Member, IEEE Rafael Diez
email: rdiez@javeriana.edu.co

Hubert Piquet
email: hubert.piquet@laplace.univ-tlse.fr

Member, IEEE David Florez
email: david.florez@usa.edu.co

Xavier Bonnin
email: xavier.bonnin@laplace.univ-tlse.fr

Current-Mode Approach in Power Supplies for DBD Excilamps: Review of 4 Topologies

Keywords: Current control, dielectric barrier discharge (DBD), power conversion, ultraviolet (UV) generation. I

This document reviews the current-mode supply approach for dielectric barrier discharge (DBD) excilamps. It briefly demonstrates why this mode assures the control of the power injected into the DBD. Considerations with the step-up transformer required for the correct operation of the currentmode are developed. This document shows and compares four different converter topologies that comply with this principle. This comparison is made in terms of electric efficiency and luminous efficacy using experimental measurements.

trying to validate the efficacy of the excilamps over the mercury-based lamps [START_REF] Guivan | Comparative inactivation of Bacillus subtilis spores using a DBD-driven xenon iodide excilamp and a conventional mercury lamp[END_REF].

The UV radiation from the DBD excilamps was studied in the beginning only from the point of view of the physics, and some characteristics, for instance the duration of the UV pulses, were not directly related with the power supply [START_REF] Liu | Double discharges in unipolar-pulsed dielectric barrier discharge xenon excimer lamps[END_REF]. These discharges were created using generalpurpose linear power amplifiers or pulsed-mode voltage converters [START_REF] Mildren | Visible and VUV emission from a xenon dielectric barrier discharge using pulsed and sinusoidal voltage excitation waveforms[END_REF]- [START_REF] Loukil | Theoretical kinetics investigation of xenon dielectric barrier discharge for excimer lamp[END_REF].

Actually, in [START_REF] Florez | DBD excimer lamp power supply with fully controlled operating conditions[END_REF] and [START_REF] Piquet | Pulsed currentmode supply of dielectric barrier discharge excilamps for the control of the radiated ultraviolet power[END_REF], some parameters of the UV radiation, like the duration and amplitude, have been demonstrated to be controlled by the current injected into the lamp, by means of a current-mode converter.

Resonant topologies controlling the current are now frequently used to deliver the power to DBD loads [START_REF] Bonnin | A high voltage high frequency resonant inverter for supplying DBD devices with short discharge current pulses[END_REF]- [START_REF] Meißer | Transformerless high voltage pulse generators for bipolar drive of dielectric barrier discharges[END_REF].

This paper revises the current-mode approach origin for DBD lamps, including the modeling of an excilamp. It has a view of four different converter structures that comply with this approach, and finally, a comparison of those structures is made in terms of electric efficiency and luminous efficacy. Practical considerations in the construction of the transformer, necessary for all the converters, are developed.

II. REVIEW OF THE CURRENT-MODE APPROACH

In this section, the development of the current-mode approach is summarized. The characterization of the static and dynamic electric behavior of the load, by means of a model, is the starting point, which allows the selection of the adequate fundamental properties of the supplies.

The latter must be able to control the energy and the power injected into the lamp, and it is obtained by means of a static converter specifically designed for this task.

A. Electrical Model

The electrical model for a DBD excilamp can be generally drawn as the typical circuit used to represent other DBDs [START_REF] Monge-Dauge | Experimental study coupled with electrical modeling for the consideration of DBD-based plasma jet[END_REF], [START_REF] Tang | Study on an engineering design method for power supply of DBD type ozone generator[END_REF], as shown in Fig. 1, where C d stands for the equivalent series capacitance of the dielectric barriers containing the gas mixture; C g represents the gas dielectric behavior before breakdown; and G g characterizes the gas conductance as a function of the gas voltage v g .

In [START_REF] Díez | Predictive model of a DBD lamp for power supply design and method for the automatic identification of its parameters[END_REF], it was demonstrated that the model can be simplified to achieve the design of the power supply of the lamp, considering that v g is almost constant once the discharge is established where i g is the gas current and V th is a constant voltage value here called the normal gas voltage. This constant voltage means that the discharge could be treated as being in the normal glow regime. Nevertheless, if more precise waveforms for the electric variables must be obtained, the model containing the dynamic evolution of the conductance is considered [START_REF] Díez | Predictive model of a DBD lamp for power supply design and method for the automatic identification of its parameters[END_REF].

v g ∼ = + V th , if i g > 0 v g ∼ = -V th , if i g < 0 ( 1 )

B. Current Mode Versus Voltage Mode

The simplified electrical model emphasizes two reasons why a DBD excilamp should be supplied with a current source. The first one is the capacitive nature of the lamp: a voltage source converter would inject a lamp current i lamp only in case of a variation in the lamp voltage v lamp , as revealed in [START_REF] Brandenburg | Antimicrobial effects of UV and VUV radiation of nonthermal plasma jets[END_REF]. In this case, the waveform of i lamp current is difficult to predict in amplitude and duration, as can be seen for a square-voltage source converter in Fig. 2 i

lamp = C d • d(v lamp -v g ) dt . ( 2
)
Conversely in a current-mode converter, as i lamp is imposed, the lamp voltage is computed using [START_REF] Wang | Synergistic effect of the sequential use of UV irradiation and chlorine to disinfect reclaimed water[END_REF]. In this case, it is possible to calculate during the design stage all the electrical variables in the converter, and this guarantees a good dimensioning of the power supply (Fig. 2)

v lamp = v g + 1 C d i lamp dt. (3)
The second reason to use a current-mode converter is that once the discharge is established in the gas, v g can be considered constant (Fig. 2). In consequence, the current of the gas capacitance can be neglected and the gas current i g (in the conductance) will be equal to the injected lamp current i lamp . Since the instantaneous power in the gas is governed by i g (4), so will be the average power of the lamp P lamp . Indeed, G g gas conductance is the only dissipative element in the DBD lamp equivalent circuit (Fig. 1)

p g = V th * |i g |. (4)
Note that for current-mode converters, the gas power is independent from the dielectric equivalent capacitance. This is not true for the voltage-mode converters, as the lamp current depends on the applied voltage [START_REF] Brandenburg | Antimicrobial effects of UV and VUV radiation of nonthermal plasma jets[END_REF].

C. Choice of the Injected Current

Considered the fact that the instantaneous power dissipated in the discharge p g is directly controlled by the gas current i g , the lamp current i lamp shown in Fig. 3 is proposed to supply the DBD load. It is possible to see that the gas voltage v g takes a determined time t th to invert its polarity and to reach the breakdown between positive and negative half-cycles.

The p g waveform is obtained with (4), then its average value is computed to obtain the average power of the lamp P lamp [START_REF] Florez | DBD excimer lamp power supply with fully controlled operating conditions[END_REF]

P lamp = J • D • V th -4 f lamp C eq V 2 th (5)
where C eq is the series equivalent capacitance of C d and C g . With this i lamp waveform, it is possible to control and adjust P lamp with three degrees of freedom: the current amplitude J , the operating frequency f lamp , and the duty ratio D. The implementation of a converter that is able to produce this current waveform is developed in the following section.

A. Rectangular Current Converter

This structure is conceived as a constant current source in cascade with a current inverter, as shown in Fig. 4. The amplitude of current J is controlled by the current source using a hysteretic control. The duty cycle and frequency of the lamp current are set by means of the inverter. The current source is built with a two-quadrant chopper, considering that bipolar voltage is found at the input of the inverter. This chopper works in Continuous Conduction Mode (CCM). A full bridge, composed by high-frequency synthesized thyristors [START_REF] Cousineau | Synthesized highfrequency thyristor for dielectric barrier discharge excimer lamps[END_REF], is used as the current inverter, to give the necessary degrees of freedom to the power supply. For the control of the lamp current shape (Fig. 3), the sequence used for the inverter switches is shown in Fig. 4 (bottom). A step-up transformer is necessary to scale the high voltage of the lamp to the range of the high-frequency semiconductors. Details about this structure are found in [START_REF] Florez | Square-shape current-mode supply for parametric control of the DBD excilamps power[END_REF] and [START_REF] Bonnin | Design of a current converter to maximize the power into homogeneous dielectric barrier discharge (DBD) devices[END_REF].

The power delivered to the lamp is computed with ( 5). This structure is the most flexible among the converters listed in this paper; it can control the power of the lamp via three independent variables (degrees of freedom: D, J , and f lamp ), for this reason, it is very useful for the identification of the optimal operating point of the load. Nevertheless, this converter is not optimized in terms of

B. Boost-Based Converter

This structure, introduced in [START_REF] Diez | Design of a current converter for the study of the UV emission in DBD excilamps[END_REF], uses a boost converter, working in Discontinuous Conduction Mode (DCM), to replace the two-quadrant chopper from previous configuration. In DCM, the current inverter can be replaced by a push-pull inverter, using a two-primary-winding transformer, reducing the number of switches and the control circuitry, as observed in Fig. 5. One can note that all switches are thyristor-like devices, according to the double polarity of v lamp [START_REF] Diez-Medina | Alimentation de puissance d'une lampe exciplexe à décharge à barrière diélectrique, en vue du contrôle du rayonnement[END_REF].

The inductance current presents, for the positive half-cycle, three different sequences: linear increase of the inductance current to i ch (S0 ON), resonant discharge (S1 ON), and blanking (all switches OFF). These sequences are repeated for the negative half-cycle, inverting the current direction, using S1 instead of S1, to comply with the charge balance required supplying this capacitive load. The duration of the discharge sequence is defined by the values of the components and by the value of the inductance current at the end of the charge sequence (i ch ). The blanking time sets the operating frequency.

The resonant discharges can be separated in two: before and after breakdown and the equivalent resonance capacitance are C eq and C d , respectively. The first resonant part, when the gas current is zero, should be minimized to obtain a gas current similar to the imposed lamp current.

The power delivered to the lamp ( 6) is calculated using the positive sequence, taking the average of the gas current and then multiplying by the constant gas voltage V th . Finally, this value is doubled to consider both the negative and positive sequences

P lamp = f lamp V th E 2 • t 2 ch L + 4n E V th C g V th -n E . ( 6
)
Being t ch , the time that the input voltage (E) linearly charges the inductance (L) to the i ch value. This expression states that stability for this converter is assured by maintaining the input voltage seen in the secondary n E less than the V th voltage. Otherwise, divergent developments for voltage and current are found [START_REF] Diez | Current-mode power converter for radiation control in DBD excimer lamps[END_REF].

The end of the discharge phase in this converter is established by the spontaneous turn-OFF of one of the two inverter switches with Zero-Current Switching (ZCS).

C. Buck-Boost-Based Converter

This converter, using a buck-boost in DCM as the unidirectional current source, has similar charge and discharge sequences as the boost-based converter (Fig. 6).

This converter works as a bidirectional current flyback converter, as detailed in The energy stored in the inductance, during the charge phase, is sent to the lamp during the discharge phase. In this way, the power delivered to the lamp can be easily computed as (assuming 100% efficiency of the converter)

P lamp = f lamp L (E • t ch ) 2 . ( 7
)
As for the boost-based converter, the buck-boost-based structure can vary the output power adjusting the charge time t ch , the input voltage E, and the operating frequency f lamp . However, current amplitude and duration are not independent variables in these converters as it was for the rectangular current converter.

Differing from the boost-based topology, the buck-boost converter is stable for all the values of the input voltage, Fig. 6.

Structure of the buck-boost-based converter. Its six operating sequences as seen in the secondary, and the inductor and output current. as demonstrated in [START_REF] Diez | Current mode converter for dielectric barrier discharge lamp[END_REF]. Here, ZCS is also assured at the end of the discharge sequence.

D. DCM Operated Series Resonant Inverter

This structure, shown in Fig. 7, is a simplification of the boost-based topology. Here, no charge sequence is allowed; hence, only discharge and blanking phases are presented.

As for the boost-based converter, the input voltage seen in the secondary must be less than the normal voltage of the gas V th ; otherwise, unstable situation occurs.

The power delivered to the lamp is calculated in the same way as for boost-based topology, as demonstrated in [START_REF] Florez | DCM-operated series-resonant inverter for the supply of DBD excimer lamps[END_REF]

P lamp = 4 f lamp V th 2 C g n E V th -n E . ( 8
)
Here, the parameters that can be controlled to adjust the lamp power are only the operating frequency f lamp and the input voltage E.

Concerning the advantages, this topology can be implemented with only two switches and it presents ZCS during turn-OFF and also at turn-ON, making it the least expensive and most efficient topology.

IV. IMPLEMENTATION AND EXPERIMENTAL RESULTS

In this section, the implementation of the four structures is made for the same load: a XeCl (308 nm) lamp with the following parameters.

As the parameters, corresponding to the normal gas voltage V th , the dielectric capacitance, and the gas capacitance, are considered constant for one lamp, the peak voltage of this lamp ( 9) is only dependent on the lamp power and the lamp frequency, as demonstrated in [START_REF] Florez | Square-shape current-mode supply for parametric control of the DBD excilamps power[END_REF]

v lamp_peak = P lamp 4 f lamp V th C d + V th 1 + C g C d + C g . ( 9
)
That means that for all the four converters the peak voltage could be as high as 5000 V for the low-frequency operation. To reduce this voltage to the semiconductor range, a step-up transformer with 1:10 ratio is designed.

A. Step-Up Transformer Design

The high-voltage transformer strongly impacts the converter performance and the delivered waveforms through its parasitic elements [START_REF] Florez | Impact of the transformer in the current mode supply of dielectric barrier discharge excimer lamps[END_REF], [START_REF] Bonnin | Designing the high voltage transformer of power supplies for DBD: Windings arrangment to reduce the parasitic capacitive effects[END_REF]; for this reason, special attention should be paid to capacitive couplings among the transformer windings.

Assuming high coupling in the transformer, these capacitive links can be encompassed into a single parasitic capacitor connected in parallel to the secondary side [START_REF] Bonnin | Designing the high voltage transformer of power supplies for DBD: Windings arrangment to reduce the parasitic capacitive effects[END_REF], forming a capacitive current divider with the low structural DBD capacitances (Table I). Therefore, this capacitance has to be minimized. Furthermore, the theoretical waveforms in Section III might be altered if the magnetizing inductance of the transformer (which is also connected in parallel with the load) presents an extremely low value.

Finally, it is important to bear in mind that transformer efficiency might be reduced if losses are not carefully considered.

These issues can be addressed by carefully winding the transformer and inserting thick enough low-permittivity insulation materials between the winding layers and the magnetic core. Single-layer windings are of major interest in that regard, since the interlayer capacitive coupling term is eliminated [START_REF] Florez | Impact of the transformer in the current mode supply of dielectric barrier discharge excimer lamps[END_REF]. Nevertheless, tradeoff with losses, weight, and magnetizing inductance has to be made, and it appears that a multilayer winding widens the field of possibilities.

As stated in [START_REF] Bonnin | Designing the high voltage transformer of power supplies for DBD: Windings arrangment to reduce the parasitic capacitive effects[END_REF], splitting the secondary in several sections connected in series (N s ) leads to the reduction of capacitive effects, while increasing the number of layers (N l ) and turns (N t ) at the secondary winding.

To show this, three Ferroxcube E80/38/20-3F3 core based transformers have been manufactured according to the lamp parameters given in Table I and experimentally compared in Table II.

The turns ratio n is chosen to be 10 to bring back a voltage that the power switches can withstand. The R c and R i parameters, respectively, stand for the copper and iron resistances, both normalized with respect to those of the transformer T1.

L m and C p , respectively, denote the magnetizing inductance and the parasitic capacitance seen in the secondary side of the transformer. The insulation materials are acrylic layers, with 4.5-mm thickness between primary and secondary, and 2 mm between the secondary layers. The sections of T3 are also separated with a 2-mm acrylic layer. As predicted, the single layer transformer (T1) offers the best capacitive behavior.

To increase the magnetizing inductance by 4 with respect to T1, T2 transformer uses a classical two-layer winding in the secondary; however, it suffers from an important electrostatic coupling term (increased by a factor 2.27 compared with T1). Example of the optimal operating point identification using the rectangular current converter. For a fixed injected power in the lamp, the UV power density depends on the operating frequency.

Finally, T3 transformer offers an interesting compromise by increasing L m by the same factor 4 and only increasing C p by 1.25. For T2 and T3, R c and R i are approximately increased by a factor 2.

These results show that increasing the number of layers and splitting the winding gives a degree of freedom to distribute copper and iron losses and to reach desired values in term of magnetic parameters, and still guaranteeing an interesting value for C p .

B. Exploitation of the Degrees of Freedom to Identify the Optimum Operating Point in Terms of Luminous Efficacy

Beyond the capability of controlling the lamp power, the current-mode converters are capable of adjusting the power in different forms. In this aspect, the rectangular current converter is the most versatile, being the only converter capable of varying independently, and during operation, the three degrees of freedom of the injected lamp current and hence the instantaneous lamp power: magnitude, duration, and frequency.

For this reason, this converter can be used to identify an optimal operating point of the lamp, where the luminous efficacy is maximized, within the range of the converters; one example of this is shown in Fig. 8. To obtain this figure, the current amplitude in the lamp is kept constant (128 mA), the frequency is fixed, and the duty cycle is adjusted to obtain different average powers delivered to the lamp. After sweeping the duty-cycle range, the operating frequency is changed, and the procedure is repeated until the power range is covered [START_REF] Florez | DBD excimer lamp power supply with fully controlled operating conditions[END_REF].

For this and other experiments in this paper, the UV average radiation is measured with an optometer GIGAHERTZOPTIK P-9710 and the UV detector SN5816, installed at 3 mm of the lamp surface.

For instance, in this figure, it is possible to see that if we desire a UV power density around 30 mW/cm 2 , the necessary power to be injected to the lamp is much lower if the operating frequency is between 50 and 80 kHz. In this range, a luminous efficacy gain of 30% is achieved comparing with the 170 kHz.

C. Comparison of the Converters

Once the optimal operating point is identified with the rectangular converter, it is necessary to design an efficient converter to supply the lamp and hence obtain an overall optimized efficiency. In this paper, a comparison of the four structures is proposed for the following conditions:

1) P lamp = 106 W;

2) f lamp = 60 kHz;

3) discharge time of 3 µs, corresponding to D = 36%. Fig. 9 shows the different behavior of the four converters, focusing on the current injected into the lamp i lamp and on the UV emitted by the lamp. The duration and shape of the UV pulses are very similar to those of the gas current, governed by the imposed lamp current, as predicted by the current-mode approach.

The UV waveform is in arbitrary units and is obtained with a photodetector THORLABS PDA-25K, configured in the 20-dB gain setting. The detector is oriented perpendicular to the lamp, placing its active area at 25 mm of the lamp surface.

To remark that the lamp peak voltage is similar in the four structures, as predicted by [START_REF] Guivan | Comparative inactivation of Bacillus subtilis spores using a DBD-driven xenon iodide excilamp and a conventional mercury lamp[END_REF]. Note that, in the four structures, the lamp voltage waveform is similar and the UV radiation waveform is different. It confirms how difficult would be to control the UV radiation by means of a voltage-mode supply.

1) Electric Efficiency: Table III compares the four topologies: for the same power injected in the lamp, the power at the input of each converter is measured (P in ). The transformer is the same for all the structures and the power at its input port, P prim , is similar and around 124 W for the four converters, giving losses near 15% in this element. Note that the transformer is the element with the highest losses for the resonant-based topologies.

Regarding the losses in the converter (semiconductors and inductor), it is possible to see that the rectangular converter presents the highest, with only 55% of efficiency, since it is fully hard switched and because the current flows continuously through the inductance and the switches. This is followed by the buck-boost converter (79% efficiency), as its initial current during the discharge phase is the highest, and so the S1 (or S1') turn-ON losses. The most efficient converter is the series resonant inverter, since it is completely ZCS, presenting 83% of efficiency (97% in the primary side circuit and 86% in the transformer).

2) Luminous Efficacy Depends on Current Waveform: The luminous efficacy is calculated as the output power density divided by the average power, measured at the lamp terminals. It is noticeable that it depends on the current shape, since the electrical lamp power is the same for all the structures, as well as the duration and energy of each pulse. In this Fig. 9. Experimental waveforms for the four converters under the same power, frequency, and discharge time. Lamp peak voltage is not dependent of the waveform. ZCS can be observed in the inductance current for the resonant-based topologies.

TABLE III

COMPARISON OF THE CONVERTERS aspect, the most efficient would be the rectangular current shape obtaining 3.1%, 5.5%, and 12.2%, more compared with the series resonant inverter, buck-boost-based converter, and boost-based converter, respectively.

3) Efficiency for the Entire System: Even though the rectangular converter provides the best luminous efficacy, it presents the worst overall efficiency, which is calculated as the output power density divided by the average power measured at the terminals of the main power source (E). In this term, thanks to its high electric efficiency, the series resonant inverter operated in DCM, presents a gain of 7.5%, 12%, and 47.2%, with respect to the buck-boost-based, boost-based, and rectangular converters, respectively.

4) Other Considerations: In terms of control of the discharge power, the buck-boost-based structure is useful for applications where a very precise constraint of the injected power is necessary or in a situation where the DBD has not been completely identified. In these cases, the charging sequence can be adjusted to increase the output power in the DBD process. It has the advantage of being always stable, while maintaining in DCM.

Finally, Table III shows that input voltage (E) must be different in the three resonant-based topologies, to obtain the same operating conditions. Note that the boost-based converter is the one with the lowest input voltage, making it worthy for applications where low input voltage is available as the main power source, like in photovoltaic and other battery-based systems.

Fig. 1 .

 1 Fig. 1. DBD excilamp. Physical structure (top) and equivalent electric model (bottom).

Fig. 2 .

 2 Fig. 2. Voltage-mode converter with square voltage output and uncontrolled current (top), and current-mode converter with square current and controlled voltage (bottom). Gas voltage is almost constant after breakdown.

Fig. 3 .

 3 Fig. 3. Rectangular lamp current waveform supplying the DBD lamp.

Fig. 4 .

 4 Fig. 4. Rectangular current converter offering three degrees of freedom to adjust the lamp current and hence the lamp power, with the trigger sequence for the high-frequency thyristors in the inverter.

Fig. 5 .

 5 Fig. 5. Boost-based converter structure, its six operating sequences as seen in the secondary and the current waveforms.

Fig. 7 .

 7 Fig. 7. Series resonant inverter topology. Its four operating sequences and its output current waveform.

Fig. 8 .

 8 Fig. 8.

TABLE I PARAMETERS

 I OF THE EXCILAMP USED DURING IMPLEMENTATION

His current research interests include the study of the coupling between electrical power sources and plasma devices, and the methodologies in designing power electronics components for plasma applications.


Abderrahim Okba

Samuel Charlot

Pierre-François Calmon

Alexandru Takacs

Hervé Aubert

Pierre-François Calmon

Hervé Aubert Cross

P-F Calmon

Cross dipoles rectenna for microwave applications

Keywords: electromagnetic energy harvesting, wireless power transfer, rectennas, printed dipoles array, satellite application

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

Recently, the electromagnetic harvesting of the spill-over losses of microwave antennas was identified as a realistic solution to power autonomous wireless sensors for health monitoring of the antenna panels of the broadcasting satellites [START_REF] Takacs | Microwave power harvesting for satellite health monitoring[END_REF]. This paper presents recent results in Ku band obtained from an innovative rectenna topology based on four printed cross dipoles antenna array and uses a low cost Schottky diode [2]. Rectenna using a cross dipole antenna was also reported in [START_REF] Takacs | Microwave power harvesting for satellite health monitoring[END_REF], [START_REF] Sun | Design of a High-Efficiency 2.45-GHz Rectenna for Low-Input-Power Energy Harvesting[END_REF] while a rectenna using a two cross dipoles array was reported in [START_REF] Takacs | Rectenna Design for K Band Application[END_REF]. The rectenna topology and the design methodology are presented in Section II while Section III shows the experimental results obtained by using the manufactured rectenna.

II. RECTENNA TOPOLOGY AND DESIGN

The proposed topology is composed of: four cross dipoles array (4CDAA) and a silicon Schottky diode -Skyworks SMS7630 [2]. The PCB layout and a photo of the manufactured rectenna are shown in Fig. 1.The antenna array and the diode are implemented on the top of the PCB while the RF shunt capacitor is mounted on the bottom side of PCB. A reflector metallic plate is added on the bottom side in order to improve the antenna gain. This compact topology (its size is fixed by the size of the antenna array) is an extension of a rectenna using two cross dipoles antenna array 2CDAA reporteded in [START_REF] Takacs | Rectenna Design for K Band Application[END_REF] and a non-resonant matching technique was used. This non-resonant matching is implemented by properly controlling (i) the input impedance of the antenna array and (ii) the input impedance of the rectifier itself. The rectifier consists of the diode and the low pass RC filter (composed of the shorting capacitor and the load itself). The 4CDAA can be viewed as an array formed by four cross dipoles printed on the PCB. Each cross dipole consists of two dipoles in cross configuration as shown in Fig. 1. The substrate used is Rogers 6002 (substrate thickness: 0.508 mm, relative dielectric permittivity: 2.94, dielectric loss tangent: 0.0012). The maximum theoretical gain (Gmax in dBi) of such an array antenna can be computed using the following expresion: where Gd=2.15 dBi is the gain of a lossless halfwavelength dipole. This gain can be increased by 3 dB when a metallic reflector is properly positioned below the antenna surface. Thus the expected maximum gain is 14.18 dBi. This theoretical gain should be considered as an upper bound for any practical 4CDAA design. There are no accurate analytical formulas to design such an array but some rules can be used in order to start the design. The length of each dipole (Ld in Fig 1 ) should be approximately half wavelength and the distance between the center of two opposite cross dipoles (L2 in Fig. 1) should be an integer multiple of half wavelength. The angle between the dipoles (α in Fig 1 ) impacts the wave polarization and the maximum achievable gain. Linear or circular polarization can be obtained by using this topology as function of the relative phase of waves exciting the crossed dipoles.

Coplanar strip lines are used to feed each cross dipole. We target here a linear polarization. Thus the diode should be mounted in the center of the array as represented in Fig. 1. A generic electrical diode model existing in the ADS software was customized with the following parameters [5]- [START_REF]Skyworks application notes 'Mixer and detector diodes[END_REF]: ohmic resistance R s = 20Ω, junction capacitance C j0 = 0.14 pF, saturation current I s = 5 µA, forward voltage V f = 0.34V, reverse breakdown voltage B v = 2V and the current at reverse breakdown voltage I bv = 0.1mA. The ADS simulation model is represented in Fig. 3. The PCB located on the bottom side of the PCB was simulated by using standard printed PCB lines and via holes founded in the ADS library. The harmonic balance port was charged by the input impedance (simulated in HFSS and depicted in Fig. 2 c) presented by 4CDAA at the input port of the diode. The initial simulations performed by using this model demonstrated that the maximum DC power was obtained at the frequency of 12 GHz approximately. Nevertheless the ADS simulations shows convergence issues of the harmonic balance engine and an important sensitivity of the DC power delivered to the load (RL) as function of the length of the printed PCB line. Thus we decided to manufacture a prototype and to keep as compact as possible the PCB layout of the bottom side in order to avoid any uncontrolled coupling between the 4CDAA (bottom side) and the PCB layout of the bottom side.

III. EXPERIMENTAL RESULTS AND DISCUSSION

The experimental setup shown in the Fig. 4 was used to characterize the rectenna. A microwave signal generated from an Anritsu MG3694B generator was injected at the input of a horn antenna which illuminated the rectenna under test with a linearly polarized E-field. An automatic acquisition routine was implemented in Labview software from National Instruments to speed-up the acquisition process. The harvested DC voltage was measured by using a DC multimeter. The DC power can be computed from the measured DC voltage as long as the load is known. The measured loss due to the coaxial cable and connectors between antenna and the signal generator was in the range of 3 dB in the operating frequency band.

The efficiency η (in %) of the rectenna can be computed by using the following definition [START_REF] Popovic | Low-Power Far-Field Wireless Powering for Wireless Sensors[END_REF]:

(2) where P DC is the harvested DC power, S is the incident electromagnetic power density A eff is the antenna effective area, G R is the gain of the (rectenna's) antenna and λ is the wavelength of the illuminating electromagnetic wave. The power density (µW/cm 2 ) can be computed as a function of E-field effective value E (V/m) on the antenna surface or as a function of the RF power P t injected to the input of the transmitting horn antenna of gain G t and positioned at the distance d from the rectenna, as follows:

( 3 ) Fig. 5. Measured DC power at the input port of a resistive load (RL=300Ω) as function of the RF power injected into the transmiting horn antenna. Fig. 6. Measured DC power at the input port of a resistive load (RL=300Ω) as function of frequency for several value of the E-field Fig. 5 displays the measured DC power on a load of RL=300Ω as function of the RF power injected in the transmitting horn antenna (of gain G R =19 dBi) for several distances between the transmitting horn antenna and the rectenna under test. We note that power up to 4.5 mW can be harvested by using the proposed 4CDAA rectenna.

The E-field and the power density illuminating the rectenna can be computed as function of the G t and d by using eq. ( 3). Fig. 6 shows the measured harvested DC power at the input port of a resitive load (RL=300Ω) as function of the frequency for several values of the E-field. The maximum DC power was measured at 12 GHz as represented in Fig. 6.

The optimal load was also determined. The electric field illuminating the rectenna under test was fixed at E=48 V/m by using the following configuration: d=36 cm, G t =19 dBi, power delivered by the microwave generator: 24 dBm, injected power at the input of the transmitting horn antenna: 21 dBm. The obtained results are depicted in Fig. 7. We remark that the maximum DC power is obtained for a load impedance RL=300Ω. The harvested DC power for RL=300Ω as function of Efield illuminating the 4CDAA at the frequency of 12 GHz is represented in Fig. 8. From a practical point a view at least 1 mW of DC power is required to supply an autonomous wireless sensors for satellite health application. Typically such a wireless sensor is composed of: a sensor (DC power comsumption in the range of few µW), a DC-to-DC convertor, a power management unit and a low-power wireless tranceiver (DC power consumption in the range of the mW). However the electromagnetic energy illuminating the antenna panels is almost constant and the DC circuitry (including the power management unit) should be minimal [START_REF] Takacs | Microwave power harvesting for satellite health monitoring[END_REF]. As represented in Fig. 8 the rectenna can provide a DC power of 1mW or higer when it is illuminated by an electric field E>38 V/m. The RFto-DC conversion efficiency of 4CDAA rectenna is computed by using eq. ( 2) and it is represented in Fig. 9 as function of the E-field illuminating the rectenna under test. The reported efficiency is limited by: (i) the ohmic resistance of the selected low-cost silicon diode (ii) by the adopted non-resonant matching technique (iii) the lack of accurate simulation models (in the Ku band) of the selected commercial diode. The overall performances of the 4CDAA rectenna can be further improved by optimizing the PCB layout on the bottom side. It was noticed that this botom side layout have a major impact on the impedance matching between the rectifier and the antenna located on the top side of the PCB. Works are under run and more results will be presented at the conference. An efficiency greater than 25% can be obtained by using a low cost silicon Schottky diode (SMS7630) when the E-field exceeds 19 V/m. The rectenna is very compact. Its size is 2.5 cm x 2.5 cm that is square wavelength at 12 GHz.

IV. CONCLUSION

A compact rectenna with an overall size close to square wavelength at 12 GHz was designed and characterized. The proposed design combines an original four cross dipoles antenna array with a rectifier using a single low cost silicon Schottky diode. The experimental results demonstrate that a DC power greater than 1 mW can be harvested in the Ku band (12 GHz) for electric field greater than 38 V/m. This harvested DC power can be used to power a wireless sensor for satellite health monitoring application. A maximum RF-to-DC conversion efficiency of 41% was obtained for a load of 300Ω and an incident electric field of 58 V/m.

Fig. 1 .

 1 Fig. 1. Top view (not to scale) of the layout of the 4CDAA rectenna, its main geometrical dimensions and the photos of top and bottom side of the manufactured rectenna. The wires shown here was used to connect a variable resistance in order to reach the optimal load.

  Fig. 2. a) Simulated (HFSS) gain in the xOz plane (phi=0°) -continous line -and xOy plane (phi=90°) -dashed-line of the 4CDAA at the frequency of 12 GHz, the inset shows the 3D radiation pattern b) Simulated (HFSS) maximum gain of the 4CDAA vs the frequency, c) the input impedance presented by the 4CDAA on the input port of the diode vs frequency.

Fig. 3 .

 3 Fig. 3. ADS circuital simulation model.

Fig. 4 .

 4 Fig. 4. Experimental setup used to characterize the rectenna

Fig. 7 .

 7 Fig. 7. Measured DC power as function of the load impedance (E=48 V/m, f=12 GHz)

Fig. 8 .

 8 Fig. 8. Measured DC power at the input of a load (RL=300Ω) as function of the illuminating E-field

ACKNOWLEDGEMENT

The authors acknowledge the support of French Space Agency within the framework of several past R&T contracts.


Member, IEEE David Florez
email: d.florez@javeriana.edu.co

Member, IEEE Rafael Diez
email: rdiez@javeriana.edu.co

Hubert Piquet
email: hubert.piquet@laplace.univ-tlse.fr

DCM-Operated Series-Resonant Inverter for the Supply of DBD Excimer Lamps

This paper presents the study of a series-resonant inverter for the supply of a dielectric barrier discharge excimer lamp. Causal analysis, based on the fundamental properties of the load, is used to detail the reasoning which has led to this topology. In order to effectively control the lamp power, the operating mode of this converter combines discontinuous current mode and soft commutation (zero-current switching), obtaining low electromagnetic emissions and reduced switching losses as well. The model of the lamp is briefly presented, and it allows a simple state plane analysis to calculate all the electric variables involved in the converter and, consequently, to select the components of the supply. The mathematical relationships obtained from this process, for injected power control by means of the available degrees of freedom, are validated with simulations and experimental results.

Index Terms-Dielectric barrier discharge (DBD), gas discharge devices, plasma sources, resonant inverter, ultraviolet (UV) sources, zero-current switching (ZCS).

I. INTRODUCTION

T HE DESIGN of an efficient power supply for a dielectric barrier discharge (DBD) excimer lamp, capable of controlling the ultraviolet (UV) emission, is a challenge because of the capacitive nature, the nonlinear behavior, and the high operating voltages of this load. In the past, different approaches have been proposed to supply different DBDs.

. Lately, voltage-mode resonant converters for the supply of capacitive

loads have been developed and implemented [START_REF] Meisser | Universal resonant topology for high frequency pulsed operation of dielectric barrier discharge light sources[END_REF]- [START_REF] Kalisiak | Resonant inverter with output voltage pulse-phase-shift control for DBD plasma reactor supply[END_REF]. The main drawback of the voltage-mode approach in these converters is the inability to control and predict the power that is supplied to the discharge.

By studying the DBD lamp electrical model, it has been proved that the DBD electrical power can be controlled by means of its current instead of using its voltage; this is shown experimentally with a current-mode converter [START_REF] Diez | Current-mode power converter for radiation control in DBD excimer lamps[END_REF]. Additionally, the authors of [START_REF] Piquet | Pulsed current-mode supply of dielectric barrier discharge excilamps for the control of the radiated ultraviolet power[END_REF] and [START_REF] Diez | Control of the UV emission of an excimer lamp by means of a current-mode power supply[END_REF] have clearly established a tight correlation between the current waveform and the temporal response of the UV radiation. In [START_REF] Flórez | DBD excimer lamp power supply with fully controlled operating conditions[END_REF], a square-waveform current supply with three degrees of freedom has been designed to study the radiation of DBD lamps; however, this converter presents hard switching, diminishing efficiency and producing electromagnetic interference (EMI).

Among the possible topologies for the supply of DBD devices, resonant topologies offer less switching losses, less EMI, and a smaller number of switching devices than the others [START_REF] Chéron | Soft Commutation[END_REF]. The voltage-mode resonant topologies proposed in [START_REF] Meisser | Universal resonant topology for high frequency pulsed operation of dielectric barrier discharge light sources[END_REF] and [START_REF] Kalisiak | Resonant inverter with output voltage pulse-phase-shift control for DBD plasma reactor supply[END_REF] for DBD lamp and exhaust gas treatment, respectively, are, in our opinion, not the best choice to an efficient control of the operating point of DBD excilamps, as explained in Section II. In [START_REF] Diez | Current-mode power converter for radiation control in DBD excimer lamps[END_REF] and [START_REF] El-Deib | Analysis and experimental validation of a new current-controlled driver for a dielectric barrier discharge lamp[END_REF], current-mode resonant converters are developed specifically for excimer lamps. The topologies proposed in [START_REF] Fujita | Control and performance of a pulse-densitymodulated series-resonant inverter for corona discharge processes[END_REF] and [START_REF] Alonso | Analysis, design, and experimentation of a high-voltage power supply for ozone generation based on current-fed parallel-resonant push-pull inverter[END_REF]- [START_REF] Bhat | A generalized approach for the steadystate analysis of resonant inverters[END_REF], based on the series-resonant inverter (SRI) or similar topologies, are adaptable to excimer lamp supplies. Using the classical SRI as basis and considering the DBD lamp electrical model, this paper presents an operating mode differing from the previous ones: It proposes the combination of the current-mode approach with the zero-current switching (ZCS). ZCS is achieved in all the switches at turn-on and turnoff, reducing EMI and increasing the overall efficiency.

This paper is organized as follows. Section II introduces the main aspects of the electrical model for a DBD excimer lamp. Section III explains the converter operating principle, using the lamp model. Section IV develops the mathematical relationships for the design of the converter, based on the state plane analysis. Section V dimensions the components for a specific XeCl excimer lamp and verifies the previous developments. Experimental results and conclusions are given in Sections VI and VII, respectively.

II. DBD EXCIMER LAMP MODEL

The modeling of DBD excilamps has already been presented in several papers, e.g., [START_REF] Oda | One-dimensional modelling of low-frequency and high-pressure Xe barrier discharges for the design of excimer lamps[END_REF]- [START_REF] Díez | Predictive model of a DBD lamp for power supply design and method for the automatic identification of its parameters[END_REF]; here, the most important elements are reminded: A coaxial DBD excimer lamp, as the one depicted in Fig. 1, confines a gas mixture between two silica walls. This lamp geometry can be modeled with the electrical equivalent circuit in Fig. 1 (bottom). The lamp silica walls, acting as dielectric barriers, are modeled as the equivalent capacitance C diel . These barriers are in series with the gas. The gas behavior is described by a gas capacitance in parallel with a gas conductance [START_REF] Díez | Predictive model of a DBD lamp for power supply design and method for the automatic identification of its parameters[END_REF] (C gas and G gas , respectively). The gas conductance is very small when the absolute value of the gas voltage is smaller than the gas breakdown voltage V th : The equivalent model of the DBD is thus the series association of C diel and C gas . When the gas voltage reaches the breakdown voltage V th , by effect of the connected power supply, the gas acquires the behavior of an almost constant voltage source of value V th , which remains in series with C diel . Experimental measurements and identification results [START_REF] Diez | Control of the UV emission of an excimer lamp by means of a current-mode power supply[END_REF] have proven that V th , which is a physical property of the gas, does not depend on the shape of the current waveform.

Taking into consideration the fact that, after breakdown, the gas presents an almost constant voltage, it is clear that the convenient supply mode to control the discharge power is to control the current which flows into the gas. From the lamp model, the current flowing through the gas conductance is equal to the lamp current (except for the time intervals, needed to install the breakdown conditions); in consequence, controlling the lamp current enables the control of the instantaneous power transferred to the gas [START_REF] Piquet | Pulsed current-mode supply of dielectric barrier discharge excilamps for the control of the radiated ultraviolet power[END_REF].

Accounting its capacitive behavior, the supply mode of the lamp must enable a bidirectional current into the lamp (null average value); otherwise, the lamp voltage would grow uncontrollably, producing damage in the converter.

In the next section, we take advantage of the capacitive nature of the DBD to implement a resonant converter that uses the load as one of the elements of the resonant circuit.

III. DISCONTINUOUS RESONANT SUPPLY MODE

The classical topology of the SRI, shown in Fig. 2 (top left), presents a convenient current-source behavior [START_REF] Chéron | Soft Commutation[END_REF], [START_REF] Casanueva | Series-parallel resonant converter for an EDM power supply[END_REF]. For this reason, this topology is chosen to implement the DBD current supply. In this topology, the inductance L is connected in series with the DBD lamp through the full-bridge current inverter. The lamp current direction is determined by the bridge configuration.

The converter operating period is divided in six steps, determined by the bridge switches and the gas state. The equivalent circuit for each stage of this operating sequence is presented in Fig. 2 (bottom).

With the switches S1 and S4 turned on, an LC seriesresonant circuit is obtained, as presented in Fig. 2(a), and the lamp current flows in the direction that will be defined as the positive one, henceforth.

Due to the resonance, the lamp current i lamp grows, as seen in Fig. 2 (top right), and consequently, the gas voltage v gas increases until it reaches the breakdown voltage V th . The breakdown occurs at time t br , and the gas is now represented by the constant voltage source V th , as shown in Fig. 2(b); however, the dielectric voltage v diel continues to grow as long as the lamp current remains positive.

When the lamp current falls to zero at the time t off , the bridge turns off (spontaneous turn-off; see Section V), and the lamp is disconnected from the source, as seen in Fig. 2(c); consequently, given the capacitive behavior of the lamp, v lamp remains constant at its positive peak value.

The next half cycle starts at T bridge /2, turning on the switch pair S3, S2. The equivalent circuit in Fig. 2(d) produces a resonant current in the negative direction. In this sequence, the gas voltage is taken from V th to -V th to reach again the breakdown condition. When v gas is equal to -V th , the gas capacitance C gas is replaced by the inverted voltage source V th in Fig. 2(e). As done previously for sequence (c), the full bridge is disconnected from the lamp, starting from sequence (f), when the lamp current reaches zero and the lamp voltage reaches its negative peak voltage. This voltage remains constant until sequence (a) restarts at T bridge . In this way, for steady state, the negative lamp peak voltage and zero lamp current become the initial condition for the equivalent capacitance of the first sequence

v lamp (t o ) = -Vlamp i lamp (t o ) = 0 A. ( 1
)
Using the discontinuous current mode (DCM) selected in this work, the lamp operating frequency is defined by only the bridge operation, as presented in Fig. 2 (top right).

The achievement of this DCM is implemented owing to a specific switch, which is presented in Section V.

IV. CONVERTER DESIGN

The converter is designed using the state plane analysis [START_REF] Chéron | Soft Commutation[END_REF], [START_REF] Oruganti | Resonant power processors, Part I-State plane analysis[END_REF]. This method allows the determination of the operating conditions for the converter-lamp system, using the equivalent circuits from Fig. 2 (bottom). Although the state plane analysis can be used to find the transient response, only steady state is presented in this paper. Hereafter, the positive current sequences are analyzed; due to symmetry, the study of the negative cycle leads to similar results.

A. State Plane Analysis

The state plane analysis is used to plot the current-voltage behavior of a resonant circuit. Fig. 2(a) shows the resonant equivalent circuit before gas breakdown occurs.

Normalized units are used, leading to the plot of circular clockwise trajectories [START_REF] Chéron | Soft Commutation[END_REF], [START_REF] Oruganti | Resonant power processors, Part I-State plane analysis[END_REF], describing the current-voltage characteristic for the lamp before ignition, as presented in Fig. 3 u

= v lamp V th (2) j = i lamp V th L C eq , with C eq = C diel C gas C diel + C gas . ( 3
)
After the gas breaks down, the equivalent resonant circuit changes as shown in Fig. 2(b) with v gas constant and equal to V th . Therefore, a new state plane is used. This plane draws the normalized current-voltage characteristic for the dielectric capacitor, being the dielectric current equal to the lamp current (Fig. 4).

As the equivalent capacitance has changed from C eq to C diel , normalization is redefined as follows, using * as notation to remember the lamp ignition:

u * = v diel V th = v lamp -v gas V th = v lamp V th -1 = u -1 (4) j * = i lamp V th L C diel . ( 5
)

B. State Plane: Before Breakdown Trajectory

As explained in Section III, at the beginning of the positive current cycle, the initial lamp voltage is equal to -v lamp peak (1), and the initial lamp current is zero.

The normalized lamp current, j in Fig. 3, starts to rise, and the operating point follows a circular path in the plane with the center in U in , as long as this equivalent circuit is valid, i.e., while the gas voltage is inverted from -V th to V th . In this way, when the gas breakdown occurs, the total voltage change in the gas is 2V th . Accordingly, at the breakdown instant (t br ), the lamp voltage U br is calculated using the capacitor voltage equation [START_REF] Florez | Series-resonant inverter in DCM mode for the supply of a DBD excimer UV lamp[END_REF] At the same instant, the lamp current value is defined as the breakdown current I br and, in the normalized form, as J br . From trigonometric equations for either of the shaded triangles in Fig. 3, we obtain

U br = u(t br ) = -Û + 2 1 + C gas C diel . ( 6
)
J 2 br = (U in + Û ) 2 -(U br -U in ) 2 . ( 7
)

C. State Plane: After Breakdown Trajectory

The initial current for the state plane in Fig. 4 is equal to the breakdown current I br . Given that normalization is different from the previous sequence, (3) and ( 5) are used to find

J * 2 br = J 2 br C eq C diel . ( 8
)
From the equivalent circuit in Fig. 2(b) and ( 4) at the instant of the gas breakdown, the normalized dielectric voltage u * (t br ) is equal to

u * (t br ) = U br -1. (9)
Equation ( 9) is the dielectric initial voltage for the state plane in Fig. 4. Now, using geometrical relations for either of the shaded triangles in the state plane in Fig. 4, we can write

J * 2 br = ( Û -U in ) 2 -(U br -U in ) 2 . ( 10
)
Using ( 6)-( 10) and solving and denormalizing the resulting equation system, we find the lamp peak value in steady state

Vlamp = V th + V 2 th C gas C diel (V th -V in ) . ( 11
)

D. Operating Conditions

One should note that the lamp peak voltage depends only on the input voltage and the parameters of the lamp, not on the inductance value. A valid solution for (11) can be found only when condition ( 12) is fulfilled, operating at the left of the asymptote V th marked in Fig. 6 V in < V th .

(

) 12
Otherwise, unstable operation occurs. The transient state plane trajectory for stable and unstable operating conditions is plotted from simulation in Fig. 5, using the DBD lamp model. The topology of the SRI used in this paper is similar to that presented in the classical resonant step-up voltage converter; the input voltage must be smaller than the output voltage in order to respect the operating principle of this topology [START_REF] Erickson | Fundamentals of Power Electronics[END_REF].

The lamp peak current must be found in two different manners depending on the operating case (Fig. 4, top or bottom). The boundary condition between these two cases is obtained graphically from the state planes in Fig. 3 for a normalized input voltage U in equal to U br (6) [START_REF] Florez | Series-resonant inverter in DCM mode for the supply of a DBD excimer UV lamp[END_REF].

For the operating case in Fig. 4 (top), the peak lamp current is

îlamp = (v lamp -V in ) C diel L . ( 13
)
Otherwise,

îlamp = (v lamp + V in ) C eq L . ( 14
)
The lamp average power is calculated as twice (positive and negative sequences) the power dissipated by the gas conductance from the time t br until the discharge dies out at t off (Fig. 2), obtaining

P lamp = 4f bridge V 2 th C g × V th V th -V in -1 . ( 15
)
Expression [START_REF] Casanueva | Series-parallel resonant converter for an EDM power supply[END_REF] shows that P lamp can be adjusted by means of two degrees of freedom: V in and f bridge .

For proper operation of the converter, the bridge must be operated at a switching frequency f bridge which allows the current to fall to zero before the beginning of a new switching sequence. Thus, considering the lamp current waveforms in Fig. 2, condition (16) should be fulfilled

T pulse < 1 2f bridge . ( 16
)
With T pulse computed using the state planes,

T pulse = θ ω + ϕ ω * = 1 ω arcsin I br V in + vlamp L C eq + 1 ω * π -arcsin I br V in -vlamp L C diel . ( 17
)
The mathematical relationships exposed in this section have been numerically verified through simulation using the PSIM circuit simulator (Fig. 6) and are used for the converter design and the component selection.

V. COMPONENT SELECTION AND SIMULATIONS

The converter is dimensioned to supply a DBD excimer lamp filled with a XeCl gas mixture. The equivalent electrical model of this lamp presents a dielectric capacitance C diel = 95 pF, a gas capacitance C gas = 28.5 pF, and a breakdown voltage V th = 1.31 kV [START_REF] Lopez | Parameters identification and gas behavior characterization of DBD systems[END_REF]. This lamp has been designed to accept approximately 90 W of electrical power.

A. Operating Point

According to the experimental results presented in [START_REF] Diez | Current-mode power converter for radiation control in DBD excimer lamps[END_REF] and [START_REF] El-Deib | Analysis and experimental validation of a new current-controlled driver for a dielectric barrier discharge lamp[END_REF] and studies in [START_REF] Lomaev | Excilamps: Efficient sources of spontaneous UV and VUV radiation[END_REF], [START_REF] Hippler | Low Temperature Plasmas: Fundamentals, Technologies and Techniques[END_REF], and [START_REF] Sosnin | Applications of capacitive and barrier discharge excilamps in photoscience[END_REF], an excimer lamp with similar characteristics to the one that we intend to supply is typically operated at current frequencies in the range of tens of kilohertz. In particular, from the results in [START_REF] Flórez | DBD excimer lamp power supply with fully controlled operating conditions[END_REF], the lamp performance is severely affected by operating frequencies above 100 kHz; consequently, we chose f lamp = 80 kHz for the converter validation. At this frequency, the theoretical voltages and currents for a maximum P lamp = 90 W are presented in Table I.

In order to validate the converter behavior, the converter control is implemented in open loop, adjusting P lamp with V in remaining in the stability region illustrated in Fig. 5 (bottom).

B. Switches

For this range of operating frequencies, high switching speed offered by the MOSFET technology is necessary. Studying the current-voltage characteristic for each switch, unidirectional current switches capable of blocking bipolar voltage should be used in the bridge. This switch characteristic corresponds to a thyristor-like device [START_REF] Cousineau | Synthesized highfrequency thyristor for dielectric barrier discharge excimer lamps[END_REF] and is implemented by connecting a diode (GB07SHT12) in series with a MOSFET (P8NK100Z) (Fig. 7).

C. Step-Up Transformer

The voltage values at the chosen operating point (Table I) lead to the use of a step-up transformer connecting the DBD lamp to the inverter. The implemented step-up transformer has been designed with a transformation ratio of ten to reduce the peak voltage of the bridge switches to approximately 400 V.

Using the theoretical lamp peak current in Table I and ten as the transformation ratio, the transformer wires are selected: 81 strands of 38 AWG litz wire for the primary and 33 AWG single copper wire for the secondary.

The construction of this transformer is a challenge, since its parasitic capacitance (C s seen in the secondary) should be much smaller than the lamp equivalent capacitance, in order to avoid any difference between the current injected by the converter and the transformed current seen from the lamp. At the same time, magnetizing inductance should be maximized to conserve the operating principle presented in this paper.

To satisfy these two opposite criteria, in accordance with [START_REF] Biela | Using transformer parasitics for resonant converters-A review of the calculation of the stray capacitance of transformers[END_REF] and [START_REF] Bonnin | Design of a current converter to maximize the power into homogeneous dielectric barrier discharge (DBD) devices[END_REF], the best solution has been found by using onelayer winding coil. The values obtained for the experimental transformer are summarized in the circuit in Fig. 7.

D. Inductance Value

The value of L (Table I) is calculated taking into account the condition ( 16) and the component current ratings [START_REF] Alonso | Analysis, design, and experimentation of a high-voltage power supply for ozone generation based on current-fed parallel-resonant push-pull inverter[END_REF]. An inductance value of 23 mH seen on the secondary is calculated based on [START_REF] Fujita | A 2-MHz 2-kW voltage-source inverter for lowtemperature plasma generators: Implementation of fast switching with a third-order resonant circuit[END_REF] to obtain a duty cycle of approximately 70% at f lamp = 80 kHz. This duty cycle provides enough dead time for the switch turn-off and for the increase of the switching frequency if necessary. Given a transformation ratio of ten, an inductance L = 231 μH is used in the primary side.

E. Simulations

The converter, including the transformer parasitic elements (Fig. 7), has been simulated using PSIM. The waveforms obtained from this simulation are presented in Fig. 8 (top). The step observed in the lamp current waveform i lamp (marked as "Gas breakdown") is a result of the gas breakdown that changes the current divider between the lamp equivalent capacitance and the transformer parasitic capacitance [START_REF] Bonnin | Design of a current converter to maximize the power into homogeneous dielectric barrier discharge (DBD) devices[END_REF]. The i lamp is not zero during the dead time due to the effect of the magnetizing inductance.

The output power P lamp obtained in simulation is presented in Fig. 6 for different values of f lamp . Because of the transformer frequency response, the equivalent transformer gain changes with the frequency operation; consequently, the equivalent input voltage is reflected to the secondary using the transformer gain measured experimentally: 9.3, 9.5, and 9.7 for 70, 80, and 90 kHz, respectively.

VI. EXPERIMENTAL RESULTS

The experimental validation of the proposed converter has been achieved by measuring the electrical signals for the system with a high-speed current probe (LeCroy AP015) and a highvoltage differential probe (Agilent N2891A). The lamp voltage is measured in the primary side of the transformer (v prim ) to reduce the impact of the voltage probe input impedance (approximately 3.5 pF) in the resonant circuit.

A. Electrical Waveforms

In Fig. 8 (bottom), the inductance current i in is shown. The lamp voltage v lamp , measured at the primary side of the transformer, does not remain constant when the current is zero because the transformer magnetizing inductance is not as big as desired. The transformer parasitic elements also affect the power transfer, as shown in Fig. 6: Simulation results taking into account these parasites are very near to the experimental measurements allowing fine adjust of the design, while theoretical ones are less precise.

B. Performance

The benefits of the SRI are validated experimentally by measuring and comparing its performance with the squarewaveform current supply previously proposed in [START_REF] Flórez | DBD excimer lamp power supply with fully controlled operating conditions[END_REF].

1) Efficiency: The measurement of the converter efficiency, in terms of electrical power supplied to the lamp, is obtained as follows: The v prim and i lamp output signals are multiplied in the oscilloscope, computing the lamp instantaneous power. Then, this power signal is averaged (averaging time of 1 ms) and multiplied by the transformation ratio, obtaining P lamp . In a similar manner, the power supplied by the constant voltage source P in is found, computing the converter efficiency as P lamp /P in . The measurement of P lamp obtained for different values of V in at f lamp = 80 kHz is presented in Fig. 6, and the corresponding converter efficiencies are shown in Fig. 9. It is found that the transformer is responsible for most of the converter losses.

In comparison, for the square-waveform current supply proposed in [START_REF] Flórez | DBD excimer lamp power supply with fully controlled operating conditions[END_REF] at the particular operating point of P lamp = 90 W, f lamp = 80 kHz, a duty cycle of 53%, and a current intensity of 125 mA, the converter efficiency obtained is 57%, against 91% for the SRI.

2) Stability: For an input voltage slightly higher than 117 V, which corresponds to approximately 1170 V in the secondary, the proximity to the asymptote (V th = 1.31 kV in Fig. 6) produces an erratic behavior of the system, with intermittent variations of up to 50 W in P lamp for a constant value of V in .

As V in approaches to the asymptote, the system is more susceptible to small perturbations caused by the main voltage source or by the dynamic behavior of the lamp, which is not included in the lamp simplified model used for this design.

3) EMI: The SRI is an advantageous supply in terms of EMI when compared with a hard-switching topology. This benefit is evaluated by performing a fast Fourier transform (FFT) of the lamp current for both topologies under similar operating conditions of f lamp and output power (Fig. 10).

4) UV Radiation: For the XeCl excimer lamp used as load, the typical radiation wavelength is 308 nm; the UV radiation power is measured with the optometer OPTIK P-9710 using the UV detector SN5816, installed at 12 mm of the lamp surface. The UV power obtained using the SRI at P lamp = 90 W and f lamp = 80 kHz is 17.7 mW/cm 2 . For the same lamp power, frequency, and pulse duration, the UV radiation obtained with the square-waveform current is 20 mW/cm 2 . This result reveals a decrease of around 10% in the UV power due to the current form factor.

The UV waveform is acquired with a Thorlabs PDA-25K photodetector, installed at 25 mm of the lamp surface. As already mentioned in [START_REF] Diez | Control of the UV emission of an excimer lamp by means of a current-mode power supply[END_REF], as can be seen in Fig. 11, the waveform of the UV radiation is similar to the i lamp lamp current waveform (absolute value).

VII. CONCLUSION

The use of the SRI topology, operating in DCM, has been proved to be a good option to supply a DBD excimer lamp. With the operating mode selected in this work, the lamp power is imposed with two degrees of freedom, and ZCS is achieved, reducing switching losses and EMI. The use of the lamp electrical model, in conjunction with the state plane analysis, gives an insight into the process and allows the calculation of the electrical values, including the lamp power, as a function of the input voltage, the inverter frequency, the components, and the parameters of the lamp. Analytical study, simulation, and experimental results are in accordance, validating the SRI as an efficient topology for the supplying of DBD excimer lamps. Satisfactory efficiency results of up to 93% have been obtained for the converter supplying a DBD UV excimer lamp.

Fig. 1 .

 1 Fig. 1. (Top) Coaxial DBD excimer lamp and (bottom) its equivalent electrical model.

Fig. 2 .

 2 Fig. 2. (Top left) Proposed SRI and (bottom) its operating sequences. (Top right) Theoretical lamp current and voltage.

Fig. 3 .

 3 Fig. 3. Two operating conditions before breakdown are plotted in the state plane: When the gas breakdown happens (top) before the peak current and (bottom) after the peak current. Only the positive current half cycle is shown.

Fig. 4 .

 4 Fig. 4. Two operating conditions are plotted in the state plane after breakdown: When the gas breakdown happens (top) before the peak current and (bottom) after the peak current. Only the positive current cycle is shown.

Fig. 5 .

 5 Fig. 5. Transient response from simulation. (Top) Unstable state plane for V in > V th and (bottom) stable state plane for V in < V th .

Fig. 6 .

 6 Fig. 6. Power injected into the DBD lamp for different input voltages at constant frequency.

Fig. 7 .

 7 Fig. 7. Converter circuit and DBD electrical model used for simulation.

Fig. 8 .

 8 Fig. 8. Waveform comparison (top) from simulation and (bottom) from the experimental validation. f lamp = 80 kHz and V in = 115 V.

Fig. 9 .

 9 Fig. 9. Measured efficiencies of the SRI for different values of output power at f lamp = 80 kHz.

Fig. 10 .

 10 Fig. 10. FFT of the lamp current for SRI and square-waveform current-source topologies.

Fig. 11 .

 11 Fig. 11. UV waveform and excilamp current for the SRI.

TABLE I THEORETICAL

 I OPERATING POINT

ACKNOWLEDGMENT

Part of this study is in the framework of French-Colombian cooperation, with the support of the ECOS program (ECOS Nord, Colciencias-ICETEX).