Mawuena Remi Degnon
email: rdegnon@ithpp-alcen.fr

Member, IEEE Anton Gusev
email: anton.gusev@univ-pau.fr

Antoine Silvestre De Ferron

Laurent Pecastaing

Gaetan Daulhac

Aleksandr Baranov

Bucur Sébastien Boisne
email: sboisne@ithpp-alcen.fr

Senior Member, IEEE Mircea Novac
email: b.m.novac@lboro.ac.uk

Student Member, IEEE Mawuena Rémi Degnon

Gaëtan Daulhac

G Daulhac

B M Novac

Off-the-Shelf Diodes as High-Voltage Opening Switches

Keywords: Pulsed power system, semiconductor opening switch, off-the-shelf diode, saturating pulse transformer

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

I. INTRODUCTION

T HE switch is one of the fundamental components of all pulsed power system and can be either a closing or an opening type. The type of switch used depends on the way the energy is stored. Closing switches are used in capacitive (electric) energy storage (CES) systems, such as Marx generators, pulse forming lines, etc. Opening switches are used in circuits based on inductive (magnetic) energy storage (IES), which have a higher energy density than the CES [START_REF] Bluhm | Pulsed Power Systems: principles and applications[END_REF]. According to [START_REF] Rukin | Pulsed power technology based on semiconductor opening switches: A review[END_REF], there are several fundamental differences between these two types of switches, that put the opening switch in a more attractive position for nanosecond pulsed power technology. An opening switch allows faster energy transfer, with the current cutting-off process increasing the output voltage, which results in a pulsed power gain.

However, while it is simpler to switch the energy stored in CES through conventional spark gap closing switches, the requirements on opening switches used in IES are usually challenging, particularly when it is required to switch-off, rapidly and repetitively, several kAs to generate hundreds of kVs or even a few MVs pulses [START_REF] Grekhov | Nanosecond semiconductor diodes for pulsed power switching[END_REF]. Solid-state devices are widely used in power electronics, such as the insulated-gate bipolar transistor (IGBT), the gate turn-off thyristor (GTO) and the metal-oxide-semiconductor field-effect transistor (MOSFET). All these are potentially usable as opening switches, however they are currently limited either by a maximum current or by their switching characteristic speed [START_REF] Scharnholz | High-power MOSFETs and fast-switching thyristors utilized as opening switches for inductive storage systems[END_REF]- [START_REF] Grekhov | Physical basis for high-power semiconductor nanosecond opening switches[END_REF]. With some very few exceptions, the plasma opening switch or the exploding wire is unsuitable for high pulsed repetition frequency (PRF) operation and has a limited lifetime [START_REF] Bluhm | Pulsed Power Systems: principles and applications[END_REF], [START_REF] Rukin | Pulsed power technology based on semiconductor opening switches: A review[END_REF].

Towards the end of the 20 th century, the semiconductor opening switch (SOS) effect was discovered in p + -p-n-n + silicon diode structure by Rukin et al. [START_REF] Mesyats | Semiconductor opening switch research at iep[END_REF]. The SOS effect is the nanosecond cutoff of high-density reverse currents in semiconductor diodes, for which a theoretical model was proposed in [START_REF] Darznek | Theoretical model of the sos effect[END_REF]. Based on this effect, SOS diodes were developed over three decades ago [START_REF] Rukin | High-power nanosecond pulse generators based on semiconductor opening switches (review)[END_REF]. That sparked a breakthrough in the development of solid-state pulsed power systems based on inductive energy storage, since it allows the improvement of their important characteristics such as current density, pulsed power, voltage, energy and PRF [START_REF] Wang | A semiconductor opening switch based generator with pulse repetitive frequency of 4 MHz[END_REF], [START_REF] Lyubutin | High efficiency nanosecond generator based on semiconductor opening switch[END_REF]. Due to high PRF of operation, long lifetime, and high average power, the SOS generators are currently used not only in research but also in modern biological, medical and industrial applications, such as X-ray pulsed sources, particle accelerators, non-thermalplasma purification of water and gas, e-beam sterilization, laser pumping sources and many other [START_REF] Sokovnin | Improving the operating characteristics of an YPT-0.5 accelerator[END_REF]- [START_REF] Takaki | Ozone synthesis using streamer discharge produced by nanoseconds pulse voltage under atmospheric pressure[END_REF].

However, the interest in the benefits of SOS for improving the performance of pulsed power systems sharply contrasts with a lack of SOS diode manufacturers. Hence, demonstrating the possibility of using off-the-shelf diodes as SOS diodes represents the main aim of the research presented in this paper. A wide range of off-the-shelf diodes have been tested as highvoltage opening switches at switching energies of up to 10 J. The results are presented in the second and third sections, respectively devoted to the 25 mJ and 10 J experimental arrangements. The last section is devoted to conclusions.

II. THE 25 MJ EXPERIMENTAL ARRANGEMENT

A. Circuit Description

A simplified circuit of the low-energy test bench is shown in Fig. 1. The circuit is designed with a single magnetic element to ensure high energy efficiency, which can be up to 70% [START_REF] Gusev | Semiconductor opening switch generator with a primary thyristor switch triggered in impact-ionization wave mode[END_REF]. For convenience, a self-breakdown spark gap SG is used as a primary switch. The ceramic capacitors C1 and C2 have a capacitance of 50 nF and 12.5 nF, respectively. The magnetic core of the pulse transformer (PT) consists of a single nanocrystalline ring (110 × 80 × 20 mm) obtained from Vacuumschmelze, with the saturation induction being 1.2 T [START_REF] Vacuumschmelze | Nanocrystalline material[END_REF]. The saturating magnetic core PT ensures two main functions. The first is to transfer the energy from the primary to the secondary circuit, stepping up the voltage. The second is to have a very low inductance of the secondary winding, when the magnetic core is driven to saturation. The primary and secondary windings of the PT have w 1 = 1 and w 2 = 2 turns, respectively. A bias winding of 2 turns (not shown) with a maximum current amplitude of 3 A is used to reset the core before the next pulse. The low-inductance resistive load R is connected in parallel to the diode D under test.

The circuit of Fig. 1 operates as follows. Firstly, C1 is charged to its initial voltage V C1 by an external DC power supply (not shown). When SG closes, C1 releases its energy and the PT charges C2, while the current flows through the diode D in the forward direction. For an SOS diode, this is the forward pumping stage, which lasts for t + while the current reaches its maximum amplitude I + (Fig. 2(a)). The circuit is designed using the voltage-time product [START_REF] Choi | Introduction of the magnetic pulse compressor (MPC) -Fundamental review and practical application[END_REF] to reach the maximum voltage across C2 at the moment when the magnetic core of the PT saturates. At this moment, C2 starts to discharge through the secondary winding w 2 of the saturated PT, generating the reverse current through the diode. This represents the reverse pumping stage for the SOS diode, where the current reaches the maximum amplitude I -after a duration t -(Fig. 2(a)). The magnitude of the reverse current, and thus the reverse current density, is greater than the forward current due to the much lower self-inductance of the saturated PT. Finally, this reverse current is cut off within the switching time t 0 (Fig. 2(a)) by the SOS diode and the energy is transferred to the load R, generating a very short nanosecond high-voltage pulse with a characteristic rise time Tr (Fig. 2

(b)).

A reverse current with a density of more than 1 kA/cm² leads to a high electric field region, which is formed in the p region of the SOS diode structure (p + -p -n -n + ) due to the electron-hole plasma motion. Hence, in the SOS diode, the current interruption occurs in the p region rather than in the p-n junction. Details of the SOS diode physics are described in [START_REF] Rukin | Pulsed power technology based on semiconductor opening switches: A review[END_REF].

All rise times in the present paper are defined as the time interval from 10% to 90% of the peak impulse. The charging voltage of C1 is measured using the Tektronix probe P6015A. The voltage across the load and the current through the diodes are obtained using the current measurements of the Pearson current monitor (CM in Fig. 1) model 410 and the resistive shunt Rsh = 0.9 Ω (Fig. 1). The waveforms are captured using Rigol DS1204B real-time oscilloscope.

B. Low-Voltage Diodes

25 types of off-the-shelf diodes were selected and tested as opening switches including rectifying, avalanche, Schottky, transient-voltage-suppression (TVS), and Zener diodes. The specifications of the studied diodes are as follows: blocking voltage ranging from 0.2 kV to 10 kV, die area from 0.01 cm² to 0.81 cm² and a recovery time from 0.1 µs to 20 µs. The die area of each diode was measured to calculate the cutting current density which, according to [START_REF] Mesyats | Semiconductor opening switch research at iep[END_REF], must be more than 1 kA/cm² in the SOS mode of operation. SOS diodes manufactured in Russia and kindly provided by the Institute of Electrophysics having 0.25 cm² die area and 3 kV rated voltage, and here termed SOS-R, are used as a reference to which the characteristics of all the off-the-shelf units are compared to.

C. Results and Discussion

Firstly, the reference SOS-R diode is tested in the circuit shown in Fig. 1 with the charging voltage V C1 fixed at 1 kV.

The results obtained using the SOS-R with a load resistance R = 28 Ω are presented in Fig. 2. A forward pumping current I + = 100 A flows through the single SOS diode within t + = 380 ns. After saturation of the magnetic core of the PT, a reverse current I -= 260 A flows through the diode for a duration t -= 120 ns. After that, the current is cut off by the SOS-R diode within a time t 0 = 34 ns. A voltage pulse with an amplitude of 3.4 kV and a rise time of 20 ns is obtained at the load. The voltage amplitude V C2 measured at the capacitor C2 is 1.7 kV, which gives an SOS-R overvoltage coefficient of 2, which is defined as

K ov = V R /V C2 .
Secondly, after testing the SOS-R, all the 25 selected offthe-shelf diodes were tested one by one, in the same configuration as the SOS-R diode. Fig. 3 shows all the current and voltage waveforms obtained during these tests in comparison with the results obtained from the SOS-R diode.

As a general observation, it is clear that not all diodes can operate in the SOS mode. Rectifier, avalanche, Zener and TVS diodes are able to open and transfer the current to the load. However, the switching time greatly varies. At the same time, the Schottky diodes, due to their structure and physics of operation, are not capable of reaching and interrupting the high reverse current. Small-area high-voltage diodes demonstrate a voltage drop during the forward current, which leads to additional energy losses and reduces the efficiency of the switch. Also, for most of the tested off-the-shelf diodes, the output voltage was limited to the level of the rated voltage for a switch consisting of a single diode.

To overcome the voltage limitation and to reduce the voltage drop during the forward current, a series-parallel connection of the diodes has been also studied. The parallel connection aims at reducing the voltage drop, while the series connection increases the blocking voltage capability. The even distribution of the voltage across the series connected SOS diodes [START_REF] Ponomarev | Investigation of the process of voltage distribution over elements of a high-power semiconductor current interrupter[END_REF] makes it possible to assemble the diodes without any voltage distribution circuit consideration. The best results obtained from the different types of single diodes are shown in Fig. 4(a); the improvement of the series-parallel connections can be seen in Fig. 4(b). The voltage capability of the off-the-shelf diodes is thus improved and, as a result, nanosecond voltages ranging from 1.8 kV to 2.5 kV were obtained on the resistive load of 28 Ω instead of 0.5 kV to 1.4 kV for the single diodes. However, the highest corresponding overvoltage coefficient of the off-the-shelf diodes is 1.5, which is less than the coefficient obtained for the reference SOS-R diode that equals 2.

Even though the off-the-shelf diodes produce pulses with a voltage amplitude of about 25% less than the SOS diode, the obtained results confirm the possibility of using the offthe-shelf diodes as opening switches for IES circuits at the low energy level of 25 mJ. From a summary of the relevant parameters presented in Table I, one can see the TVS diodes, in particular, have the fastest switching time of 13 ns compared to the other types of tested diodes. In addition, the full width at half maximum (FWHM) of the off-the-shelf diodes voltages are 1.6 to 3 times longer than the SOS-R.

Furthermore, a 3.15 kV output voltage with a rise time of 10 ns and a FWHM of 40 ns was obtained on a 110 Ω load by using an assembly of 64 (8 series x 8 parallel) TVS diodes at a charging voltage across C1 of V C1 = 1.9 kV (Fig. 5). In this configuration, the forward current of duration t + = 360 ns reached an amplitude I + of 170 A while the reverse current after flowing for t -= 100 ns reached the amplitude I -of 375 A with the diode having a current cutoff time of 30 ns.

III. THE HIGH ENERGY 10 J EXPERIMENTAL ARRANGEMENT A. Circuit Description

The equivalent electrical circuit of the high-energy test bench is presented in Fig. 6. This circuit is similar to the one presented in Fig. 1. A modification of the components was however implemented in order to increase the initially stored energy and, thereby, voltage amplitude across the load. Here, the pulse transformer PT is based on a nanocrystalline magnetic core obtained from Finemet FT-3L, with the magnetic core parameters provided in [START_REF] Holma | Prototype Inductive Adders with Extremely Flat-Top Output Pulses for the Compact Linear Collider at CERN[END_REF]. The primary winding circuit consists of a film capacitor C1 = 200 nF, a triggered spark gap switch SG, and a single turn primary winding w 1 . The secondary winding circuit consists of a ceramic capacitor C2 = 2 nF, a 10-turn secondary winding w 2 , a diode D and a resistive load R. To prevent any breakdown, the diode and the load are both mounted under oil. Since the charging voltage of the primary capacitor is limited to 10 kV, the maximum initial electrostatic energy that can be stored is 10 J. The additional inductors L1 and L2 are further installed in order to vary the parameters of the forward and reverse pumping. The resetting circuit (not shown) consists of a 5-turn bias winding driven by a DC current source with an amplitude up to 3 A. A choke (not shown) decouples the resetting circuit from the main circuit, preventing energy losses and protecting the current source. The operation of the circuit is similar to the one previously described in Section II.

The voltages V C1 and V C2 are measured using Tektronix P6015A and Northstar PVM100 probes, respectively. The waveforms are recorded by a DS1204B Rigol oscilloscope. The currents through the diode and the load are measured by two homemade resistive shunts (0.5 Ω and 0.15 Ω) with a usable rise time of about 0.5 ns. The voltage across the load is found using Ohm's law. A 7 GHz Tektronix TDS7704B oscilloscope is used to capture the extremely fast signals generated by the diode and the load circuits. Wide bandwidth attenuators by Barth (26 dB, 30 GHz) and RF-Lambda (6 dB and 20 dB, 4 GHz) are used to attenuate the high-voltage signals obtained from the resistive shunts.

B. High-Voltage Diodes

Several elementary off-the-shelf rectifier diodes were connected in series to build a high-voltage diode assembly having an overall blocking voltage of about 100 kV. This diode is termed OTS-100. The characteristics obtained for the OTS-100 on the 10 J test bench are compared with those of the SOS-180-4 diode [START_REF] Gusev | Semiconductor opening switch generator with a primary thyristor switch triggered in impact-ionization wave mode[END_REF], rated for 180 kV which serves as a reference.

C. Results and Discussion

Firstly, the SOS-180-4 diode was tested on the 10 J test bench. The charging voltage of C1 (Fig. 6) was fixed at 6 kV. A tubular non-inductive ceramic resistor R = 70 Ω was used as a load. For the SOS-180-4 diode, the following parameters were obtained (Fig. 7(a)): forward pumping current I + = 400 A, duration t + = 440 ns, reverse pumping current I -= 1.3 kA and reverse pumping time t -= 90 ns while the cutoff time t 0 is 32 ns. The voltage pulse generated on the resistive load has an amplitude of 58 kV with a rise time of 19 ns, and a pulse duration of 55 ns (FWHM). The overvoltage coefficient K ov of the SOS-180-4 diode is 1.2.

Secondly, the current and voltage pulse parameters obtained using the OTS-100 operated under the same condition as the SOS-180-4 are as follows (Fig. 7(b)): forward pumping current I + = 370 A, duration t + = 440 ns, reverse pumping current I -= 0.4 kA and reverse pumping time t -= 45 ns. Cutoff time t 0 was 23 ns. The load voltage pulse has an amplitude of 42 kV, rise time of 22 ns and pulse duration of 108 ns (FWHM). The overvoltage coefficient of the OTS-100 is K ov = 0.85.

Both the SOS-180-4 and OTS-100 have practically the same forward pumping parameters I + , t + and voltage drop (Fig. 7). However, the behavior of the OTS-100 during the reverse pumping is changing dramatically: its reverse pumping time t -is two times less when compared to the SOS-180-4 diode. Eventually, this leads to the threefold decrease of the reverse current I -, which prevents storing energy in the inductive energy storage (L2 and parasitic inductance). While the reverse to forward current ratio (I -/I + ) of the SOS-180-4 is 3.2, this ratio is only 1.1 for the OTS-100. Hence, in the latter case, one part of the energy still remains stored in the C2 at the current cutoff phase. Then both parts of the energy are switched into the load. As a consequence, the voltage pulse across the load has two clearly distinguished stages (Fig. 8). The first highvoltage stage could be driven by the energy stored in the inductance L2; the second low-voltage stage could be driven by the discharge of the remaining energy in C2. Since the time constant of the capacitor discharge is increasing, this effect is accentuated for high-impedance loads. For example, for a 1 kΩ load, the complete discharge of the capacitor into the load occurs after a few µs (Fig. 8).

D. Optimization of the OTS-100 Operating Mode

This section is dedicated to an examination of the main factors affecting the reverse pumping parameters of the OTS-100 when operating as an opening switch. An experimental study was undertaken to find ways to increase the reverse pumping time, the inductive stored energy and therefore, all the output pulse parameters.

Firstly, amplitude and duration of the forward and reverse pumping currents were varied, by changing V C1 (Fig. 6) from 3 kV to 10 kV. During these tests, by changing V C1 and simultaneously adjusting the bias current, the voltage V R across the 70 Ω load was adjusted almost linearly from 10 kV to 70 kV (Fig. 9(a)). This demonstrates a possibility of building an adjustable pulse power generator based on an opening switch combined with a saturating pulse transformer.

The maximum output voltage V R = 70 kV with a rise time of 23 ns and duration of 100 ns (FWHM) was obtained for a 70 Ω load and for a charging voltage V C1 = 10 kV, which corresponds to 10 J energy stored in C1 (Fig. 9(a)). The corresponding forward and reverse currents through the OTS-100 diode are I + = 0.6 kA and I -= 0.8 kA. The load current reaches 1 kA, resulting in a load peak power of 70 MW.

The influence of V C1 on the diode pumping is presented in Fig. 9(b) and Fig. 9(c). When V C1 increases, both I + and I - increase, respectively, from 160 A to 650 A, and from 70 A to 800 A. At the same time, t + slightly decreases from 480 ns to 400 ns while t -decreases from 80 ns to 30 ns. Consequently, the ratio of the forward to reverse current duration t + /t -also increases. In addition, the ratio I -/I + increases from 0.4 to 1.3 without approaching the SOS-180-4 diode current ratio of 3.2. It is worth mentioning a constant ratio of the forward and reverse electric charges Q + /Q -calculated as Q = i(t)dt during the diode forward and reverse pumping. For this experiment, the bias current (Ib in Fig. 9(b)) was fixed at zero for V C1 from 3 kV to 5 kV; at 1 A for V C1 from 6 kV to 7 kV; at 2 A for V C1 from 8 kV to 9 kV; and 3 A for V C1 = 10 kV.

To examine the impact of the I -magnitude on the OTS-100 switching, an additional inductance L1 has been added in series with the capacitor C1, shown in Fig. 6. The Fig. 10 summarizes the results. The inductance L1 was varied from 0 to 8.6 µH, causing the variation of I -from 0.4 kA to 0.1 kA. During these experiments, I + and t + were changing as well, t -remained constant. For this experiment, a 50 Ω TVO less-inductive resistor load is used. The charging voltage V C1 was fixed at 6 kV. It was noticed that increasing L1 causes the forward current duration to increase and the forward and reverse current amplitudes to decrease, while the reverse current duration remains about the same. This results in an increasing of the ratio I -/I + to 2.4. The t + /t -ratio obviously increases, as well as the forward to reverse electric charges.

High values of the inductance L1 leads to a decrease in the maximum voltage at C2 and, therefore, lower voltage across the load. Although the current ratio I -/I + is improved by adding L1, the load current and voltage amplitudes drop, thus the use of a less inductive primary circuit is recommended.

According to the literature [START_REF] Grekhov | Nanosecond semiconductor diodes for pulsed power switching[END_REF], a nanosecond current cutoff in semiconductor diodes with a switching power from MW to GW can be realized using the drift step recovery diode (DSRD) or the semiconductor opening switch. However, it seems that the results obtained in this work can not be fully explained by these two mechanisms. While the limit of DSRD is 200-300 A/cm² [START_REF] Grekhov | Nanosecond semiconductor diodes for pulsed power switching[END_REF], in the present work the OTS-100 diode operates at a current density of more than 1 kA/cm², which is usually considered as a threshold of the SOS mode [START_REF] Mesyats | Semiconductor opening switch research at iep[END_REF]. Also, even though the OTS-100 was tested at forward pumping mode required to the SOS mechanism, reverse pumping mode parameters were dramatically different from those expected from an SOS diode. In particular, reverse pumping time t -, which was limited by the reverse conductivity of the diode, was two times less compared to the SOS-180-4 diode. What is more important, t - is almost insensitive to the forward pumping parameters such as t + and I + . However, the cutoff time of the OTS-100 diode (tens of nanoseconds) is close to an SOS diode cutoff time at comparable voltage and power levels on the load. These facts probably require another mechanism of current interruption to be considered. At this moment, it is assumed that specific diode structure -engineered for a fast recovery -could be a reason for the fast current cutoff. However, to shed light on this question, one needs to know the exact doping profile of the diode, which is usually a trade secret of the manufacturer.

(η = E R E C1 ) R (Ω) L2 (µH) V R (
Finally, the inductance L2 (Fig. 6) was installed to investigate its impact on the shape of the output voltage and on the energy transferred to the load. An experiment was performed on 50 Ω and 1 kΩ loads with L1 = 0. The results are presented in Fig. 11(a) and Fig. 11(b); and Table II summarizes the parameters of the output voltage pulse and the energy efficiency as a function of the inductance L2. The energy delivered into the load is numerically estimated as the integral of the load power. The stored energy in the capacitor is calculated as the half product of the capacitance and the square of the voltage

(E C1 = C1U 2 C1 2 ).
As shown in Fig. 11(a) for the low-impedance load, the inductance L2 reduces the amplitude of the load voltage pulse and increases pulse duration. The rise time is also extended and the input to output energy efficiency is not improved (Table II). On the contrary, for high-impedance loads (Fig. 11(b)), L2 improves, in the first instance, the high-voltage part of the voltage pulse. The amplitude and duration of the high-voltage part are probably increased due to an increase in the energy stored in L2, which changes from 80 mJ to 260 mJ for L2 equal to 1 µH and 8.6 µH, respectively. In addition, the energy efficiency is slightly improved, though the rise time is increased (Table II).

IV. CONCLUSION

The use of off-the-shelf diodes as semiconductor opening switches has been investigated. Among the 25 off-the-shelf diodes tested with the low-energy test bench, the TVS diodes showed the best results in terms of switching time. The switching power of the off-the-shelf diodes was increased by series-parallel connection. Series connection of the off-theshelf diodes increased the voltage capability of the switch, whereas parallel connection reduced its energy losses. It was shown that the output voltage can be linearly adjustable using a variable primary charging voltage combined with an appropriate resetting current. In order to optimize the energy efficiency of the circuit, the inductance of the primary circuit of the transformer should be minimized, while an appropriate secondary inductance should be determined depending on the load. The off-the-shelf diodes have shown a good stability in voltage switching after a large number of shots, with no degradation of the diodes being observed during experimentation. When combined with a solid-state primary switch and the implementation of an efficient cooling, the off-the-shelf diode assemblies represent a serious candidate to become a major asset in the development of high repetition rate nanosecond pulsed power systems.

Fig. 1 .

 1 Fig. 1. Circuit diagram of the 25 mJ experimental arrangement. Explanations are provided in the text.

Fig. 2 .

 2 Fig. 2. Typical waveforms of the current flowing through the SOS-R diode (a), and the voltage across the load R = 28 Ω for V C1 = 1 kV (b).

Fig. 3 .

 3 Fig. 3. Current (a) and voltage (b) waveforms of the tested off-the-shelf diodes in comparison with the SOS reference diode.

Fig. 4 .

 4 Fig. 4. The current and voltage curves of the best pulse of each type of: the single diode (a)-(b); the diodes connected in series-parallel (c)-(d) (1 -Rectifier: 2 series x 2 parallels; 2 -Avalanche: 2 series x 20 parallels; 3 -Fast recovery: 2 series; 4 -TVS: 7 series x 3 parallels) at the load of 28 Ω.

Fig. 5 .

 5 Fig. 5. Waveforms of the current flowing through the 64 (8 series x 8 parallel) TVS diodes assembly (1), and voltage pulse across the 110 Ω load at V C1 = 1.9 kV (2).

Fig. 6 .

 6 Fig. 6. Circuit diagram of the 10 J experimental arrangement. Explanations are provided in the text.

Fig. 7 .

 7 Fig. 7. Waveforms of the current through the diode D (1, 3) and voltage across the load R = 70 Ω (2, 4) at V C1 = 6 kV for the SOS-180-4 (a) and OTS-100 (b).

Fig. 8 .

 8 Fig. 8. Waveform of the voltage across the load R = 1 kΩ at V C1 = 6 kV.

Fig. 9 .

 9 Fig. 9. Evolution of the voltages across C2 (square) and load (round) (a); current through the diode (b); ratios of the pumping currents (square), pumping times (round), and electric charges (triangle) (c) as a function of the charging voltage V C1 and time, using the OTS-100 diode and the resistive load R = 70 Ω.

Fig. 10 .

 10 Fig. 10. Ratios of the pumping currents (square), pumping times (round) and electric charges (triangle) as a function of the inductance L1 obtained for the OTS-100 at the resistive load R = 50 Ω and charging voltage V C1 = 6 kV.

Fig. 11 .

 11 Fig. 11. Load voltage at different L2 on 50 Ω load (a), and on 1 kΩ load (b) using the OTS-100 diode at charging voltage V c1 = 6 kV.

  Mawuena R. Degnon (Student member, IEEE) was born in Lomé, Togo in 1996. He received his M.Sc. in electrical engineering and industrial computing from the Université de Pau et des Pays de l'Adour (UPPA), Pau, France in 2020 after his M.Eng. in electrical engineering received from the Université de Lomé, Lomé, Togo in 2018. He is currently pursuing the Ph.D. degree with the department of electrical engineering of the UPPA. His research interests include high-voltage pulsed power systems, solid-state switches and nanosecond high-voltage generators for industrial applications.

  Anton I. Gusev (Member, IEEE) was born in Miass, Russia, in 1988. He received his M.S. degree in electrophysics (2012) from the Ural Federal University (UrFU) and his Ph.D. degree in engineering sciences (2019) from the Institute of Electrophysics of the Ural Branch of the Russian Academy of Sciences (IEP) in Yekaterinburg, Russia. From 2008 to 2019, he has been with IEP as an Intern, Ph.D. Student, and Junior Researcher in the Pulsed Power Laboratory. At the same time, from 2014 to 2019, he has been with UrFU as a Senior Teacher. In 2019, he became a Postdoc at the Université de Pau et des Pays de l'Adour (UPPA) in Pau, France. Since 2020, he is an Assistant Professor in the SIAME laboratory at UPPA. His research interests include semiconductor physics, high-power semiconductor switches, and high-voltage solid-state generators, which provide nano-and subnanosecond pulses. Dr. Gusev is a member of the International Society on Pulsed Power Applications (ISP) and the Association for the Advancement of Pulsed Power (A2P2). He has been awarded as a young researcher at major international pulsed power conferences (EFRE 2016, EAPPC 2018, GDP 2021) including two supported by IEEE (PPC 2017 and IPMHVC 2018). Antoine Silvestre de Ferron was born in Tarbes, France, in 1977. He received the master degree in electrical and electronic engineering from the University of Toulouse, Toulouse, France, and the Ph.D. degree in electrical engineering from the University of Pau, Pau, France, in 2002 and 2006, respectively. From 2006 to 2008, he was a Researcher with the Atomic Energy Commission (CEA), a French government-fund technological research organization in Le Barp, France. He is currently an engineer at the head of the High Voltage Processes Teams in the SIAME laboratory of the University of Pau, France. His research interests include high-pulsed power generation, with military and civil applications. He is specialized in Marx generator and pulse forming lines in high voltage generation, in high voltage transient probes associated and in high current discharges in liquids. Laurent Pecastaing (M'13-SM'17) he received the Ph.D. and Research Directorship Habilitation degrees in electrical engineering from the Université de Pau et des Pays de l'Adour (UPPA), Pau, France, in 2001 and 2010, respectively. He is currently a Full Professor in pulsed power with University of Pau. He is the director of the SIAME laboratory, and he is also the Director of a Common Laboratory between UPPA and CEA, France. His current research interests include high-power microwave sources, compact pulsed power systems, and ultrafast transient probes. Dr. Pécastaing was the Chairman of the EAPPC/BEAMS/MEGAGAUSS Conference in France in 2021. He is also a member of the International Steering Committees for both the BEAMS Conferences and the Euro-Asian Pulsed Power Conferences. Gaëtan Daulhac was born in Brive la Gaillarde, France, in 1987. He graduated from the ENSIAME and he received a research master degree from the Université de Valencienne (UVHC), Valenciennes, France in 2010. He is currently an Engineer at ITHPP. He works on high pulsed power generator. More precisely, on resonant generator, dedicated to pulse electron beams sterilization. Aleksandr Baranov received his Master of Engineering (M.Eng.) in Industrial Electrical Energy and Engineering from Togliatty State University, Togliatty, Russia, in 2015. He is currently R&D engineer in ITHPP, Thégra, France. His research fields of interests are high-voltage nanoseconds generators, electron emission and pulsed power systems. Sebastien Boisne Sébastien BOISNE was born in Thionville, France, in 1979. He holds a Master's degree in Global Management of Organizations, Strategy and Finance from the University of Paris Dauphine PSL. In 2002, he joined Thomson CSF Linac, Orsay, France, a leader in electron accelerators, where he is in charge of the development of electron beam range of products, intended to be employed in high demands industrial uses. He is currently at the head of BETA BEAMS (ITHPP-ALCEN group), Donzenac, France, specializing in the design and supply of electron beam accelerators, installed on endusers production sites, and mainly used in surface and core sterilization of pharmaceutical products. Bucur M. Novac (Senior Member, IEEE) received the M.Sc. and Ph.D. degrees from the University of Bucharest, Bucharest, Romania, in 1977 and 1989, respectively. He joined Loughborough University, Loughborough, U.K., in 1998, where he is currently a Professor of pulsed power. His research interests include compact and repetitive high-power systems, explosively and electromagnetically driven magnetic flux compression generators and their applications, electromagnetic launchers, ultrafast magneto and electro-optic sensors, and 2-D modeling of pulsed power systems. He has coauthored two books on explosive pulsed power and has published more than 200 refereed articles and conference contributions. Prof. Novac is a member of the International Steering Committees for the MEGAGAUSS Conference and the Euro-Asian Pulsed Power Conference (EAPPC). He is a fellow of the Royal Academy of Engineering and a Chartered Engineer and a fellow of the Institution of Engineering and Technology, U.K. He was a Voting Member of the Pulsed Power Science and Technology Committee of the IEEE Nuclear and Plasma Science Society, a member of the Organizing Committee of the IEEE International Power Modulator and High Voltage Conference, and the Co-Chairman of the U.K. Pulsed Power Symposia.

TABLE II LOAD

 II VOLTAGE AMPLITUDE, RISE TIME, WIDTH AND ENERGY EFFICIENCY AT DIFFERENT L2 ON 50 Ω AND 1 KΩ

This research was carried out within the framework of the E2S UPPA project (S2P2 and PULPA Chairs) supported by the French "Investissements d'Avenir" programme managed by ANR (ANR-16-IDEX-0002). This work is also funded by ITHPP.

M. R. Degnon is with the Universite de Pau


Thomas Martinez
email: thomas.martinez@satie.ens-cachan.fr

Denis Labrousse

Gaël Pillonnet

Dejan Vasic

François Costa

Gael Pillonnet

Francois Costa

Traveling wave piezoelectric transformer for multi-level insulated gate-driver power supply

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

Introduction

Strong emphasis is put currently on the development of multi-level cascaded power inverters. By reducing the constraints on switching elements, it allows replacing high-voltage transistors by multiple lower voltage ones [START_REF] Krishna | A brief review on multi level inverter topologies[END_REF]. However, with the number of transistors increasing, the number of gate drivers and their complexity also increase. Especially, the need for insulated power supply for the driver is of particular importance. The galvanic insulation for gate-drive circuits is generally provided by magnetic coupled transformers [START_REF] Nicolas | A 2W, 5MHz, PCB-integration compatible 2.64cm 3 regulated and isolated power supply for gate driver[END_REF]. However piezoelectric transformers have found a particular interest thanks to several inherent advantages: low electro-magnetic radiation, high efficiency and for the application considered: high voltage withstand and strong galvanic insulation [START_REF] Flynn | Fundamental limits on energy transfer and circuit considerations for piezoelectric transformers[END_REF]. The interest of piezoelectric transformers in gatedrive circuits has focused on standing wave piezoelectric transformer to convey the electromechanical conversion [START_REF] Vasic | Piezoelectric transformer for integrated MOSFET and IGBT gate driver[END_REF], [START_REF] Valenta | Piezoelectric transformer for high-side MOSFET driver supplying[END_REF]. This type of behavior limits the transformer to three electrodes and in practice we need one piezoelectric transformer to perform insulation for each gate-drive circuit which limits their application to multilevel converters. We have proposed a new topology of piezoelectric transformer that uses a traveling wave instead of a standing wave [START_REF] Martinez | Study and Modeling of a Traveling Wave Piezoelectric Transformer[END_REF] as shown in Fig. 1. The limitation of standing waves in piezoelectric transformer arises from the fact that the wave present nodes and antinodes that limits the number of position of Fig. 1: Solutions for the insulation of multi-level gatedrive power supply electrodes usable on the transformer for maximum power conversion. In the case of a traveling-one, the mechanical wave presents the same maximum amplitude but propagates. Thus, when the wave passes over electrodes, the voltage amplitude will remain the same for all electrodes but with phaseshift depending on their position. Thus, we can obtain a polyphaser system of voltages at the output of the transformer with a travelling wave. These different phases can then be rectified at the secondary side to generate the multiple insulated power supply for the gate-drivers. There are no theoretical limits to the number of phases and output voltages obtainable with this topology apart from the power considerations. Thus, the travelingwave piezoelectric transformer (TWPT) can be suitable for multi-level converters drivers.

In this paper, we will firstly present the traveling wave piezoelectric transformer, its operating principle and its performances. Secondly, we will focus on the topology of the insulated gate-drive power supply using the traveling wave piezoelectric transformer. In the following part, we will present the experimental results obtained with this structure on a resistive load and supplying directly drivers. Finally, we will discuss the results and present perspectives of improvement.

2 Operating principle of the traveling wave piezoelectric transformer

Geometry and generation of the traveling wave

In order to generate a traveling wave in a piezoelectric ceramic, a solution mainly used in ultrasonic motors is to use a cylinder or ring geometry [START_REF] Duan | A novel ring type ultrasonic motor with multiple wavenumbers: design, fabrication and characterization[END_REF] . As the traveling wave propagates along the circumference of the ring, there will not exist any reflection on the boundaries of the medium that would allow the generation of a standing wave. The interest of using this geometry is also to work at the resonance of the ceramic element to benefit of low-loss conversion and maximize the power transfer. In Fig. 2 we show the chosen geometry which consists in a hollow thin cylinder. The electrodes on the interior and exterior surface allows to apply the input voltages for the wave generation and to obtain the output voltages. In the following, we will consider one voltage is applied between two electrodes directly facing each other on the interior and exterior surface.

The generation of the traveling wave needs a particular electrode scheme. Indeed, mathematically, a traveling wave is the sum of two standing waves with a π/2 phase shift and a λ/4 displacement between them as shown in equation ( 1), λ being the wavelength of the wave.

ℎ(𝑥, 𝑡) = 𝑈cos(𝜔𝑡) cos ( 2𝜋𝑥 𝜆 ) + 𝑈 sin(𝜔𝑡) sin ( 2𝜋𝑥 𝜆 ) = 𝑈 cos (𝜔𝑡 - 2𝜋𝑥 𝜆 ) (1)
Thus, in order to obtain the traveling wave, we must generate those two standing waves. The generation of a standing wave is done by applying voltage between electrodes. The electrode scheme is shown in Fig. 3. This electrodes scheme allows for the generation of the third mode of resonance shown in Fig. 4 with a minimum of 12 electrodes. The electrodes are separated into three sets. The input electrodes A are responsible for the generation of the first standing wave while electrodes B generate the second wave. The remaining electrodes are outputs. The number and size of outputs determine the number of phases at the secondary side. In this case, we will obtain a four-phase system.

Experimental results of the traveling wave piezoelectric transformer

The designed piezoelectric transformer is shown in Fig. 5 with its PCB interface. This piezoelectric transformer was designed for the validation of the concept of TWPT. Thus, it was not optimized for the particular operation of gate-drive power supply. The piezoelectric material is PZT and the geometric properties are summarized in Table 1.

In Fig. 6 we show the circuit responsible for the generation of the input voltages. A function generator generates the two synchronized input signals with a π/2 phase shift to follow eq. ( 1). Operational amplifiers TL081 in inverting configuration allow to generate the opposite voltages. They are then amplified by linear audio amplifiers LM1876.

We represent in Fig. 7 the output voltages with the electrode command scheme of Fig. 3. The output electrodes are loaded with 2.2 kΩ resistors. The operating frequency is the resonant frequency f = 84 kHz. We see that we obtain the expected multiphase system of voltages electrodes with the traveling wave behavior.

Insulated Gate-Drive Power Supply Circuit Topology

The traveling wave piezoelectric transformer presents the same inherent advantages than classic topologies of piezoelectric transformer for insulated gate-drive power supply. However, the main interest of this topology is to output a multiphase system of voltages at the output with each set of output electrodes insulated between each other. For this particular operation, it presents two main interests. In Fig. 8 we show the overall circuit for the generation of the insulated supplies. The first interest is thus to separate the different phases at the secondary side to supply different gatedrivers. In the example, we have four phases at the output but it is possible to increase either the number of phases available by dividing each output electrode in two or to obtain more instances of the same phases. There is a trade-off between the number of outputs and the power that the piezoelectric transformer is able to supply for a given topology of the device (heigth, diameter, thickness).

The second interest of the circuit proposed lies again in the number of phases available at the end. We choose to separate the four-phase system into two to have two phases for each gate-drive power supply. This separation combined to the proposed topology of two-phases full wave rectifier allows to generate the positive and negative voltages needed for the drive of the transistors. Furthermore, the use of several phases allow limiting the size of the decoupling capacitors at the output of the rectifier.

Experimental results for the TWPT insulated power supply

For the test of the insulated power supply, we choose the same configuration for the generation of the traveling wave as presented in Fig. 3. Thus, we will obtain four output voltages that we separate into two to supply two drivers as represented in solid line in Fig. 8.

Measurement with a resistive load

Firstly, we tested the proposed topology with a resistive load at the output of the rectifier. The aim of this experiment is to determine the power that can supply the piezoelectric transformer to the driver. We set a power consumption of 1 W for each driver and the circuit must provide a bipolar voltage level of +15 V/-15 V. In order to emulate this power consumption, we plug a load resistance RL = 470 Ω in parallel with each output capacitor. The generation of the TWPT input voltages is the same as presented in section 2.2.

In order to reach the desired voltage level, we can adjust either the operating frequency of the piezoelectric transformer or the amplitude of the input voltages. We measured the input power directly at the input of the piezoelectric transformer after the electrode driving circuit (the efficiency of the amplifiers are not included). The output power is directly measured after rectifying. In Fig. 9 we represent the power at stake for different operating frequencies and the input voltage amplitude that allows to reach 15 V at the output.

The output power remains constant at 2 W whereas the input power is 3.3 W corresponding to the design constraints we set. This leads to an overall efficiency of the TWPT and the rectifier of 60 %. It is noticeable that variations of the excitation frequency around the resonance do not influence the power performances of the circuit.

Only the input voltage can be controlled to insure the supply voltage reaches the aimed value. With this experiment, we show that the TWPT can provide the power needed to supply drivers. However, the input currents of gate drivers are not constant with peak during switching and we need to study the dynamic behavior of the insulated power supply.

Measurement on a half-bridge

Consequently, we tested the proposed topology to supply gate-drive circuits themselves responsible for the switching of a MOSFET half-bridge. The are subject to maximum 3.3 kV/µs, and to maximum 2.65 kV/µs during the other phase with no critical influence on the gate voltages. In Fig. 12, we also represent the voltages Vo directly at the output of the transformer. We find the multi-phase system of voltages that we expected. Moreover, compared to Fig. 7 the phases are better balanced, which leads to equivalent supply voltages value. Furthermore, we notice that when changing the power leg duty cycle, the changes on the supply voltage are negligible.

After studying the behavior at a particular frequency, we wanted to test the performances of our TWPT insulated power supply. For this purpose, we measured the power at the input of the piezoelectric transformer and the power at the output of the rectifier supplying the optocoupler. Thus we can directly obtain the efficiency of the circuit TWPT+rectifier. In this experiment, we keep the same operating frequency of 83.5 kHz for the different measurements but we vary the power leg switching frequency of the power stage. For each measurement, the amplitude of the input voltages of the TWPT are set to provide desired supply voltage to the optocoupler. In Fig. 13, we represent the input and output power and the efficiency of the circuit. As expected, when increasing the power leg switching frequency, the power consumption increases. Up to 200 kHz, the efficiency remains constant around 73 % with power consumption under 600 mW for the two gate-drive circuits.

When the switching frequency increases more, the power grows then quickly and the efficiency drops down. Comparing to the results of Fig. 8, we see that the efficiency is very much related to the power provided by the TWPT.

Discussion and Perspectives

The experimental performances of the proposed circuit for insulated power supply are encouraging. Indeed, we tested the circuit for supplying the gatedrives of two transistors in a simple half-bridge. At the frequency tested of 150 kHz, the power consumed by the two drivers is equal to 500 mW. Moreover, we also proved that the circuit can provide up to 2 W to resistive loads. Thus, we can expect that the circuit could supply insulation and power for many more drivers simultaneously, e.g. for multi-level converter applications or a fullbridge. With this TWPT, the four outputs were combined to supply two drivers. However, it is also possible to use these four outputs to supply four drivers depending on the power considerations.

The input/output configuration can also be modified with four inputs and eight outputs as shown in Fig. 8 but the critical aspect is still the power that can provide the TWPT. Nonetheless, a global optimization of the circuit still needs to be done. As we stated in section 3.3, the interest of the TWPT is to provide several phases to allow for polyphaser rectifying. Thus, a reduction of the size of the decoupling capacitance is possible that was not the point of interest here. As stated, the number of output phases can be much higher and thus the decoupling capacitances could be reduced further. Moreover, the transformer was firstly conceived to validate the concept of the traveling wave and not optimized for this application. Thus, there exists strong parasitic capacitances between side-by-side electrodes (up to 110 pF) Even in these conditions, the TWPT insulated power supply performs well thanks probably to the symmetrical configuration of the electrodes used in this application. However, this would need to be reduced. A global design of the transformer is possible to reduce its size and increase the efficiency and power. Different parameters have an influence on the performances: the geometry, e.g. ring instead of cylinder, the piezoelectric material, the electrode scheme, the input/output configuration. A modelling of the TWPT has already been done in [START_REF] Martinez | Modeling of a multi-electrodes traveling-wave piezoelectric transformer[END_REF].

Conclusion

In this paper, we propose the use of the traveling wave piezoelectric transformer as an insulated gate-drive power supply. The circuit consisting of the TWPT and its rectifier has been tested and can supply a bipolar voltage level of +15 V/-15 V to the two drivers of a power half-bridge with switching frequency as high as 500 kHz. In these conditions the converter supply 1.3 W to the drivers but when supplying resistive loads, the power delivered is as high as 2 W.

The generic topology for the use of the TWPT in multi-level converters is also presented. Following the experiment results, we can expect the designed TWPT to supply at least four drivers for switching frequencies lower than 200 kHz. A global optimization of the circuit and especially of the TWPT is still yet to be done to increase the performances of the proposed topology.

Fig. 2 :

 2 Fig. 2: Geometry of the traveling wave piezoelectric transformer

Fig. 3 :Fig. 4 :Fig. 6 :Fig. 7 :

 3467 Fig. 3: Electrode scheme for the generation of the traveling wave

Fig. 5 :

 5 Fig. 5: TWPT with its interface PCB

Fig. 8 :

 8 Fig. 8: Topology of the generic insulated voltage supply for the gate-driver.

Fig. 9 :

 9 Fig. 9: Input and output power and input voltage amplitude of the TWPT + rectifier circuit.

Fig. 11 :

 11 Fig. 11: Waveforms of the output voltages of the TWPT

Fig. 12 :Fig. 13 :

 1213 Fig. 12: Waveforms of the output voltages of the TWPT

Table 1 :

 1 Geometrical parameters of the TWPT

	Parameter	Value Units	Notation
	External Radius	20	mm	𝑅 𝑒
	Internal Radius	19	mm	𝑅 𝑖
	Width	10	mm	𝑤
	Thickness	1	mm	ℎ 𝑝