondary winding. The
N
_{1}
and
N
_{2}
represent the turn numbers of the primary and the secondary windings, respectively.
Structure and magnetic field of the Tesla transformer
For simplicity we assume that the axial magnetic field in the magneticcores is uniform and the influence of eddy current is ignored. The magnetic fields of the outer and the inner magneticcores are represented by
H
_{11}
and
H
_{12}
, respectively. The fields in the spacing between the magneticcores include a radial and an axial component, which are
H
_{21}
,
H
_{22}
, and
H
_{3}
, respectively.
Since the main magnetic flux of the transformer is determined by a radial component, the axial component
H
_{3}
is ignored in the analysis. Assuming the primary winding current
I
_{1}
is uniformly distributed in the primary winding which is located at middle of the magneticcore, boundary conditions are the same at both ends of the magneticcore. Consequently, the transformer has a symmetrical magnetic field distribution. Thus, if the effective crosssectional area of inner and outer magneticcores are equal, that is
A
_{e1}
=
A
_{e2}
=
A
_{e}
, the magnetic field in the magneticcores
H
_{1}
and the magnetic field in the spacing between the magneticcores
H
_{2}
can be defined as follows, respectively
According to the flux conservation of inner and outer magneticcores,
Φ
=
A
_{e}
H
_{1}
=
A
_{e}
H
_{2}
(
r
),
r_{i}
≤
r
≤
r_{o}
, the relationship between
H
_{1}
and
H
_{2}
is given by
From Ampere’s circuital law, the relationship between current and magnetic field is as follows
where
β
=
r
_{o}
r
_{i}
.
Relationship of the storage energy in the magneticcores
W
_{1}
and the storage energy in the spacing between the magneticcores
W
_{2}
, substituting Eq. (3), gives the following:
where
μ
_{0}
is the permeability of free space. Magnetic field energy is mainly concentrated in the spacing between magneticcores because
μ
_{r}
>>
π
l
_{T}
(
l
_{T}

l
_{K}
)
A
_{e}
ln
β
. Therefore, the first term of Eq. (4) can be neglected, and then magnetization inductance
L_{μ}
is defined as follows
Assuming that
H
_{P}
is the magnetic field produced by the primary winding current
I
_{1}
and
H_{S}
is the reverse magnetic field produced by the secondary winding current
I
_{2}
, leakage inductance
L
_{s}
is represented by
The method for calculating the magnetic field produced by the secondary winding is the same as that for the primary windings described above, therefore, leakage inductance
L
_{s}
is defined as follows
If the coupling coefficient
K
has a value close to 1, according to the Eqs. (6) and (8),
K
is defined by
where
F
(
β
) = (
β
−
1
)(
2
β
−
1
)
β
^{2}
.
Assume the leakage inductance of the primary winding
L
_{s1}
equals that of the secondary winding
L
_{s2}
, that is
L
_{s1}
=
L
_{s2}
2=
L
_{s}
. So the inductances of the primary and the secondary windings,
L
_{1}
and
L
_{2}
, are calculated as follow
3. Design and Fabrication of the Magneticcore
 3.1 Design of the magneticcore structure factor
The coupling coefficient of the transformer,
K
, as shown in Eq. (9), is determined by a geometric factor such as the length and the radius of the magneticcore. Optimization of the magneticcore geometric structure is required to maximize
K
.
The length of magneticcore is designed by the required pulse length, which is given by
where
τ
is pulse width,
ε
_{r}
is the dielectric constant of the insulating material used as dielectric in the secondary capacitor, and
c
is the light velocity in free space.
The radius of the magneticcores is designed in consideration of the dielectric strength of the secondary capacitor. If
β
is satisfied with the following equation, the withstand voltage of the secondary capacitor has the maximum value.
As shown in
Fig. 2
for Eq. (9), when
l
_{T}
and
β
(=
e
) have a constant value,
K
can be maximized in a condition of
l
_{K}
=
l
_{T}
/
2
. From
Fig. 2
, a significant relationship between the coupling coefficient
K
and the aspect ratio
l
_{T}
/
r
_{o}
can be inferred;
K
becomes larger in proportion to the aspect ratio. So, choosing the length of the magneticcore properly can lead to a larger
K
. However, larger aspect ratio is also limited by the engineering implementation. In this paper, an aspect ratio of 5:1 is achieved in consideration of the transformer size and fabrication feasibility.
Relationships between structure factor of the magneticcore and coupling coefficient.
The effective crosssectional area of magneticcore must be designed in consideration of the magnetic saturation. To avoid the saturation of the magnetic material, the effective crosssectional area of magneticcore should be determined by the condition which the maximum deviation of magnetic induction in magneticcore is less than the saturation magnetic induction of the material. The effective crosssectional area of magneticcore
A
_{e}
can be described in the expression
[8]
.
where
ΔB
_{max}
is the maximum deviation of magnetic induction in magneticcore,
V
_{max}
is the maximum charging voltage of secondary capacitor, and
T
_{ch}
is the charging time.
 3.2 Manufacture of the proposed magneticcore
The performance of magneticcore is determined by magnetic material and structure. A highly conductive magnetic material should be used because magneticcore is act as the conductor of secondary capacitor of the transformer. Also, the loss of magneticcore can be reduced by structure of magneticcore with laminated thin magnetic sheets.
Considering the abovementioned issues, we proposed a novel openloop cylindrical magneticcore adopting the quaddivision lamination structure. As shown in
Fig. 3
, the proposed magneticcore is composed of the lamination body, ultrathin magnetic sheets, and the crossshaped frame. Lamination body is formed by stacked lamination of the rectangle magnetic sheets in the same size. This lamination method makes it easy to fabricate the lamination body and maximize the stacking factor. Lamination area is divided into quadarea by the crossshaped frame which is used to support the lamination body. The surface of the crossshaped frame is curved identically to the outside curvature of the magneticcore. Lamination bodies are arranged so that their lamination directions are orthogonal each other in the adjacent areas. These structural features are effective to reduce material damage and stress that occur during the cutting work for forming into cylindrical shape.
Cross section of the proposed magneticcore
The photograph of the proposed magneticcore is shown in
Fig. 4.
Material of the magneticcore adopts nonoriented silicon steel with a thickness of 0.1 mm and saturation flux density of 1.8 Tesla.
Photograph of the proposed magneticcore
4. Development of Highvoltage generator Based on Magneticcore TESLA Transformer.
 4.1 Design and construction of highvoltage generator
Electrical parameters for designing the Tesla transformer are shown in
Table 1.
Where
C
_{1}
and
C
_{2}
are capacitances of the primary and the secondary capacitors, respectively.
R
_{1}
and
R
_{2}
are resistances of the primary winding and the secondary windings, respectively.
R
_{k1}
and
L
_{k1}
are a stray inductance and a stray resistance of the primary circuit, respectively.
Electrical parameters of the Tesla transformer
Electrical parameters of the Tesla transformer
A highvoltage generator based on Tesla transformer with the proposed magneticcore is designed and constructed. The prime electric energy of the generator, as shown in
Fig. 5
, is supplied by a rechargeable battery (DC 48 V, 7 Ah), and the primary capacitor
C
_{1}
is charged to the initial voltage 800 V through the fullbridge DCDC converter and pulse charger. The primary winding
L
_{1}
is made of a copper strip with a thickness of 0.5 mm, the conical secondary winding
L
_{2}
is made of 700 turns of a 0.18 mmdiameter copper wire.
Circuit diagram of the highvoltage generator
Components of the generator, as shown in
Fig. 6
, are housed in the pressure vessel. Insulation oil is filled in the Tesla transformer, which is pressurized through an oil conservator in order to raise their electric insulation level. The sparkgap switch is filled with insulation gas. Two capacitive voltage dividers CD1, CD2 are used to measure the charging voltage of the secondary capacitor
C
_{2}
and the output voltage of the highvoltage generator, respectively. A capacitive voltage divider is made up of a dielectric film of 0.15 mm thickness covered with copperclad in both sides. Their selfcapacitances are 765 pF and 479 pF, respectively. Their division ratios are 1:19300 and 1:4360, respectively. The photograph of the highvoltage generator is shown in
Fig. 7.
The generator has a small size, whose dimensions are 280 mm × 150 mm in length and diameter, respectively.
Cross section diagram of the highvoltage generator.
Photograph of the highvoltage generator.
 4.2 Measurement and results
Commercially available software is used to calculate the charging voltage of
C
_{2}
of the circuit simulation schematic shown in
Fig. 8
. The values of circuit parameters in
Fig. 8
are defined by the design values given in
Table 1.
The simulation voltage waveform of charging
C
_{2}
is shown in
Fig. 9.
The waveform has a peak voltage of 460 kV and a charging time of about 2.2 μs for reaching the peak in its first cycle.
Circuit simulation schematic of the transformer
Simulated voltage waveform of charging the secondary capacitor
In experiment, the breakdown voltage of the sparkgap switch is set to slightly lower voltage than the maximum charging voltage of the secondary capacitor. The experimental voltage waveform of charging
C
_{2}
is shown in
Fig. 10.
Experiment voltage waveform of charging the secondary capacitor
When initial charging voltage of
C
_{1}
is 800 V, the peaking charging voltage of
C
_{2}
is obtained as high as 450 kV and the charging time is about 2 μs. Experiment result shows good agreement with simulation one shown in
Fig. 9.
From the experiment result, the voltage gain of the transformer is 1 : 563 and energy transmission efficiency is calculated to be about 50 %.
A highvoltage pulse is generated when the transformer works together with sparkgap switch. Output voltage pulse of the highvoltage generator is shown in
Fig. 11.
It is clearly shown that the voltage pulse across the open load has an amplitude of 450 kV, a full width at half maximum (FWHM) of 2.5 ns, and a rise time of 1.5 ns. The design value of FWHM is 2ns by the Eq. (12). But, the measured value of FWHM is slightly increase by finite transition time of sparkgap switch. Output power of the highvoltage generator is calculated to be about 1.25 GW for the 50Ω load. In the
Fig. 11
, there exist sequent steplike oscillations in the back edge of the waveform, which is result from the multiple voltage reflection due to the impedance mismatch between load and coaxialtype secondary capacitor.
Output voltage pulse of the highvoltage generator
5. Conclusions
A novel openloop cylindrical magneticcore applicable in the magnetcore Tesla transformer is proposed and manufactured. Highvoltage generator based on Tesla transformer using the proposed magneticcore is designed. The designed generator has a batterypowered operation and compact size of 280×150 mm in length and diameter, respectively. Experiment results show that the generator can export highvoltage pulse with an amplitude of 450 kV and FWHM of 2.5 ns, with an energy conversion efficiency of about 50%. Output power of the generator is about 1.2 GW for the 50 Ω load. The developed highvoltage generator can be applied for the compact and portable UWB HPEM source.
BIO
YoungKyung Jeong received his M.S. degree in Computer Science & Engineering, Changwon, Koera, in 1999. He is currently working on his Ph.D. course in the Department of Electrical and Computer Engineering, University of Seoul, Korea and a researcherincharge in the Replex. Co., Ltd., Seoul, Korea. His research fields of interests are the HPEM and pulsed power systems.
DongGi Youn received M.S. and Ph.D. degrees in Electronics Engineering from Kyungnam University, Changwon, Korea, in 1997 and 2000, respectively. He is currently a chief executive officer in the Replex. Co., Ltd., Seoul, Korea. His research fields of interests are the HPEM and RF engineering.
MoonQue Lee received M.S. and Ph.D. degrees in Electronics Engineering from Seoul National University, Seoul, Korea, in 1994 and 1999, respectively. He is currently a Professor in the Department of Electrical and Computer Engineering, University of Seoul, Seoul, Korea. His research fields of interests are the design of RFCMOS and MMIC.
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