Electrical modelling approach for

IOP PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 42 (2009) 045213 (8pp)
doi:10.1088/0022-3727/42/4/045213
Electrical modelling approach for
discharge analysis of a coaxial DBD
tube filled with argon
U N Pal1 , A K Sharma1 , J S Soni1 , Sonu Kr1 , H Khatun1 , M Kumar1 ,
B L Meena1 , M S Tyagi1 , B-J Lee2 , M Iberler2 , J Jacoby2 and K Frank3
1
Microwave Tubes Area, Central Electronics Engineering Research Institute (Council of Scientific and
Industrial Research), Pilani, Rajasthan-333031, India
2
Institute of Applied Physics, Johann Wolfgang Goethe University, 60438 Frankfurt am Main, Germany
3
University of Erlangen-Nuremberg, Erwin-Rommel-Str. 1, D-91058 Erlangen, Germany
E-mail: [email protected]
Received 25 July 2008, in final form 13 November 2008
Published 30 January 2009
Online at stacks.iop.org/JPhysD/42/045213
Abstract
Dielectric barrier discharges (DBDs) occur in the presence of at least one insulating layer in
contact with the discharge between two planar or cylindrical electrodes connected to a high
voltage supply. A quartz coaxial DBD tube, filled with argon, has been studied and an electrical
model characterizing the discharges has been proposed. The proposed model considers the
geometry of the DBD tube, gas gap spacing and the properties of the dielectric barrier
material. A sinusoidal voltage up to 2.4 kV peak with frequencies from 20 to 100 kHz has been
applied to the discharge electrodes for the generation of microdischarges. By comparisons of
visual images and electrical waveforms, the filamentary discharges have been confirmed. The
simulated discharge characteristics have been validated by the experimental results. A good
correlation between the experimental and simulated results was found, which is used to deduce
the circuit impedance and other electrical parameters, in particular, the conduction current,
charge accumulation, energy deposited and consumed power during discharges.
(Some figures in this article are in colour only in the electronic version)
on experimental conditions such as discharge gas, gas pressure,
gas gap, dielectric surface properties and applied voltage
waveform [5–11].
In the recent literature, many researchers have explored
new efficient VUV and UV sources based on the radiation
of excimer or exciplexes excited by DBDs. DBD modelling
has been of interest in the literature. DBD configuration and
dielectric phenomenon are represented by analogous electrical
components. Kogelschatz [12], Chiper et al [13] and Naud´e
et al [14] included a variable resistor, which represents the
microdischarge channels. Bhosle et al [15, 16] included a
resistor ignited by a TRIAC device in order to implement the
single filamentary discharge and the highly nonlinear variable
impedance to represent the discharges. Liu and Neiger [17]
proposed an electrical model of a DBD under an arbitrary
excitation voltage. Valdivia-Barrentos et al [18] have used the
1. Introduction
Dielectric barrier discharges (DBDs), also referred to as silent
discharges, are generated in discharge configuration with at
least one dielectric barrier between two planar or cylindrical
electrodes connected to an ac or pulse power supply. These
dielectric layers act as a current limiter and prevent the
formation of a spark or an arc discharge. DBDs are the easy
way to a generate non-thermal and non-equilibrium plasma at
atmospheric pressure [1]. DBDs are considered as promising
alternatives to conventional mercury based discharge plasmas
producing highly efficient vacuum ultraviolet (VUV) and
ultraviolet (UV) radiations and have found a number of
industrial applications ranging from plasma display panels
to surface treatment [2–4]. The discharge appearance of
DBDs can be either filamentary or homogeneous, depending
0022-3727/09/045213+08$30.00
1
© 2009 IOP Publishing Ltd
Printed in the UK
J. Phys. D: Appl. Phys. 42 (2009) 045213
U N Pal et al
and the inner electrode of Cusil foil has been inserted into the
coaxial tube in close proximity to the inner wall. A high voltage
signal is applied on the inner electrode, while the outer mesh
electrode is grounded. The inner radius of the outer quartz
tube is 18.5 mm and the thickness is 1.5 mm, while the inner
radius of the inner quartz tube is 15 mm and the thickness is
2 mm. The gas gap is 1.5 mm. The total length of the DBD
tube is 30 cm while the outer mesh and the inner foil electrode
wrap 9 cm of the tube.
2.2. Set-up
Figure 2 shows the experimental set-up. A sinusoidal high
voltage supply (Huttinger HF Generator TIG 10/100 PSC)
up to 2.4 kV peak with frequencies from 20 to 100 kHz has
been applied to the discharge electrodes for the generation of
microdischarges. The variable oscillator circuit capacitances
of the generator (parallel connection of individual capacitors
within a block) make it possible to change the operating
frequencies and matching to the output load. The DBD cell
has been mounted on an ultra-high vacuum pump station. It
has been evacuated to 8 × 10−9 mbar pressure and baked up
to 450 ◦ C to achieve an ultimate pressure of 5 × 10−9 mbar.
At room temperature, argon gas of 99.99% purity (BOC
Gases) has been filled in the DBD cell. The gas flow has
been controlled by a mass flow controller (Matheson: 82720453). The pressure has been measured by pressure gauges
(Leybold: 16040, Pfeiffer: PKR251) and the pressure has
been maintained by vacuum valves (Matheson: 316L, Varian:
9515091). The outer wire mesh electrode acts as a cathode
while the inner foil electrode as an anode. The wire mesh
electrode allows the radiation to come out of the tube for
spectroscopic analysis. An external capacitor Cext (500 pF)
has been used to measure transferred charges. A 1 : 1000
high voltage probe (Tektronix P6015A) measures the voltage
across the DBD tube and the Rogowski-type Pearson current
monitor, Model 110 (0.1 V A−1 , 1 Hz–20 MHz, 20 ns usable
rise time) measures the total current flowing through the DBD
tube. The total current and applied voltage waveforms are
visualized by means of a four-channel Tektronics TDS 3034B
digital oscilloscope. The oscilloscope is interfaced with the
personal computer for real time analysis and recording the
voltage and current waveforms.
Figure 1. (a) Fabricated coaxial DBD tube and (b) schematic
description of the coaxial tube.
concept given in [17] to simulate the model by superimposing
microdischarges on the displacement current waveform for
different operating frequencies.
We have proposed a novel simulation model of DBD
based on the equivalent electrical circuit for an argon
filled DBD cell. In our approach, we have compared the
experimental and simulated DBD discharge characteristics
explicitly, which includes the total current, applied voltage, gas
gap voltage, discharge current, supplied power and consumed
power. We have also deduced the change in the plasma
impedance based on the correlation of the experimental
and simulated results of all discharge characteristics, which
differs from earlier works [15–18].
A quartz coaxial
DBD cell filled with argon gas has been used for the
experiments and the discharges are characterized under
different operating conditions. Experimental data have been
used for numerically solving the circuit equations to determine
the discharge characteristics such as the gap voltage, discharge
current, charge accumulation and the power consumed during
discharge. This model is implemented using MATLAB
Simulink in which the observed discharge conditions have
been included. The results obtained from the simulated model
have been compared with the experimental results. With good
correlation between the experimental discharge characteristics
and the simulated results the dynamic nature of discharge
impedance has been deduced.
3. Electrical analysis and modelling
3.1. Equivalent electrical circuit
An electrical analogous circuit of the DBD tube is shown in
figure 3. The equivalent electrical model of the DBD tube
consists of three capacitors in series connection. The inner and
outer quartz tubes form the dielectric barrier capacitance Cd1
and, Cd2 whereas the gas gap forms the capacitance Cg . Since
Cd1 and Cd2 are in series combination, it can be represented by
a single capacitance Cd . The equivalent capacitance has been
calculated theoretically using coaxial topology of a two quartz
barrier.
With the experimental values of voltage and current,
the effect of the additional capacitance Cs in parallel to
2. Experimental set-up
2.1. DBD cell design
Figure 1(a) shows the picture of a coaxial DBD cell filled with
argon. Figure 1(b) depicts the schematic of the coaxial DBD
lamp consisting of two fused quartz tubes. The outer surface
of the quartz tube is wrapped by a copper wire mesh electrode
2
J. Phys. D: Appl. Phys. 42 (2009) 045213
U N Pal et al
DBD Tube
Pressure
Gauge
HV
Probe
HF Generator
TIG 10/100 PSC
(20-100 kHz)
Valve
Rogowski coil
Gas
Cylinder
Cext
Computer
Vacuum
Pump
Oscilloscope
Figure 2. Experimental set-up.
Itc(t)
where Vd = Vd1 + Vd2 is the voltage across the dielectric
and Cd = Cd1 Cd2 /(Cd1 + Cd2 ) is the total capacitance of the
dielectric:
dVg (t)
Idg (t) = Cg
.
(5)
dt
Differentiating equation (1) with respect to time and
substituting (4) and (5) in (1),
Idbd(t)
Cd1
Isc(t)
Vd1(t)
Sw
Va(t)
Cs
Cg
Vg(t)
Zd
Idis(t)
dVa (t)
Idbd (t)
1
.
(Idbd (t) − Idis (t)) +
=
dt
Cg
Cd (t)
Idg(t)
Cd2
Vd2(t)
Rearranging equation (6),
Cg
dVa (t)
Idbd (t) − Cg
Idis (t) = 1 +
Cd
dt
Figure 3. Equivalent electrical circuit of the DBD tube.
the DBD cell has been noticed. It represents the parasitic
capacitance along with the cable capacitance of the RF supply
and additional electrical circuit components. The impedance
of microdischarges is represented by Zd , which is in parallel
to Cg . Two discharges are taking place for a particular time
interval during one complete cycle of the applied voltage
waveform [18]. The switch Sw is used to act as a virtual circuit
component to represent this phenomenon. The discharge
plasma is represented by a voltage controlled current source
Idis (t). This conductive discharge current depends on the
gas gap voltage Vg (t). In this model Va (t), Vd1 (t), Vd2 (t),
Idg (t), Isc (t) and Itc (t) are the externally excited voltage,
the voltage across the inner and outer dielectric barriers, the
displacement current through the gap, the displacement current
through the Cs and the external current, respectively. Using
Kirchoff’s theorem for the circuit given in figure 3, we obtained
the following equations:
Va (t) = Vd (t) + Vg (t),
(1)
Itc (t) = Idbd (t) + Isc (t),
(2)
Idbd (t) = Idis (t) + Idg (t).
(3)
dVd (t)
,
dt
(7)
The dielectric barrier voltage, Vd (t), and the gas gap voltage,
Vg (t), are
1
Itc (t) dt + Vm0 ,
(8)
Vd (t) =
Cd
1
Vg (t) = Va (t) −
Itc (t) dt − Vm0 ,
(9)
Cd
and the memory voltage for ac voltage excitation is given by
Vm0 = −
1
2Cd
T /2
Idbd (t) dt.
(10)
0
In equations (8) and (9), Vm0 corresponds to the memory
voltage, induced by charge accumulation on the dielectric
barriers during the previous half period. In other words,
Vm0 ‘memorizes’ the previous discharge events. The memory
voltage has a different value corresponding to the applied
voltage waveform [17].
The numbers of data points for Va (t) and Itc (t) curves
have been obtained by connecting the oscilloscope to the
computer. These experimental values are used to solve the
above equations for evaluating all the discharge characteristics.
Instead of directly using the capacitance value of the DBD cell
from the numerical calculation or the LCR meter, we have
deduced the values from the experimental data. The effect of
stray capacitance is observed when an analytical study has been
done in the no discharge activity region of the Itc (t) curves. In
The total external current through DBD, Idbd (t), and the
displacement current through the gap, Idg (t), can be written as
Idbd (t) = Cd
.
(6)
(4)
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J. Phys. D: Appl. Phys. 42 (2009) 045213
U N Pal et al
However, parameters governing ignition and extinction of
microdischarges are taken into account. The effect of discharge
phenomenon on the gas gap capacitance is considered, which
has also been proved as an efficient way of analysing the plasma
impedance during discharge.
The capacitance values used in this simulation model
have been deduced from figure 4. The pulse generator which
derives the switch Sw is programmed according to ignition
and extinction discharge timings. The timing is deduced from
the observed breakdown voltage and the frequency of the
experimental results. The switch Sw , which is actually a virtual
circuit component for numerical analysis of experimental data,
is effectively used in this simulation to investigate the effect
of impedance in the discharge phenomenon. It reduces the
whole circuit to a purely capacitive circuit when no discharge
is taking place. During the discharge period, when the
switch Sw is on, the plasma impedance is introduced into the
circuit. The plasma impedance comprises a capacitor Cdis in
series with resistance Rdis , which represents the resistance of
filamentary microdischarges. The capacitor Cdis is different
from the gas capacitance Cg as it varies due to a change in
the relative permittivity of gas during ionization [20]. Since
it is not possible to determine the values of Cdis and Rdis
experimentally, simulation has been done on multiple values of
impedance until a good correlation between experimental and
simulated results has been achieved. The controlled current
source block has been modelled cautiously so that it cannot
deviate from equation (7). Rc represents the resistance of the
wires and connectors in the circuit, which is of the order of
tens of ohms. Different values of voltage, current and power
are directly measured by providing measuring components at
various nodes of the circuit. Thus, this modelling proves faster
methods of analysing discharge characteristics as compared
with the long numerical calculations.
1000
750
Ceq (pF)
500
250
0
-250
-500
-750
-1000
0
5
10
Time (µs)
15
20
Figure 4. Equivalent capacitance waveform of the DBD cell for one
period.
4. Results and discussion
4.1. Discharge mode
Figure 5. Simulation model in Simulink.
In the experiment the voltage applied to the metal foil
electrode and mesh electrode has been manually increased
very slowly. When the applied voltage rose to a certain
value, Vbd (breakdown voltage), the discharge began with some
filaments distributed on the dielectric wall, but the intensity
of the visible light emitted from the discharge gap was very
low. If the applied voltage is increased further, the numbers
of filaments increases and finally gets diffuse. Figure 6(a)
shows the average image of discharges taken with a digital
camera (SONY DSC-P100, exposure time: 25 ms). The image
makes sure that the diffuse discharge covers the entire surface
of the electrodes. Figure 6(b) shows the total current trace
together with the applied voltage, where the discharge current
waveform having a number of current pulses with nanosecond
order, which are superimposed on the total current, confirms
filamentary discharges [12].
this region the total DBD can be considered as a pure capacitive
circuit. During this duration, the total displacement current
through the DBD cell can be written as Itc (t) = Ceq Va (t)/dt,
which is given in figure 4. The average value of the curve
is determined without considering the effect of peaks, which
arises due to numerical singularities occurring during the zero
crossing of the denominator [19]. This value of the average
capacitance is carefully used to nullify the effect of the stray
capacitance and other unwanted circuit noise so that it cannot
influence the actual discharge characteristics.
3.2. Equivalent Simulink model
The simulation model made in Simulink is shown in
figure 5. This simulation model is based on the equivalent
electrical circuit proposed in figure 3, in which gas properties
are not considered.
Thus, emphasis has been mainly
laid on the electrical operating conditions of the circuit.
4.2. Discharge characteristics
Figure 7(a) represents the applied voltage Va (t) and the
total current Itc (t) waveforms measured at 1000 mbar argon
4
J. Phys. D: Appl. Phys. 42 (2009) 045213
U N Pal et al
Figure 6. DBD in argon atmosphere (pressure: 1000 mbar,
f = 45.7 kHz): (a) picture of the diffused discharge and (b) applied
voltage and total current waveforms.
atmosphere for 45.7 kHz frequency. Figure 7(b) represents
the simulated results for the same operating conditions. The
amplitudes of total current for both experimental and simulated
curves are same but the phases after the occurrence of
discharges are different. This difference is owing to discrete
time modelling of the simulation model, in which the plasma
impedance is affected for a particular time only and the decay
time of this effect is nearly zero. Furthermore, the inclusion
of the plasma impedance is a one time phenomenon which is
evident from the single discharge peak in the simulation result.
This simulation model is a basic step towards a novel approach
to analyse dynamic behaviour of the plasma impedance in nano
time scale. The emphasis is mainly on the overall performance
of simulation in terms of the amplitude and nature of discharge
peaks.
The dynamic behaviour of different voltages for the
DBD cell has been calculated from theoretical equations and
given in figure 8. The dielectric barrier voltage Vd (t) and
memory voltage Vm0 are calculated using equations (8) and
(10), respectively. Discharge occurs when the applied voltage
reaches the breakdown voltage and results in significant
electron production. After that, the produced electrons move
towards the momentary anode driven by gap voltage and
reverse the polarity of the initial memory voltage, increasing
its magnitude in the direction opposite to the applied voltage
Va (t). It is clearly evident that the gap voltage attains a positive
value prior to the applied voltage which confirms the effect of
the memory voltage (figure 8).
The gas gap voltage has been calculated according to
equation (9). Figure 9 shows that the gap voltage increases
with the external applied voltage nearly at the same rate till the
external voltage reaches the breakdown value. The small hump
in the gap voltage marks the ignition condition. The discharge
hump corresponds to the weakening of the internal electric field
Figure 7. Applied voltage and total current waveform (gas: argon at
1000 mbar, f = 45.7 kHz): (a) experimental and (b) simulated
results.
Va (t)
Vg (t)
Vm0 (t)
Vd (t)
1000
Voltage (V)
500
0
-500
-1000
0
5
10
15
Time (µs)
20
25
Figure 8. Experimental values of different voltages (gas: argon at
1000 mbar, f = 45.7 kHz) for the DBD cell.
in the gas gap due to the momentary flow of charges during
discharge. It is observed that when the breakdown occurs,
the gas gap voltage and the external applied voltage are 310 V
and 392 V, respectively. During the second discharge, the gas
gap voltage increases to −561 V while the external voltage to
5
J. Phys. D: Appl. Phys. 42 (2009) 045213
1000
U N Pal et al
(a)
60
Va(t)
Vg(t)
(a)
Idis(t)
Itc(t)
40
Current (mA)
Voltage (V)
500
0
-500
20
0
-20
-40
-1000
-60
0
5
10
15
20
25
0
Time (µs)
(b)
10
15
80
25
(b)
Itc(t)
Idis(t)
60
500
40
Current (mA)
Voltage (V)
20
Time (µs)
Va(t)
Vg(t)
1000
5
0
-500
20
0
-20
-40
-60
-1000
-80
0
5
10
15
20
25
0
Time (µs)
Pdis (t) = Vg (t)Idis (t).
(12)
15
20
25
Figure 10. Comparison of the total current Itc (t) and the
discharge current Idis (t) (gas: argon at 1000 mbar, f = 45.7 kHz):
(a) experimental and (b) simulated results.
−380 V. From the total current Itc (t), the discharge current is
extracted according to the relation given in equation (7). The
time evolution of the discharge current in figure 10 shows two
current pulses, one in the rising half cycle and other in the
falling half cycle. The width of the first current peak is larger
than that of the second current peak. The discharge current
Idis (t) has its peak values only during the discharge period and
a very low value or nearly zero for the remaining time.
The instantaneous input power delivered by the electric
supply, Psup (t), and the power consumed, Pdis (t), during the
discharge are, respectively,
(11)
10
Time (µs)
Figure 9. Comparison of experimental and simulated values of the
gap voltage (gas: argon at 1000 mbar, f = 45.7 kHz):
(a) experimental and (b) simulated results.
Psup (t) = Va (t)Itc (t),
5
The electrical energy deposited in one discharge is
Wdep =
Pdis .
2f
(15)
The instantaneous values of the input power and the consumed
power during the discharge have been obtained using equations
(11) and (12) and the comparison is shown in figure 11. The
real power input occurs during the discharge phase. Figure 11
shows that the external circuit provides the same power during
both discharges. However, the consumed power in the second
discharge is higher, as the memory charges from the previous
discharge deposited on the dielectric surface contribute to
the energy consumed [17]. The average power supplied and
consumed in the DBD cell are calculated using equations (13)
and (14) and are found to be 15.09 W and 4.85 W, respectively.
The energy deposited by a single discharge, Wdep , has been
calculated by equation (15) and is 53 µJ. This deposited
energy can also be calculated by the enclosed area of the
Lissajous figure. From figure 12, the enclosed area is 44.8 µJ.
The theoretical calculated energy and the measured energy
obtained from Lissajous figure are nearly equal. With all these
The mean value of the supplied power Psup and the consumed
power Pdis are as follows:
1 T
Psup (t) dt,
(13)
Psup =
T 0
1 T
Pdis (t) dt.
(14)
Pdis =
T 0
6
J. Phys. D: Appl. Phys. 42 (2009) 045213
30
U N Pal et al
(a)
the experiment it is not possible to determine the plasma
impedance. In this model, the plasma impedance during the
discharge is taken into account, which has been brought into
effect in the simulation model as discussed in section 3.2.
The good correlation between the experimental and simulated
discharge characteristics helps in inferring the value of this
plasma impedance. It is observed that during the discharge,
the gap capacitance reduces to 42% of its original value. The
resistive part of the impedance is nearly 4.8% of the total
discharge impedance. Thus, with this simulation model we
can infer the dynamic nature of the plasma impedance. The
ongoing research includes the effect of the applied frequency
on the plasma impedance which will help us in achieving the
maximum efficiency condition for the DBD cell and also in
designing an efficient power supply for the system.
Psup(t)
Pdis(t)
25
20
Power (W)
15
10
5
0
-5
-10
-15
0
5
10
15
20
25
Time (µs)
30
(b)
5. Conclusion
Psup(t)
Pdis(t)
25
150
The discharges are analysed in the coaxial DBD cell and are
found to be the filamentary. An electrical circuit has been
proposed for the discharge analysis of the DBD cell. For
this, equations based on the equivalent electrical circuit have
been formulated. The dynamic behaviour of the discharge
parameters (gas gap voltage, discharge current, supplied
power, consumed power and the energy stored, etc) has been
studied. The behaviour of memory charges gave logical
reasons for the observed dynamic changes in the gap and
dielectric barrier voltages.
An analogous model for the proposed electrical circuit
has been implemented in the MATLAB Simulink. A good
correlation has been achieved between the dynamic behaviour
of the discharge characteristics evaluated with the simulation
model and the experimental values, which validates the
functionality of the model. The model allows us to estimate the
plasma impedance, which cannot be directly measured during
the experiment. During discharge, the gap capacitance value
reduces to 42% of its original value and the resistive part is
4.8% of the total plasma impedance.
100
Acknowledgments
Power (W)
20
15
10
5
0
-5
0
5
10
15
20
25
Time (µs)
Figure 11. Instantaneous Psup (t) and Pdis (t): (a) experimental and
(b) simulated results.
Qdbd (nC)
200
The work has been carried out under the CSIR Network
Programme and under the CSIR-DLR collaboration Science
Programme. The authors are grateful to Dr S N Joshi and Dr
V Srivastava for their useful suggestions.
50
0
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-1000
-500
0
Va (V)
500
1000
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