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Laser and Particle Beams
cambridge.org/lpb
Original Study
*Current address: Northwest Institute of
Nuclear Technology, No. 28, Pingyu Lu, Baqiao
Qu, Xi’an, Shaanxi 710024, People’s Republic
of China
Cite this article: Su J-C, Li R, Cheng J, Yu B-X,
Zhang X-B, Zhao L, Huang W-H. A coaxial-
output rolled strip pulse forming line based on
multi-layer films. Laser and Particle Beams
https://doi.org/10.1017/S026303461700091X
Received: 24 May 2017
Accepted: 10 December 2017
Key words:
Coaxial output; multi-layer films;
pulse-forming line; rolled strip line
Author for correspondence:
Binxiong Yu, Science and Technology on High
Power Microwave Laboratory, Northwest
Institute of Nuclear Technology, Xi’an, Shaanxi
710024, China. E-mail: yubinxiong@nint.ac.cn
© Cambridge University Press 2018
A coaxial-output rolled strip pulse forming line
based on multi-layer films
Jian-Cang Su, Rui Li, Jie Cheng, Bin-Xiong Yu*, Xi-Bo Zhang, Liang Zhao
and Wen-Hua Huang
Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology, Xi’an,
Shaanxi 710024, China
Abstract
A coaxial-output rolled strip pulse-forming line (RSPFL) with a dry structure is researched for
the purpose of miniaturization and all-solid state of pulse-forming lines (PFL). The coaxial-
output RSPFL consists of a coaxial-output electrode (COE) and a rolled strip line (RSL). The
COE is characterized by quasi-coaxial structure, making the output pulse propagate along the
axial direction with a small output inductance. The RSL is rolled on the COE, whose trans-
mission characteristics are analyzed theoretically. It shows that the RSL can be regarded as a
planar strip line when the rolling radius of the strip line is larger than 60 times of the thickness
of the insulation dielectric layer of RSL. CST modeling was carried out to simulate the dis-
charging characteristic of the coaxial-output RSPFL. It shows that the coaxial-output
RSPFL can deliver a discharging pulse with a rise time <6 ns when the impedance of the
RSL matches that of the COE, which confirms the theoretical analysis. A prototype of the
coaxial-output RSPFL was developed. A 49-kV discharging pulse on a matched load was
achieved when it was charged to 100 kV. The discharging waveform has a pulse width of
32 ns, with a rise time of 6 ns, which is consistent with the simulation waveform. An
energy-storage density of 1.9 J/L was realized in the coaxial-output RSPFL. By the method
of multi-stage connection in series, a much higher output voltage is convenient to be obtained.
Introduction
A pulse-forming line (PFL) is the key component of a pulsed power device to generate high-
voltage pulses with a width ranging from ns to μs. According to the structure, the PFL can be
divided into the coaxial PFL, the strip PFL, the spiral PFL, and so on. Miniaturization of the
PFL is an important direction for the development and application of pulsed power technol-
ogy. Different methods have been applied to minimize the size of the PFL, including the
stacked Blumlein line (Coogan et al.,1990; Davanloo et al.,1998; Liu et al.,2009), Marx tech-
nology (Zhang & Liu 2013), the transmission line transformer (Graneau 1990;Yuet al., 2014),
generator based on Tesla transformer and pulse forming network (Su et al., 2009), and so on.
Compared with a conventional single coaxial PFL, the charging voltage of a PFL using one of
the aforementioned methods is decreased, making it possible to employ insulation material
with high-energy density as the energy dielectric to minimize the size and weight of a PFL.
In recent years, great progress has been made in the manufacturing technology of insulated
film. Polypropylene (PP) films with good frequency characteristics and high-energy density are
widely used in pulse capacitor under electric field strength >200 kV/mm (Laihonen & Gäfvert
2007). So, it is feasible to use the PP films as energy dielectric in the plane-plate PFL or the
strip PFL to miniaturize a PFL. A strip PFL has three foil electrodes including two low-voltage
(LV) foil electrodes and a high-voltage (HV) electrode. The HV foil electrode is located
between the two LV foil electrodes, which forms an electromagnetic field distribution similar
to that of a coaxial PFL. Due to its weak magnetic leakage, it is feasible to roll the strip PFL
without waveform distortion when forming a pulse. But, there are some problems as to this
technology. On one hand, since a rolled strip pulse-forming line (RSPFL) has two LV elec-
trodes, the connecting inductance is large when the strip line is connected to the discharging
circuit. As a result, it will distort the output pulse waveform. On the other hand, in order to
improve the output voltage of the RSPFL, liquid insulation such as transformer oil is employed
as an assistant insulation dielectric of the RSPFL, which goes against the tendency of all-solid
state. Some researchers have already paid attention to the RSPFL (Yang et al., 2010;Liet al.,
2015). The RSPFLs mentioned in the references have the advantages of compactness,
portability, and long pulse achievability. However, apart from dipping in transformer oil,
these RSPFLs are connected with the discharging circuit through a point, which leads to a
large circuit inductance and an insufficient current flow capacity. So, the output pulses have
rise times slower than 10 ns, at the same time, overheating occurs at the connection point.
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A coaxial-output RSPFL based on multi-layer films is devel-
oped in this paper. It has a small discharging inductance due to
its coaxial-output structure. Instead of impregnation process,
heat treatment is employed to eliminate the bubbles of edges of
the foil electrodes, so that it has a dry structure. It is a feasible
method for miniaturization and all-solid state of a PFL.
Principle of the coaxial-output RSPFL
Transmission characteristics of the rolled strip line (RSL)
The cross-sectional view of a strip line is shown in Figure 1.It
contains three copper-foil electrodes, two insulation dielectric lay-
ers, and an isolation dielectric layer. The thicknesses of the three
copper foils are d
0
, and their widths are w. The thicknesses of the
two insulation dielectric layers are both d. the width of two insu-
lation dielectric layers and isolation dielectric layer are both w
1
.
As shown in Figure 2, the strip line is rolled around the center
axis with a rolling radius of R, and the rolled degree is 2w
0
.
Assume that a constant current, I
0
, flows in HV foil electrode,
and the current of I
0
/2 flows in each of the two LV foil electrodes
with opposite directions. According to the Faraday’s law, the
currents will induct a magnetic field. In a cylindrical coordinate
system, the current density in the HV electrode at point P
1
(R,w,z)
is jdzdl,wherej=I
0
/w, and the magnetic flux density at point
P(R
0
,0,z
0
)is
d
B=m0
4p
jdzd
l×r
r3
=m0j
4p
R[(z−z0)
er1 +(R−R0cos w)
ez]dwdz
((z−z0)2+R2
0+R2−2R0aR cos w)3/2.(1)
Its axial component is derived as
dBz=m0j
4p
R(R−R0cos w)
(R2
0−2R0Rcos w+R2+(z1−z0)2)3/2dwdz.(2)
So, the total axial magnetic flux density inducted by currents
in the three foil electrodes is
Bzt =m0I
4pw
w
0
−
w
0(f(R)−1
2f(R+d0
2+d)−1
2f(R−d0
2−d)dw,
(3)
where
f(x)= x(x−R0cos w)
R2
0−2R0xcos w+x2
w−z0
R2
0−2R0xcos w+x2+(w−z0)2
+z0
R2
0−2R0xcos w+x2+z2
0
(4)
when Rgoes to infinite large, the RSL becomes a planar strip line
whose maximum magnetic flux density is μ
0
I/2w. When w≫d,
the leakage magnetic flux of the planar strip line is much small.
In this condition, a planar strip line could generate ideal rectan-
gular pulses. In order to analyze the variation law of the magnetic
flux density versus the rolling radius Rin the RSL, parameters of
the RSL are set as w=20d,d
0
= 0, and z
0
=w/2. The magnetic flux
densities normalized by μ
0
I/2wagainst R/dare shown in Figure 3
for the case of a whole loop (w
0
=π) and a part loop with a small
degree (w
0
= 0.03π), respectively.
Figure 3(a) shows the variation of magnetic flux density in the
inner insulation dielectric layer (R
0
=R−d/2) and the outer insu-
lation dielectric layer (R
0
=R+d/2) versus R/dwhen the strip line
Fig. 1. Cross-sectional view of the strip line.
Fig. 2. Sketch of the RSL.
2 Jian-Cang Su et al.
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is rolled into a loop. From this figure, it is found that the two lines
of magnetic flux density in the inner insulation dielectric and in
the outer insulation dielectric get close to the value of μ
0
I/2w
rapidly as R/dincreases, which is the magnetic flux density in a
planar strip line. Figure 3(b) shows the magnetic flux density in
the outer insulation layer of the RSL when it is rolled with a
small degree of 0.03 π. It shows that the magnetic flux density
is gradually close to μ
0
I/2wwhen R>60d, which illustrates that
the magnetic flux density of the RSL is contributed by the current
unit nearby if R>60d. In this condition, the magnetic flux density
will not be affected by the current in adjacent turns of the RSL. So,
it is concluded that the RSL can be regarded as a planar strip line
when R>60dwith a characteristic impedance (Pozar, 2006).
Z0=60pd
1
r
√w+0.882d()
,w/2d.0.35,(5)
where ε
r
is the relative permittivity of the insulation dielectric
(PP films).
According to the principle of transmission line, the unit capac-
itance C
0
and the unit inductance L
0
of the RSL is
C0=
1
r
√
cZ0=2
1
0
1
rw+0.882d()
d,
L0=Z0
1
r
√
c=m0d
2w+0.882d()
.
⎧
⎪
⎪
⎨
⎪
⎪
⎩
(6)
The discharging pulse width τis
t=2l
1
r
√
c.(7)
The copper-foil electrodes should be thicker than the depth of
penetration to conduct large discharging current. The depth of
penetration caused by the skin effect is
h=
1
pfm0s
,(8)
where fis the average frequency of the discharging pulse; μ
0
is the
permeability of vacuum; ε
0
is the permittivity of vacuum; cis the
speed of light in vacuum; σis the conductivity constant of copper;
lis the length of the strip line.
Principle of coaxial output
A simplified sketch map of the coaxial-output RSPFL is shown in
Figure 4. The simplified coaxial-output electrode (COE) can be con-
sidered as a short coaxial line, which contains an inner cylinder, an
outer cylinder, and an insulation support. The RSL is rolled on the
COE around the center axis. Starting ends of the two LV electrodes
of RSL are connected to the outer cylinder, and the starting end
of HV electrode of the strip line is connected to the inner cylinder
through a hole in the outer cylinder. The coaxial-output structure
is required to discharge along the axial direction at first, and
the rise time of the discharging pulse is fast because the coaxial
discharging inductance is small. Then, the pulse generated by the
RSL is injected into the coaxial-output structure, and output
along the axial direction. It is required that the characteristic
impedance of the RSL equals to the circular impedance of the
COE. So, the pulse generated by the RSL will reach each point of
the circle of the coaxial-output structure without reflection. The
circular impedance of the COE is approximately derived as
Z1=60pd1
1
r1
√S,(9)
where d
1
and ε
r1
are the thickness and the relative permittivity of the
insulation support, respectively. Sis the effective width of a
coaxial-output structure.
Development of coaxial-output RSPFL
Design of the RSL
A PFL with a characteristic impedance of 4.4 Ωis required in our
laboratory to generate pulses with a pulse width of 30 ns, and its
maximum charging voltage is 100 kV. The thickness of the insu-
lation dielectric layer, d, is designed as 1 mm formed by 10-μmPP
films of 100 layers. According to the test results, the breakdown
voltage of PP films of 100 layers is as high as 200 kV. The relative
permittivity of PP films, ε
r
, is 2.2. It is derived that the width of
three copper-foil electrode, w, is 28.4 mm according to Eq. (6).
Fig. 3. Normalized magnetic flux density versus R/din insulation dielectric of the RSL: (a) w
0
=π; (b) w
0
= 0.03π.
Laser and Particle Beams 3
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The average frequency of the discharging pulse with a width of
30 ns is about 30 MHz. According to Eq. (8), the depth of pene-
tration in copper is calculated as 12 µm. The thickness of the elec-
trodes, d
0
, should be larger than 12 µm. Actually, copper foils
with a thickness of 50 µm are used. The width of the insulation
dielectric layer, w
1
, is determined as 70 mm. The isolation dielec-
tric layer is located between the two LV foil electrodes, and there
is no potential difference in the isolation dielectric layer. So, the
thickness of the isolation dielectric layer is determined as
0.2 mm, including 20 layers of 10-μm PP films. The length of
the strip line, l, is determined as 3 m to generate a pulse with a
width of 30 ns according to Eq. (7).
Structure of the COE
The COE plays a role of coaxial output. Its structure is shown in
Figure 5. It contains an inner metal electrode, an insulation
support, an outer electrode with a cavity, a cover of the cavity,
and a connective electrode. The inner metal electrode and the
outer electrode could be considered as the inner and the outer cyl-
inders of a coaxial line, respectively. The insulation support is
located between the inner and the outer electrodes, and it is
made of polyimide material. It could endure the voltage between
the inner and the outer electrodes. There is a rectangular hole in
the outer electrode. The connection electrode, which is electrically
connected with the inner electrode, is located in the middle of the
rectangular hole. In the middle of the connection electrode, there
is a perforating strip hole, through which the starting end of the
HV foil of the strip line connects to the inner electrode. The area
where the rectangular hole is located should be carefully treated to
make sure the surface is smooth.
R
a
is the smallest rolling radius of the RSL, and it is 120 mm,
which is larger than 60 times of the width of the insulation dielec-
tric layer. The outer diameter of the COE, D
0
, is 284 mm, and its
Fig. 4. A simplified sketch map of the coaxial-output RSPFL consisting of an RSL and a COE.
Fig. 5. Stretch of the COE:1, inner electrode; 2, insulation support; 3, outer electrode; 4, cover of the cavity; 5, connective electrode; 6, rectangular hole; 7,
perforating strip hole.
4 Jian-Cang Su et al.
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maximum length, L, is 94 mm. The effective width of the COE, S,
is 60 mm. According to Eq. (9), the matched thickness of the
insulation support is about 4 mm. However, the real thickness
is determined as 10 mm in order to endure the charging voltage
of 100 kV.
The total RSPFL
A rolling machine with multiple rolling axes is employed to roll
the strip line. At the beginning, all the ends of films and foil elec-
trodes are fixed on the COE. The distance between the starting
end of the HV foil and the starting ends of the two LV foils are
both 3 cm in order to reduce the connection inductance between
the RSL and the COE. Starting ends of 100 layers of PP films
forming the insulation dielectric layer are uniformly distributed
in a distance of 3 cm, so as to reduce air gap in the 3-cm area.
After all ends of the strip line are well fixed, the strip line is rolled
in the cavity of the outer electrode. Then, they are heated to 125°C
for 3–5 h to eliminate the air bubbles beside the foil electrodes, by
this means, discharging voltage along the surface will increase. At
the same time, the developed RSPFL has a dry structure with a
compression factor close to 1, which is convenient for the param-
eter design of the RSL (Fig. 6).
The picture of the COE is shown in Figure 7a, and the devel-
oped coaxial-output RSPFL without a cover is shown in Figure 7b.
Co-simulation of circuit and transient field
Modeling was done using CST Microwave Studio. A transient
solver (Petrella, et al., 2016) using a co-simulation of both ideal
circuit elements and three-dimensional (3D) models was used
to combine circuit models of the resistor and power supply
with a physical model of the RSPFL. Figure 8 demonstrates this
concept and shows the hybrid setup. The figure shows a voltage
supply in series with the resistor (R
1
), an inductor (L
1
) and the
RSPFL. Parameters of the RSPFL model are shown in Table 1,
which are mostly the same as the theoretic design in the section
“Development of coaxial-output RSPFL”.
The real thickness of the foil electrodes, d
0
, was 50 µm, which
made the finite-element numbers in simulation too many to carry
out. In order to lower the simulation difficulty, d
0
was set as 1 mm
in the modeling. According to Cohn (1955), the edge capacitance
of the foil electrodes would cause the characteristic impedance of
the RSL a little smaller. This influence could be accurately calcu-
lated in the simulation. According to finite-element simulation,
the characteristic impedances of planar strip lines with d
0
of
50 µm and 1 mm were calculated as 4.32 and 4.22 Ω, respectively.
Fig. 6. Sketch of connection between the COE and RSL: 1,
inner electrode; 2, insulation support; 3, outer electrode; 4,
cover of the cavity; 5, connecting electrode; 6, rectangular
hole; 7, perforating strip hole; 8, HV foil electrode; 9, LV
foil electrode; 10, isolation insulation layer; 11, insulation
dielectric layer.
Fig. 7. Picture of the developed coaxial-output RSPFL: (a) The COE; (b) The RSPFL without the cover.
Laser and Particle Beams 5
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Besides, as the volume of the RSL became larger, the smallest roll-
ing radius of the RSL (R
a
) was decreased to 100 mm in the mod-
eling. However, R
a
was still larger than 60 d.
An equivalent circuit of the discharging progress is simulated.
The voltage supply is a step signal with an amplitude of 1 V, and
L
1
and R
1
are set as 20 nH and 4.4 Ω, respectively. There is a
probe (P
1
) to record the voltage differential V
0
on R
1
, whose the-
oretic amplitude is R
1
/(R
1
+Z
0
). The pulse waveform of V
0
is the
same as the discharging waveform of the RSPFL on R
1
.
The simulations were carried out when the thickness of the
insulation support (d
1
) was set as 4 and 10 mm, respectively.
The simulation result was shown in Figure 9. From the figure,
it was found that the voltage pulse on R
1
has a pulse width of
33 ns, with amplitude of 0.51 V. So, the simulation impedance
of the RSL, Z
0
, was calculated as Z
0
=(1–0.51)/0.51 × 4.4 =
4.227 Ω, which was the same as the impedance of a planar strip
line with the same cross-section. It shows that the RSL can be
regarded as a planar strip line when the rolling radius of the
strip line is larger than 60d. As the simulation impedance of
the strip line with d
0
of 50 µm was 4.32 Ω, while the theoretic
value was 4.4 Ω. the relative error was 2.8%, which was acceptable
for an engineering design.
There was a reflection in the rise time of the output pulse when d
1
was 10 mm, and the reflection was much smaller when d
1
became
4 mm. As the analysis in the subsection “Structure of the COE”,
the reflection occurred because the impedance of the RSL did not
match the impedance of the COE when d
1
= 10 mm. The pulse
width of the pulse is 33 ns, which was larger than the theoretic
design as the COE was contributed to the pulse width, which
generated the additional three nanoseconds.
Fig. 8. The CST Microwave Studio co-simulation. (a) A combination of 3D modeling
and discrete circuit elements. (b) A sectional view of the coaxial-output RSPFL model.
Table 1. Parameters of the RSPFL in the CST modeling compared with the
design value
Parameters Values in the modeling Design value
w28.4 mm 28.4 mm
d
0
1 mm 0.05 mm
w
1
70 mm 70 mm
d1mm 1mm
l2.8 m 2.8 m
d
1
4 and 10 mm 10 mm
R
a
100 mm 120 mm
Fig. 9. Simulation equivalent discharging pulse waveform of the RSPFL.
Fig. 10. Structure sketch of the testing circuit of the RSPFL.
Fig. 11. Output pulse waveform of the RSPFL on a 4.4-Ωload.
6 Jian-Cang Su et al.
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Experiments and results
The capacitance of the developed RSPFL, which contains the
capacitance of the COE and the capacitance of the RSL, was mea-
sured as 3.54 nF by an RLC meter. The capacitance of the COE
was measured as 140 pF. So, the capacitance of the RSL was
3.4 nF, while the value calculated by Eq. (7) was 3.41 nF. The
relative error was smaller than 1%.
Voltage endurance capability of the developed RSPFL was tested
in a high-pressure atmosphere as the structure sketch shown in
Figure 10. A DC supply was applied to charge the RSPFL. When
the RSPFL was charged to 100 kV, the spark gap located between
the RSPFL and the load broke down. Then, a voltage pulse with
an amplitude of 49 kV was generated on the 4.4-Ωceramic resistor
load. The output waveform is shown in Figure 11.
The amplitude of the discharging pulse is less than the theoretic
amplitude on a matched load, which is 50 kV because of the loss in
the spark gap. The discharging voltage pulse has a pulse width of
32 ns, with a pulse rise time as short as 6 ns and the amplitude
fluctuation of the pulse flattop is <5%. Similar with the simulation
waveform, there is a reflection in the rise time of the discharging
pulse as d
1
is 10 mm in order to ensure the voltage endurance
capability of the COE.
The maximum charging voltage of the developed coaxial-
output RSPFL is 100 kV with a lifetime of less than pulses because
breakdown along the surface, and the lifetime will increase to
10,000 pulses because of volume breakdown if the charging
voltage decreases to 80 kV. The maximum energy density of
the developed coaxial-output RSPFL is calculated as 1.9 J/L. the
energy density of the RSPFL is much larger than that of trans-
former oil. However, the pulse lifetime is shorter than foiled
capacitor impregnated in oil. There are two reasons: the first
one, as the insulation thickness of the RSPFL is 1 mm, while
that in the capacitor is usually smaller than 0.1 mm. So, the elec-
tric field enhance in RSPFL is much large than that in the capac-
itor if the even electric field is the same. The second one, the
RSPFL with a dry structure is difficult in heat dissipation so
that corona breakdown occurs.
The coaxial-output RSPFL is modularized, and it is convenient
to realize multi-stage connection in series to acquire a much
higher operating voltage (Graneau, 1990). As shown in Figure 12,
The PFL of the generator based on Tesla transformer is formed
by 11 stages of RSPFLs, which has a similar structure with the
PFL shown in (Su et al., 2009). The inner electrode of the front
stage of RSPFL is connected to the outer electrode of the next
stage, and the like. If the charging voltage of each RSPFL is
80 kV, then the charging voltage of PFL formed by 11 stages of
RSPFLs will reach 800 kV. At the same time, the output waveform
will be much better than that shown in (Su et al., 2009), because
the RSPFL has a coaxial-output structure, which will decrease the
inductance of series loop. This work is under process.
Conclusions
A coaxial-output RSPFL based on stacked films has been proposed
and developed in this paper. Three advantages of the RSPFL were
achieved as follows. Firstly, its energy density reached as high as
1.9 J/L, which was much higher than that of a coaxial PFL using
transformer oil as the insulation material. So, it is feasible to realize
the miniaturization of the PFL. Secondly, it can deliver a discharg-
ing pulse with a rise time of 6 ns on a matched load, and the
amplitude fluctuation of the pulse flattop was < 5%. Finally, modu-
larization and miniaturization of the coaxial-output RSPFL are both
realized, and it is convenient to obtain high output voltage through
connecting multi-stage of modules in series. The pulse discharging
test showed that the RSPFL can generate a 49-kV pulse with a pulse
width of 32 ns on a matched load of 4.4 Ω. It is necessary to increase
the lifetime of the RSPFL in future work before the RSPFL can be
used in a repetitive frequency-operating generator.
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Fig. 12. Structure of a Tesla-style pulse generator based on
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