DIELECTRIC barrier discharge (DBD) is usually generated

Transcription

1 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 3, MARCH Electrical Model and Experimental Analysis of the Atmospheric-Pressure Homogeneous Dielectric Barrier Discharge in He Zhi Fang, Member, IEEE, Shengchang Ji, Jun Pan, Tao Shao, Member, IEEE, and Cheng Zhang Abstract A dynamic electrical model for a plane parallel configuration homogeneous dielectric barrier discharge (DBD) is investigated using the MATLAB Simulink. The electrical model is based on an equivalent electric circuit, in which the DBD is represented by a voltage-controlled current source associated to a resistance and a capacitance value. In addition, a plane parallel DBD cell filled with He gas is used for the experiments, and a sinusoidal voltage of up to 5-kV peak value at frequencies of 10 khz is applied to the discharge electrodes for the generation of homogeneous discharges. The electrical characteristics of homogeneous DBD under different operating conditions are studied using the electrical model simulations and experiments, and a comparison between them is conducted. It is shown that the simulated voltage and current waveforms and Lissajous figures are consistent with the experimental ones, which validates the functionality of the model. The dynamic behavior of the discharge parameters (such as gas gap voltage, discharge current, discharge consumed power, and transported charges), which are not measurable in the real process, is studied with the electrical simulation model, and the voltage current curves are also obtained from simulation and used to analyze the evolution trajectory of the homogeneous DBD. Index Terms Dielectric barrier discharge (DBD), electrical model, equivalent electric circuit, gas discharge, homogeneous discharge, simulation. I. INTRODUCTION DIELECTRIC barrier discharge (DBD) is usually generated between two metallic electrodes, of which at least one is covered by a dielectric barrier, with a high voltage (HV) of ac or pulse applied to these electrodes. Experimental diagnoses are the usual ways by which one can study the discharge Manuscript received November 15, 2011; revised December 12, 2011; accepted December 12, Date of publication January 11, 2012; date of current version March 9, This work was supported in part by the National Natural Science Foundation of China under Grant , by the Opening Project of the State Key Laboratory of Electrical Insulation and Power Equipment in Xi an Jiaotong University under Contract EIPE11205, and by the Qing Lan Project in Jiangsu Province of China. Z. Fang and J. Pan are with the School of Automation and Electrical Engineering, Nanjing University of Technology, Nanjing , China ( myfz@263.net). S. Ji is with the State Key Laboratory of Electrical Insulation and Power Equipment, Xi an Jiaotong University, Xi an , China ( jsc@mail.xjtu.edu.cn). T. Shao and C. Zhang are with the Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing , China, and also with the Key Laboratory of Power Electronics and Electric Drive, Chinese Academy of Sciences, Beijing , China ( st@mail.iee.ac.cn). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TPS characteristics and mechanism of DBD, and numerous experimental studies concerning the characteristics and mechanism of DBD under atmospheric pressure have been undertaken. It is shown that the discharge characteristics of DBD depend on the operation parameters of the discharge system, such as reactor configuration (gas gap distance, shape of electrode, and dielectric barrier thickness), gas properties, and amplitude and frequency of applied voltage [1], [2]. This results in a large number of time and trivial workload for experimental research studies. Therefore, both numerical discharge simulation models and electrical discharge simulation models have been developed to help study the mechanism and characteristics of DBD [3], [4]. The numerical models are mainly based on the continuity equations coupled with Poisson equation and boundary conditions, and they are widely used to study the discharge process and mechanism of DBD. However, various gas ionization processes should be considered to simulate the physical process in DBD plasma, and the related numerical simulation models are complicated to set up and calculations are time consuming. From an electrical point of view, the DBD system typically consists of a power supply and a discharge reactor, and both of the two units can be modeled by an equivalent electric circuit. Therefore, the whole DBD system can be modeled by an equivalent electrical model, which complies with a power law. The equivalent electrical model is relatively convenient and simple, and it reveals the interaction between the power supply and the DBD reactor. Using this kind of model, the dynamic relations between the external parameters (i.e., applied voltage, total current, operating gas, dielectric materials, and arrangements of reactor) and internal electrical parameters (i.e., dielectric voltage, gas voltage, discharge current, displacement current, and transported charges) for DBD systems under different operation conditions can be obtained; hence, it considerably facilitates the study and analysis of the dynamic electrical behavior of DBD systems, thus allowing not only the determination of the optimal working condition in DBD reactors but also designing of appropriate HV power sources for DBD applications. Several equivalent electrical models have been developed and used to help study the discharge characteristics and behaviors of DBD systems. Kogelschatz [1] and Laroussi and Lu [5] reported a model characterizing the DBD, in which the discharge plasma is represented by a temporally variable resistance, and several researchers used this model to study and analyze the discharge /$ IEEE

2 884 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 3, MARCH 2012 characteristics of DBD [6] [9]. Koudriavtsev et al. [10] presented a model using a diode full bridge and a constant dc voltage source to represent the DBD discharge plasma, and they used the model to study the characteristics of a DBD ozone generator. Ponce-Silva et al. [11] used this model to design the power supplies for DBD ozone generators, and Sugimura et al. [12] and Olivares et al. [13] also used this model to study the characteristics and luminous efficiency of DBD lamps. Naudé et al. [14] used two Zener diodes and an RC circuit to model DBD, and they also used the established model to study the transition from a Townsend to a filamentary DBD in nitrogen by means of PSpice software. Bhosle et al. [15], [16] presented a model for axisymmetric multifilament mode DBD lamps, in which variable conductance or voltage-controlled conductance was used to model the discharge. Chen [17] developed a model to study the electrical characteristics of one atmosphere uniform glow discharge plasma by means of PSpice software; two voltage-controlled current sources (CCSs), whose output current obeys the classical exponential function with discharge voltage, were used to model the discharge of the positive and negative periods. Liu and Neiger [18] proposed a model of a DBD through a theoretical analysis, in which the conduction discharge current of the discharge plasma was represented by a voltage CCS rather than a temporally variable resistance or a diode bridge. This model was proven valid for an arbitrary excitation voltage, and it was used and enriched by researchers to study the discharge characteristics of DBD under different reactor configurations and power supplies. Based on this model, Valdivia-Barrientos et al. [19] set up a dynamic model of a cylindrical DBD configuration driven by a high-frequency power supply, and the model was implemented in Simulink software and used to study on the influence of operating frequency on the efficiency of the DBD reactor; Zhang et al. [20] set up a dynamic model of a plane parallel configuration DBD driven by a 50-Hz power supply, and it was used to study the effect of several factors on the characteristics of DBD in atmospheric air; and Pal et al. [21] set up a model of a coaxial argon-filled DBD configuration driven by a high-frequency power supply, and it was used to study the dynamic behavior of the discharge parameters. Flores-Fuentes et al. [22] used the concept proposed in [18] to set up a model of plane parallel configuration DBD driven by a high-frequency power supply, in which the discharge plasma was also represented by a voltage CCS that is based on the power law proposed by Chen [17], and the voltage and current characteristics of DBD in helium, argon, and nitrogen were studied using this model. DBDs can exist either in the filamentary mode or in the homogeneous mode, depending on the parameters of power supply and reactor configuration. Homogeneous DBDs can be generated in helium, nitrogen, and neon at atmospheric pressure and could be one of the most promising candidates for several industrial applications taking advantage of their uniform plasma characteristics [23] [26], and many numerical simulations and experimental studies have been also carried out for studying their discharge characteristics and understanding their discharge mechanism. However, there are yet few reports about the electrical models characterizing homogeneous DBDs [14], [17], [18], and there are few reports about studying the Fig. 1. Equivalent electric circuit of the DBD: (a) before discharge; (b) during discharge. discharge characteristics of homogeneous DBDs using the electrical discharge simulation models and the comparison of the results with those of experimental works. In this paper, for electrical discharge analysis and to understand DBD phenomenon in variation of operating conditions, a dynamic electrical model based on the equivalent electric circuit for a plane parallel configuration homogeneous DBD was developed. The homogeneous DBD plasma was modeled by a voltage CCS associated to a dynamic resistance and a dielectric capacitance value controlled by switches, and other factors that can influence the accuracy of simulation, such as lead and stray capacitance values of the circuit, were also considered in the simulated model. This model was implemented in Simulink software and was used to study the dynamic electrical characteristics of homogeneous DBD in atmospheric He. The results obtained from the simulated model are validated with experimental results, and the dynamic behavior of the discharge parameters and evolution trajectory of the homogeneous DBD are also studied with simulation results. II. ANALYSIS AND ELECTRICAL MODEL A. Equivalent Electric Circuit DBD is a kind of self-extinguishing discharge. There are two regions of operation for the DBD, and the discharge turns on and off during each half cycle of applied voltage [1], [5]. This electrical behavior of DBD can be represented by an equivalent electric circuit model shown in Fig. 1. If the applied voltage is not high enough to cause electric breakdown in the gap between electrodes, the discharge in the gas gap does not occur and it is in the off state. In this stage, the equivalent electric model of the DBD reactor can be considered as consisting of two capacitors in a serial connection, with C g and C d representing the equivalent capacitance values of gas gap and dielectric barriers, respectively, as shown in Fig. 1(a). When both of the two electrodes are covered by a dielectric barrier, C d is the total series capacitance of the two dielectric barriers. When the applied voltage exceeds the breakdown voltage, gas ionization in the gap causes the discharge current to remarkably increase in the gap and the discharge is in the on state. In this stage, the equivalent electric model of the DBD reactor can be considered as consisting of a nonlinear gaseous discharge in series with a capacitance value C d, which plays a major role in limiting

3 FANG et al.: MODEL AND EXPERIMENTAL ANALYSIS OF HOMOGENEOUS DBD IN HE 885 Fig. 2. Dynamic electrical simulation model of homogeneous DBD in Simulink. the gap current, as shown in Fig. 1(b). It is known that the variation of the ionization level after breakdown leads to the alteration of the value of the relative permittivity of the gas, thus modifying the equivalent capacitance of the gap from C g to C g1. During the discharge period, the plasma impedance can be represented by a C g1 value in parallel with a resistance R, which represents resistance of homogeneous discharge. Based on the phenomenology of DBD, the DBD plasma itself can be modeled as a voltage CCS whose current characteristic is defined by the applied voltage [17], [18]. There are relatively large effects of parasitic capacitance that is between the high potential and ground on the discharge, and there are also effects of impedance of the wire and connectors in the circuit. These two factors are usually ignored in most of the referenced models [22]. In our electrical model, these two effects were considered to make the simulation more accurate, and additional capacitance C in parallel with the DBD cell and a parallel RL component in series with the DBD cell are added to represent the effect of parasitic capacitance and impedance of the wire, respectively, as shown in Fig. 2. In this model, v a (t) is the applied voltage, i a (t) is total external circuit current, v d (t) is the voltage across the dielectric barriers, v g (t) is the voltage across the gas gap, i g (t) is the displacement current in the gas gap, i d (t) is the displacement current in the dielectric barrier, i CCS (t) is the current voltage-controlled source that represents the discharge current in the gas gap, and i s (t) is the displacement current through C S. According to the electrical scheme given in Fig. 1(b), the following equations can be obtained by using Kirchhoff s laws [18], [21]: V g (t)+v d (t) =V a (t) (1) I s (t)+i d (t) =I a (t) (2) I g (t)+i CCS (t) =I d (t) (3) dv d I d (t) =C d (4) dv g I d (t) I CCS (t) =C g (5) dv a (t) I s (t) =C S. (6) To simplify the analysis, the voltage drop in the RL component is not considered because it can be ignored compared with v g (t) and v d (t). From the above equations, i CCS (t) can be deduced in terms of the external measurable parameters i a (t) and v a (t) as follows: I CCS (t) = ( 1+ C )( ) g dv a (t) I a (t) C S C d dv a (t) C g. (7) It is shown in (7) that i CCS is controlled by applied voltage v a (t) and is strongly related to i a (t). Thus, the experimental measured values of the v a (t) and i a (t) curves are used to solve the above equations for evaluating all the discharge characteristics. B. Electrical Simulink Simulation Model Based on the equivalent circuit proposed in Fig. 1, an electrical simulation model, which contemplates the previous electrical analysis, was implemented on Simulink of MATLAB, as shown in Fig. 2. In this model, ignition and extinction of the homogeneous discharge are controlled by two ideal switches of Sw1 and Sw2. A pulse generator (see Pulse in Fig. 2), which is programmed according to ignition and extinction discharge timings, is used to control the open and close actions of the two switches, and the timing is deduced from the measured breakdown voltage V b and frequency of the applied voltage. In each half cycle of the applied voltage, before the phase of breakdown, the Pulse block controls Sw1 to be closed and Sw2 to be open; hence, the whole circuit can be considered to be a purely capacitive circuit (C S is in parallel with C g and C d ) when no discharge is taking place. In the phase of breakdown, the Pulse block controls Sw1 to be open and Sw2 to be closed. This action disconnects C g from the circuit and leads to the connection of the equivalent circuit of the discharge, which comprises a capacitor C g1 in parallel with a resistance R 1 and a CCS. In Fig. 2, for a given configuration and operation conditions, C g and C d can be calculated by using the following

4 886 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 3, MARCH 2012 Fig. 3. (a) CCS block. (b) Control block. formulas for the calculation of the capacitance of the plate capacitor: C d = S dε 0 ε d 2l d (8) C g = S gε 0 ε g l g (9) where ε 0 is the permittivity of vacuum, ε d is the permittivity of the dielectric barrier, ε g is the permittivity of gas, S d is the area of the dielectric barrier, S g is the area of the electrodes, l d is the thickness of the dielectric barrier, and l g is the gas gap distance [17], [20]. The values of C S can be deduced by using the capacitance values measured when no discharge activity occurs. The values of C g1 and R 1 cannot be experimentally determined; hence, multiple values of impedance were selected to run the simulation until a very high correlation between the experimental and simulation results was achieved. Finally, the values of C g1 and R 1 were selected to be 0.5 C g and 5 kω, respectively. R and L are used to model the effect of impedance of the wire and connectors in the experiments, whicharesettobe100ω and 0.5 mh, respectively. The CCS block coupled with the Control block is to work along the principle of formula (7), and the CCS block mainly consists of a derivative block, two Gain blocks, and an Add block, as shown in Fig. 3. In addition, different values of voltage, current, and power are directly measured by providing measuring blocks such as V1 V3, I1 and I2, and Lissajous blocks at various nodes of the circuit, and the measured results of these blocks are displayed on the oscilloscope blocks of Scope1 Scope3. III. EXPERIMENTAL SETUP Fig. 4(a) and (b) shows a schematic of the experimental setup and the DBD reactor configuration used for generating the homogeneous DBD plasma in He. The discharge was generated between two plane parallel electrodes that are 50 mm in diameter. A cylindrical quartz glass chamber is inserted between the two electrodes as a reactor. The upper and bottom surfaces (both with a thickness of 2 mm) of the chamber are used as dielectric barriers, and the gas gap between them is 8 mm. He with a purity value of 99.99% is fed into the reactor through a tube in the left side of the chamber. It should be pointed out that, in Fig. 4. reactor. (a) Schematic of the experimental setup. (b) Picture of the DBD our experimental setup, He is directly flowed into the open air through a tube in the right side of the chamber; thus, a small amount of air impurities, which is due to the diffusion of air into the chamber through the outlet tube, are inevitably present in the discharge regime even with the gas flow. This discharge is powered by an ac HV source operated at a frequency of 5 25 khz and an adjustable voltage of 0 12 kv (peak-to-peak value). The flow rates of He from 1 to 6 L/min 1 are controlled by a manually adjustable flowmeter. The voltage applied to the electrodes is measured via a voltage probe (Tektronix P6015A). The discharge current and transported charges are measured by placing a 50-Ω noninductance resistor r and a 22-nF capacitor C 0 between the bottom electrode and the ground, respectively. The Lissajous figure can be obtained on the oscilloscope screen by plotting the transported charge on the Y -axis and the applied voltage on the X-axis. The voltage and current waveforms and the Lissajous figure are recorded by a Tek TDS3054c (500 MHz, 5 G/s) digital oscilloscope. The light emission images of the discharges are taken by a Canon 400D digital camera with an exposure time of 1/30 s. IV. RESULTS AND DISCUSSIONS A. Comparison of Simulation and Experimental Results For the experimental study, the frequency of the applied voltage is fixed at 10 khz, the gas gap distance is fixed at 8 mm, and the gas flow rate is fixed at 3 L/min. Under these conditions, the discharge characteristics are experimentally studied with the applied voltage amplitudes changing from 1 to 5 kv. In the experiments, the voltage applied to the two electrodes is manually increased very slowly. When the applied voltage rose to breakdown voltage V b (1.3 kv for the electrode arrangement), the discharge began in the gas gap. The experimental results of the current and voltage waveforms, Lissajous figures, and light emission images for different

5 FANG et al.: MODEL AND EXPERIMENTAL ANALYSIS OF HOMOGENEOUS DBD IN HE 887 Fig. 5. Measured applied voltage and total current waveforms, Lissajous figures, and light emission images of homogeneous DBD in He under different applied voltage amplitudes [(a), (d), and (g) applied voltage and total current waveforms at 2, 3, and 4 kv; (b), (e), and (h) Lissajous figures at 2, 3, and 4 kv; and (c), (f), and (i) light emission images at 2, 3, and 4 kv]. applied voltage amplitudes are shown in Fig. 5. It is shown in the light emission pictures in Fig. 5(c), (f) and (i) that no filament can be observed, and the discharge is homogeneous in the entire discharge region. With increasing of the applied voltage to 4 kv, the light emission becomes strong, but the discharge is still in homogeneous forms. From the current and voltage waveforms in Fig. 5(a), (d) and (g), a single current pulse, which has the same periodicity as the external voltage, is observed per half cycle of the applied voltage in all cases. The amplitude of the current is typically of several milliamperes, and its duration is about 2 μs. With increasing of the applied voltage from 2 to 4 kv, the maximum amplitude of current pulse increases from 4.5 to 7.5 ma, suggesting increase of intensity of the homogeneous discharge with applied voltage. It is noted that, between two consecutive discharges, the current is weak but not equal to 0. At higher applied voltage amplitudes of 3 and 4 kv, a small increase in current after 2 μs ofthe appearance of the first large current pulse was observed in the current waveforms. This small current is named as residual current peak by some researchers, and it is an indication that the number of electrons in the gap will be sufficient to produce the next breakdown under a low electric field, which is a necessary condition to obtain a homogeneous DBD in He [8]. The amplitudes of residual current peak increase with the amplitude of the applied voltage, and they are 0.8 and 1.8 ma for 2 and 4 kv, respectively. It is shown in Fig. 5(b), (e) and (h) that the shape of the Lissajous figures for single current pulse homogeneous DBD is not a parallelogram, and the discharge transition (corresponding to the perpendicular edges of the Lissajous figures) shows a region where the data points form a vertical line, corresponding to the peak in the current waveforms. In addition, the enveloped area of Lissajous figures increases with the applied voltage amplitude, which suggests the increase in discharge power with the applied voltage amplitude. The discharge characteristics obtained are similar to those reported by previous works [8], [28], [29], and it can be concluded that the discharges studied in this paper operate in the homogeneous mode. The electrical simulation model was run at the same values of operating parameters with those of experimental conditions shown in Fig. 5, and the parameters used in the simulation are from calculations or experimental data. The values of capacitance C d and C g are calculated by substituting the geometry of the DBD cell to formulas (8) and (9), and they are and 2.2 pf, respectively. The value of C S is an estimate of the parasitic capacitance between the high potential of the DBD cell and the ground. It is deduced by using the capacitance values measured when no discharge activity occurs, and 0.1 pf is used in the simulation. The value of V b is obtained from experimental data, and it is 1.2 kv for 8-mm atmosphericpressure He gas gap. The simulated results of the current and voltage waveforms and Lissajous figures for different applied voltage amplitudes are shown in Fig. 6. The comparison between the experimental and simulated results shows that the results of simulations in Fig. 6 are in good agreement with the experimental measurements in Fig. 5, and this validates

6 888 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 40, NO. 3, MARCH 2012 Fig. 6. Simulated applied voltage and total current waveforms and Lissajous figures of homogeneous DBD in He under different applied voltage amplitudes [(a), (c), and (e) applied voltage and total current waveforms at 2, 3, and 4 kv; (b), (d), and (f) Lissajous figures at 2, 3, and 4 kv). the effectiveness of the electrical model. In addition, it can be seen that both of them are consistent in discharge ignition time, current amplitude, current pulse duration, and envelope of Lissajous figures, which proves the accuracy of the proposed model for simulating the homogeneous DBD. Therefore, it can be used to estimate and study the electrical characteristics of homogeneous DBD qualitatively and quantitatively and to optimize the design of the DBD reactor under different conditions, which is of great interest for the applications of DBD plasmas. It should be pointed that this paper only reported the simulation results for homogeneous DBD in He, and the flexibility of the model enables one to study the electrical characteristics of homogeneous DBD in other gases, provided that several appropriated parameters are adjusted for each applied gas. For simulating homogeneous DBD in other gases such as nitrogen and neon, the values of C d and C g in Fig. 1 should be calculated using the geometry of the DBD cell and the permittivity of applied gas, and the values of C S and V b should be determined from experimental measurement data in each applied gas, then the same methods described in this paper for simulating the homogeneous DBD in He can be used for simulation. The reported model can be also used to study the electrical characteristics of filamentary mode DBD because, whether for homogeneous DBD or for filamentary DBD, discharge current i CCS follows the same principle of formula (7) with applied voltage v a (t) and external circuit current i a (t). For simulating filamentary DBD, except for the above adjustments for simulating homogeneous DBD in other gases with this model, the Pulse block in Fig. 2 should be also adjusted to open and close more times according to ignition and extinction discharge timings of filamentary DBD because a number of current pulses appear per half cycle of the applied voltage for filamentary DBD. Fig. 7. Simulated evolution of v g(t), i CCS (t), v a(t), andi a(t) at applied voltage of 3 kv. B. Dynamic Behaviors of the Discharge Parameters The dynamic behavior of those discharge parameters (such as gas gap voltage v g (t), dielectric voltage v d (t), discharge current i CCS (t), and displacement current i d (t)), which are not measurable in the real process, can be also obtained using the electrical simulation model, and this considerably facilitates the study of the dynamic behavior of DBDs. Fig. 7 shows the evolution of v g (t) and i CCS (t), along with that of the applied voltage v a (t) and total external circuit current i a (t) in homogeneous DBD in He. It is shown that, in each half cycle of applied voltage, v g (t) increases nearly at the same rate with applied voltage v a (t) before discharge occurs. Discharge occurs when v g (t) reaches the breakdown voltage at 1.85 kv, and this results in quite abruptly exponential discharge current i CCS (t); i CCS (t) has its peak values only during the discharge period and a very low value or nearly zero for the remaining time. After the peak values of i CCS (t), charges accumulated on the dielectric surfaces induce a negative voltage, leading to a rapid decrease in v g (t) until the current becomes too small to compensate for the increase in the external voltage, thus resulting in the extinction of the discharge.

7 FANG et al.: MODEL AND EXPERIMENTAL ANALYSIS OF HOMOGENEOUS DBD IN HE 889 Fig. 8. Variation of the discharge power and transported charges with the applied voltage amplitude from the simulation. at near the maximum value of negative and positive voltage cycles, which correspond to the two discharge current pulses in Fig. 5, suggesting the repetitive periodic behavior of the homogeneous DBD system from cycles to cycles. On the positive half cycle of applied voltage, v g increases from zero steadily, but i g stays around the zero point. Breakdown occurs when v g rises to point A, after which i g sharply increases, whereas v g shows slight reduction until point D. According to the classical gas discharge theory, it is the Townsend discharge mode between A and B. The current growth is halted at point D when the differential conductivity of the gas gap changes from being negative to positive. With a positive differential conductivity value, the discharge current starts to decrease while the gas voltage continues to decrease until point E when the discharge is extinct and the whole process is over. Due to its positive differential conductivity, the discharge process between B and D belongs to glow discharge mode [30]. Fig. 9. Simulated current voltage curves of the homogeneous DBD in He at applied voltage of 2 kv. The electrical parameters of discharge power and transported charge are of interest for optimizing the design of the DBD reactor, and they are also important parameters to estimate the efficiency of the DBD system [1], [18], [20]. The proposed model also enables one to determine the average power consumed P and transported charge per voltage cycle Q of the DBD. They are calculated through simulations by using (10) and (11), and changes in P and Q with the amplitude of the applied voltage are shown in Fig. 8 P = 1 T Q = T 0 T 0 v g (t)i CCS (t) (10) i a (t). (11) It is shown that both P and Q increase with applied voltage in all cases. When the applied voltage increases from 1.5 to 5kV,P increases from 80 to 278 mw and Q increases from 13 to 58 nc, indicating increases in efficiency at a higher applied voltage. The voltage current curves can provide a valuable signature of dynamic behaviors of atmospheric DBDs, and some researchers have obtained the curves using a numerical simulation and used it to analyze the evolution trajectory of homogeneous DBDs [14], [25]. Using the proposed electrical model, the voltage current curves of the homogeneous DBD in He can be easily obtained, and Fig. 9 shows the curve of the discharge current and gas voltage obtained from the electrical model simulation. It is shown that it consists of two individual closed loops interlinked by two lines. Each of the two rings locates V. C ONCLUSION In this paper, an equivalent electric circuit for characterizing the electrical behavior of a homogeneous DBD has been introduced; a voltage CCS associated to a resistance and a capacitance value has been used to represent the homogeneous discharge in the gas gap. Based on the equivalent electrical circuit, a dynamic electrical model for a plane parallel Hefilled configuration homogeneous DBD is investigated using the MATLAB Simulink, and the effects of parasitic capacitance and wire impedance are also considered to make the simulation more accurate. Experimental studies on the discharge characteristics of a plane parallel He-filled DBD under different applied voltages are conducted, and the voltage and current waveforms, Lissajous figures, and light emission images are obtained. It is found that the discharges studied operate in the homogeneous mode. The electrical characteristics of homogeneous DBD under different operating conditions are obtained using the electrical model simulations and are compared with the experimental ones, and they agree well both qualitatively and quantitatively. Therefore, the electrical model is proven to reflect discharge process accurately, and it can be used as an effective method for the study of the electrical characteristics of homogeneous DBD. The dynamic behavior of the discharge parameters (such as gas gap voltage, discharge current, discharge consumed power, and transported charges), which are not measurable in the real process, is studied with the developed simulation model, and the effect of applied voltage amplitude on the discharge power and transported charges is also studied using the electrical model, with the increases in discharge efficiency at a higher applied voltage being verified. 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D, Appl. Phys., vol. 37, no. 7, pp , Apr [29] Z. Navrátil, R. Brandenburg, D. Trunec, A. Brablec, P. St ahelp, H.-E. Wagner, and Z. Kopecký, Comparative study of diffuse barrier discharges in neon and helium, Plasma Sources Sci. Technol., vol. 15, no. 1, pp. 8 17, Feb [30] Y. T. Zhang, D. Z. Wang, and M. G. Kong, Complex dynamic behaviors of nonequilibrium atmospheric dielectric-barrier discharges, J. Appl. Phys., vol. 100, no. 6, pp , Sep Zhi Fang (M 10) was born in Heilongjiang Province, China. He received the B.S., M.S., and Ph.D. degrees from Xi an Jiaotong University, Xi an, China, in 1999, 2002, and 2005, respectively, all in electrical engineering. He is currently an Associate Professor at Nanjing University of Technology, Nanjing, China. His current research interests are the study of atmosphericpressure gas discharge plasmas and the development of atmospheric-pressure plasma sources for material surface processing applications. Shengchang Ji was born in Shandong, China, in He received the B.S. and Ph.D. degrees in electrical engineering from Xi an Jiaotong University, Xi an, China, in 1998 and 2003, respectively. He is currently an Associate Professor at the State Key Laboratory of Electrical Insulation and Power Equipment, Xi an Jiaotong University. His main research fields are high-voltage insulation, gas discharge, and pulsed-power technology. Jun Pan was born in Jiangsu Province, China, in He received the B.S. degree in electrical engineering in 2010 from Nanjing University of Technology, Nanjing, China, where he is currently working toward the M.S. degree. His research interests are in the experimental study and simulation on nonequilibrium atmosphericpressure plasmas.

9 FANG et al.: MODEL AND EXPERIMENTAL ANALYSIS OF HOMOGENEOUS DBD IN HE 891 Tao Shao (M 10) was born in Hubei, China, in He received the B.Sc. degree from Wuhan University of Hydraulic and Electrical Engineering, Wuhan, China, in 2000, the M.Sc. degree in electrical engineering from Wuhan University, Wuhan, in 2003, and the Ph.D. degree in electrical engineering from the Graduate University of the Chinese Academy of Sciences, Beijing, China, in He is currently with the Institute of Electrical Engineering, Chinese Academy of Sciences. From 2009 to 2010, he was a Senior Visiting Scholar with the State Key Laboratory of Control and Simulation of Power Systems and Generating Equipment, Tsinghua University, Beijing. His current research interests focus on high-voltage insulation, gas discharge, plasma application, and measurement. Cheng Zhang was born in Wuxi, Jiangsu, China, in He received the Ph.D. degree in electrical engineering from the Graduate University of the Chinese Academy of Sciences, Beijing, China, in He is currently with the Institute of Electrical Engineering, Chinese Academy of Sciences. His current research interests focus on gas discharge and application.