Julien Weckbrodt

Nicolas Ginot

Christophe Batard

Thanh Long Le

Stéphane Azzopardi

A Bidirectional Communicating Power Supply circuit for Smart Gate Driver boards

Keywords: Communication channel, driver circuits, electrical isolation, power system monitoring, isolated power supply, SiC MOSFET

In power circuits, the gate drivers are required to provide an optimal and safe switching of power semiconductor devices. Nowadays, the gate driver boards include more and more features such as short-circuit detection, soft-shutdown, temperature sensing, on-state voltage monitoring… Research works are in progress on the integration of on-line monitoring features for a predictive maintenance. The instrumentation of the gate drive system supposes the integration of a communication system to transmit the monitoring data. In high power designs, a galvanic isolation is mandatory on the gate driver board. The parasitic capacitance seen on the isolation barrier is critical in these designs as it can lead to the circulation of common mode currents during the switching. Adding extra optocouplers or transformers on the isolation barrier is therefore risky due to ElectroMagnetic Interference (EMI) constraints. In this paper, a new bidirectional data transmission method is proposed for gate drivers used for driving 1.2kV SiC power MOSFETs. The proposed method enables the energy transmission and a bidirectional data exchange on a single power supply transformer. Experimental results are provided demonstrating 1Mb/s for TxD and 16kb/s for RxD. The targeted application is the health monitoring of SiC power MOSFETs using the gate driver board.

I. INTRODUCTION

Silicon Carbide (SiC) power transistors such as SiC power Metal Oxide Semiconductor Field Effect Transistor (MOSFETs) are more and more used in power converters. These components are excellent candidates to replace the Silicon-based devices in power circuits. The interesting properties of SiC power components enables operation at higher frequency and higher temperature. Indeed, compared to Silicon devices, the fast switching of SiC MOSFET reduces considerably the switching losses. Their performances in high temperature conditions also enable a higher power density for energy converters. Many research works on robustness have been carried out since the emergence of SiC-based power transistors. Recent studies have pointed out ageing indicators which could be used for health monitoring purposes such as the evolution of the gate leakage current [START_REF] Nguyen | Effect of short circuit aging on safe operating area of SiC MOSFET[END_REF][START_REF] Nguyen | Investigation on Reliability of SiC MOSFET Under Long-Term Extreme Operating Conditions[END_REF][START_REF] Othman | Robustness of 1.2 kV SiC MOSFET devices[END_REF][START_REF] Ouaida | Gate oxide Degradation of SiC MOSFET in Switching conditions[END_REF][START_REF] Wang | Temperature-dependent short-circuit capability of Silicon Carbide power MOSFETs[END_REF] or the on-state resistance [START_REF] Nguyen | Effect of short circuit aging on safe operating area of SiC MOSFET[END_REF][START_REF] Nguyen | Investigation on Reliability of SiC MOSFET Under Long-Term Extreme Operating Conditions[END_REF][START_REF] Othman | Robustness of 1.2 kV SiC MOSFET devices[END_REF][START_REF] Ouaida | Gate oxide Degradation of SiC MOSFET in Switching conditions[END_REF], [START_REF] Dusmez | Remaining Useful Lifetime Estimation for Degraded Power MOSFETs Under Cyclic Thermal Stress[END_REF]. The on-line monitoring of these electrical parameters requires measurement circuits and a data exchange on the gate drive system. Implementing such methods could help to prevent damages by detecting ageing before failures. The targeted application is the predictive maintenance for high reliability power circuits in aeronautical environments.

In power electronics designs, the gate driver provides an optimal command of the power semiconductor device using an electrically isolated circuit. For safety reasons, this electric isolation is mandatory in high voltage circuits. As a result, the driver board is divided in two parts: the primary circuit connected to the control unit and the secondary circuit close to the power semiconductor device. The ground potential on the secondary circuit is fixed by the source/emitter voltage of the power component (Kelvin connection). The galvanic isolation represents a major constraint for the integration of intelligent circuits on the gate driver board. The new SiC power semiconductor devices can reduce the energy losses during the switching as it can switch faster than Silicon ones. As a result, electromagnetic interferences are even more restrictive in SiC gate driver designs due to high dv/dt during the turn-on and the turn-off.

Although optocouplers or optical fibers can be used to transmit switching orders, transformers are always used in gate drive topologies, at least to provide supply voltage to the secondary circuit. In conventional gate driver boards, the only information transmitted across the isolation barrier is the switching orders (PWM) and an error signal, in the event of a fault detection [START_REF] Ginot | MOSFET et IGBT : circuits de commande, sécurisation et protection du composant à semi-conducteur[END_REF][START_REF] Herzer | New Gate Driver Solutions for Modern Power Devices and Topologies[END_REF][START_REF] Kumar | An Intelligent Medium Voltage Gate Driver with Enhanced Short Circuit Protection Scheme for 10kV 4H-SiC MOSFETs[END_REF][START_REF] Anurag | A Gate Driver Design for Medium Voltage Silicon Carbide Power Devices with High dv/dt[END_REF]. Nowadays, new "smart gate drivers" enable data exchange by the addition of transformers dedicated to communication across the electrical isolation [START_REF] Weckbrodt | Short Pulse Transmission for SiC Communicating Gate Driver Under High dv/dt[END_REF][START_REF] Bouguet | Communicating Gate Driver for SiC MOSFET[END_REF][13][START_REF][END_REF]. Adding extra transformers across the isolation is quite cumbersome and it can lead to the circulation of parasitic common mode currents as they introduce extra capacitances between the primary and the secondary circuit. The common mode current is a well-known issue in gate drive topologies. Several research works proposed optimizations to reduce this parasitic current [START_REF] Anurag | A Gate Driver Design for Medium Voltage Silicon Carbide Power Devices with High dv/dt[END_REF][START_REF] Weckbrodt | Short Pulse Transmission for SiC Communicating Gate Driver Under High dv/dt[END_REF][START_REF] Friebe | High-side driver supply with reduced coupling capacitance[END_REF][START_REF] Wang | Gate Driver Design for 1.7kV SiC MOSFET Module with Rogowski Current Sensor for Shortcircuit Protection[END_REF][START_REF] Nguyen | and Analysis of an Innovative Gate Driver and Power Supplies Architecture for HF Power Devices with High dv/dt[END_REF][START_REF] Nguyen | Gate Driver Supply Architectures for Common Mode Conducted EMI Reduction in Series Connection of Multiple Power Devices[END_REF]. In [START_REF] Friebe | High-side driver supply with reduced coupling capacitance[END_REF], a supply circuit is studied to reduce the coupling capacitance using a coupled filter inductor on the power circuit. Cascaded gate driver supply architectures were analyzed in [START_REF] Nguyen | and Analysis of an Innovative Gate Driver and Power Supplies Architecture for HF Power Devices with High dv/dt[END_REF][START_REF] Nguyen | Gate Driver Supply Architectures for Common Mode Conducted EMI Reduction in Series Connection of Multiple Power Devices[END_REF]. Architectures were proposed in which the power supply circuits are pooled in order to reduce the resulting common mode current under very high

Manuscript received July 24, 2019… … … … … … … … …
A c c e p t e d M a n u s c r i p t dv/dt. This solution treats the problem of EMI interference at the converter level considering several power transistors. As explained in [START_REF] Friebe | High-side driver supply with reduced coupling capacitance[END_REF][START_REF] Wang | Gate Driver Design for 1.7kV SiC MOSFET Module with Rogowski Current Sensor for Shortcircuit Protection[END_REF][START_REF] Nguyen | and Analysis of an Innovative Gate Driver and Power Supplies Architecture for HF Power Devices with High dv/dt[END_REF][START_REF] Nguyen | Gate Driver Supply Architectures for Common Mode Conducted EMI Reduction in Series Connection of Multiple Power Devices[END_REF], the electromagnetic perturbations are due to the high dv/dt applied between the primary and the secondary ground potentials during the switching of the power device.

The interest of communication on power circuitry is not new and many works have been carried out in the field of Power-Line Communication (PLC) [START_REF] Stefanutti | Power Line Communication in Digitally Controlled DC-DC Converters Using Switching Frequency Modulation[END_REF][START_REF] Jousse | Power Line Communication Management of Battery Energy Storage in a Small-Scale Autonomous Photovoltaic System[END_REF][START_REF] Yigit | Power line communication technologies for smart grid applications: A review of advances and challenges[END_REF]. However, such methods of communication are not applicable for highly constrained isolated designs confronted to high dv/dt due to the proximity of the switching cells. In this context, the addition of communication features within the gate driver board with no significant impact on the common mode current represents a real challenge. Yang et al. [START_REF] Yang | An Isolated Full-Bridge DC-DC Converter With 1-MHz Bidirectional Communication Channel[END_REF] reported an isolated full-bridge DC-DC converter with a 1MHz bidirectional communication channel. Unfortunately, no test was performed to check the dv/dt immunity since the operating principle and the targeted application are different from the presented method.

In this paper, power supply structures based on the DC-DC Push-Pull operating principle are described in the following section. A method for DATA exchange using the power supply circuit is proposed in section III. The operating principle and simulations using SPICE models are detailed. Experimental setup and waveforms are then provided in order to check the feasibility of the proposed solution. Finally, the designed circuit is confronted with high dv/dt to test the communication system in a severe environment. Experimental waveforms corresponding to a 400V/200A switching in a DC-DC Buck converter are also provided.

II. CONVENTIONAL POWER SUPPLY TOPOLOGIES USED IN GATE DRIVER BOARDS

In the case of gate drivers used to drive Insulated Gate Bipolar Transistors (IGBTs), a symmetrical supply voltage is often required (+15V/-15V). Since the new SiC power MOSFETs generally require a +20V/-5V gate-source voltage for optimal switching, a 25V power supply voltage is required for driving such components. There are two main solutions for providing the supply voltage: a bootstrap circuit or an isolated DC/DC converter. Power supply circuit based on bootstrap circuit is generally chosen in low-cost or low-voltage applications. In most cases, the isolated DC/DC converters are preferred as an additional isolation is often required between the high side (HS) transistor and low side (LS) transistor in a half-bridge configuration. The isolated DC/DC converters used in gate drivers are generally realized by a Push-Pull converter or sometimes by a Flyback topology [START_REF] Ginot | MOSFET et IGBT : circuits de commande, sécurisation et protection du composant à semi-conducteur[END_REF][START_REF] Anurag | A Gate Driver Design for Medium Voltage Silicon Carbide Power Devices with High dv/dt[END_REF][START_REF] Volke | IGBT Modules. Technologies, Driver and Application[END_REF][START_REF] Kusaka | Galvanic isolation system for multiple gate drivers with inductive power transfer -Drive of three-phase inverter[END_REF]. Gate drivers using an optical power transfer have also been studied [START_REF] Rouger | CMOS SOI gate driver with integrated optical supply and optical driving for fast power transistors[END_REF][START_REF] Zhang | A 15 kV SiC MOSFET gate drive with power over fiber based isolated power supply and comprehensive protection functions[END_REF]. Although these methods provide an optimal commonmode rejection, the low efficiency of the photoelectric transducers makes them inadequate for power modules command (power consumption >1W). In this work, only the Push-Pull DC/DC converters used as a power supply circuit in driver boards will be considered.

V IN 0V V H -V L 0V Reg. V H -V L V IN 0V V IN V H -V L V SEC V IN 0V Ref. V H -V L
The classical structure of Push-Pull converters is shown in Fig. 1. The transistors at primary side are alternately switched on and off, a short deadtime is observed in order to avoid short circuits. The particularity of the Push-Pull converter is that the current is drawn from the line during both halves of the switching cycle. The stability of the output voltage is typically ensured by a feedback using an optocoupler. However, as explained before, the addition of elements over the isolation barrier is problematic in gate drive boards. Consequently, openloop strucutres are always preferred for power supplies in the gate drivers boards. The power consumption in gate driver boards is relatively low (<10W) in comparison with the driven power circuit (several kW). In addition, this low energy transfer allows circuit simplifications as efficiency is not a critical parameter in these designs. In Fig. 2, a state of the art of the power supply circuits used in gate driver boards is presented. These low-power DC/DC converters in open loop configuration are derived from the Push-Pull converter topology. The main characteristics of the driver boards mentioned in Fig. 2 are described in Table I. In the rest of the paper, the circuit presented in Fig. 2 (d) was chosen for demonstrating the communication principle. In this circuit, a square signal with fixed duty cycle is used to apply ±15V on the primary windings.

The secondary voltage VSEC periodically varies from +30V to -30V. On the secondary side, the output voltage VOUT corresponds to the double of the input voltage (transformer turns ratio 2:1) reduced by the diodes voltage drop.

III. PROPOSED STRUCTURE FOR DATA EXCHANGE USING THE ISOLATED POWER SUPPLY CIRCUIT

A. Operating principle

Since the addition of extra transformers or optocouplers decreases the quality of the isolation barrier, the method proposed in the present paper enables energy transfer and DATA exchange on the same transformer. As explained in Fig. 3, the isolated power supply circuit is used as a communication channel between the primary circuit and the secondary circuit. The operation can be divided in two steps: phase A and phase B.

During the first period of time TA, the TxD signal is transmitted using a Manchester code applied to the command signal Cmd instead of the square signal described in section II. The decoding of this signal can be realized at the secondary side using a XOR logic gate. During this period, the energy and the TxD signal are both transmitted through the transformer. A RCseries snubber circuit was implemented in order to optimize the switching of the transistors Q1 and Q3. Due to the Manchester coding, the operating frequency of the proposed DC/DC converter is not fixed. The frequency spectrum is spread between 500kHz and 1MHz.

During the phase B, the energy transfer through the transformer is stopped during a predetermined time (here TB=11µs). At this moment, the transformer is demagnetized by switching OFF the transistors Q1 and Q3 at the same time. Oscillations may occur during the demagnetizing process. These oscillations can be reduced by the addition of resistive loads connected to the primary windings as shown in Fig. 5. These loads are disabled during the phase A (signal En). They also help to transmit pulses from the secondary winding to the primary ones. The transformer is then available for data transmission from the secondary side to the primary side (RxD). At this moment, the power supply transformer operates as a pulse transformer: a positive pulse corresponds to a high logic level request and a negative pulse corresponds to a low logic level request. The typical signals are described in Fig. 4. As shown in Fig. 6 (b), the RxD pulses are generated by the transistors Q5 to Q8 which were added on the diode bridge circuit (phase B). The transistors Q5 and Q6 are P-channel MOSFETs so their commands require level shifter circuits. An example of level shifter topology is presented in Fig. 6 (b).

Concerning the timing constraints, the pulses width was fixed at tpulse=200ns considering the supply transformer design. A bit time of tbit=500ns was therefore implemented for RxD DATA in order to preserve the integrity of the pulses. Based on simulations, a 2µs timeout was implemented in order to avoid transmission errors before the beginning of the RxD pulses generation. An additional timeout of 1µs was observed at the end of the phase B in order to disconnect the primary load before the starting of the power converter. The cycle (A+B) is then repeated every TA+TB=1ms in our example. Regarding the timing constraints presented in Fig. 4, a bit rate of maximum 1Mb/s for TxD and 16kb/s for RxD can be achieved. Indeed, the Manchester code was designed to transmit 1bit/µs which correspond to a theoretical bit rate of 1Mb/s when TB << TA. The RxD bit rate is dependent on the TB value as described in Fig. 9. In the case of TB=11µs, the RxD bit rate is 16kbit/s corresponding to 16bits/cycle with a 2+1µs timeout between each phase. The health monitoring is a long process so monitoring data does not require a high speed transmission as measurements are not performed at every cycle.

The proposed method supposes the integration of programmable circuits on the gate driver such as FPGA circuits for data management. Considering the timing constraints, a minimal clock frequency of 10MHz is required for FPGA implementation. An Universal Asynchronous Receiver Transmitter (UART) protocol should be implemented for complex DATA exchange between the primary circuit and the secondary circuit of the gate driver.

B. Simulation using SPICE models

The circuit presented in Fig. 7 was simulated using SPICE models for active components and a transformer behavioral model. The references of the components used and the associated SPICE models are given in the table presented in Fig. 7. The supply transformer was realized by a planar transformer integrated in a 6-layers board.

The simulations presented in Fig. 8 suggest an extra consumption due to the RxD pulses during the demagnetizing period. This effect is due to the ±15V applied on the primary load resistances. The energy consumed by a single pulse E1 pulse can be calculated using [START_REF] Nguyen | Effect of short circuit aging on safe operating area of SiC MOSFET[END_REF].

𝐸 1 𝑝𝑢𝑙𝑠𝑒 = 𝑉 𝐼𝑁 2 𝑅 𝐿,𝑃 • 𝑡 𝑝𝑢𝑙𝑠𝑒 (1)
where RL,P is the primary load resistance. Since the positive pulses are dissipated in the upper load resistance and the negative ones are dissipated in the lower load resistance, the resulting extra power consumption 𝑃 𝑅𝑋𝐷 during TB can be expressed as follows:

𝑃 𝑅𝑋𝐷 = 𝑛 • 𝑉 𝐼𝑁 2 𝑅 𝐿,𝑃 • 𝑡 𝑝𝑢𝑙𝑠𝑒 𝑇 𝐵 ( 2
)
where n is the number of RxD pulses, corresponding to the number of changes in the logic levels (0→1 or 1→0). In the worst case, n=(TB-3µs)/tbit=16 which leads to an additional power consumption during TB of 545mW considering the timing constraints proposed in section II. A. As explained before, the demagnetizing oscillations can be reduced depending on the primary load resistance seen by the primary windings of the transformer. The influence of the primary load resistance value on the demagnetizing is also

7 Q 8 Q 5 Q 6 V IN V OUT ' Cmd V OUT-REG ' C OUT [1:2] V SEC ' load En
RxD pulses generation Manchester coding (TxD) presented in Fig. 8. A low RL,P resistance can reduce the demagnetizing oscillations but it would increase the power consumption due to the RxD pulses. Based on simulations, the primary load resistance was chosen RL,P=120Ω.

Q 3 Q 4 V IN Q 1 V IN Q 2 DC/
The main inconvenient of the proposed method is the output voltage drop during the phase B due to the complete demagnetization of the supply transformer. The duration of this period is critical and should be reduced as much as possible. Fortunately, the voltage drop can be compensated by adding extra output capacitors COUT as shown in Fig. 9. As expressed in (3), the observed variation ΔVOUT on the output voltage VOUT is also dependant from the total power consumption P.

𝛥𝑉 𝑂𝑈𝑇 = 𝑉 𝑂𝑈𝑇 (𝑒 - 𝑇 𝐵 𝑅 𝐿𝑂𝐴𝐷 •𝐶 𝑂𝑈𝑇 -1) ≈ - 𝑃 • 𝑇 𝐵 𝑉 𝑂𝑈𝑇 • 𝐶 𝑂𝑈𝑇 (3)
RLOAD is the equivalent resistance seen at the output. The Fig. 9 illustrates the compromise between the RxD bit rate and the dropout voltage at the output.

III. EXPERIMENTAL RESULTS

A. DATA exchange

A 6-layers Printed Circuit Board (PCB) was designed to check the viability of the proposed method. The duration of the phase B was fixed at TB=11µs in order to transmit 2 Bytes using a 500ns bit time (=8µs) after the 2µs-deadtime. Once the transmission is complete, another 1µs-deadtime was observed in order to prevent any conflict.

The transformer used is a planar transformer with 5 turns in the primary windings and 10 turns in the secondary winding. As shown in Fig. 10, two planar transformers were integrated in a 6-layers board (High Side and Low side) corresponding to a Half-Bridge application. The planar transformer is a shell form in which the magnetic core is realized by a E-shaped ferrite core associated to a 3F3 ferromagnetic material. The windings of the transformer are located on the internal layers of the PCB. The electric isolation is realized by a 500µm epoxylayer, which guarantees a reliable isolation between primary and secondary circuits. The resulting parasitic common mode current is relatively low since the coupling capacitor of the

Q 5 D 1 Q 7 D 3 V IN V IN En LOAD V OUT ' Cmd ' V OUT-REG ' = 25V C OUT [1:2] V SEC ' TxD RxD En Manchester coding (TxD) Q 3 Q 4 V IN Q 1 V IN Q 2 LPF LPF LPF Manchester decoding 0V 0V Q 6 D 2 Q 8 D 4 En Pulses decoding DC/DC BUCK TxD A Dead time Q 5 D 1 Q 7 D 3 V IN V IN En LOAD V OUT ' Cmd ' V OUT-REG ' = 25V C OUT [1:2] V SEC ' TxD RxD En Q 3 Q 4 V IN Q 1 V IN Q 2 LPF LPF LPF Manchester decoding 0V 0V Q 6 D 2 Q 8 D 4
Level shifter Q 5 Level shifter Q 6

RxD pulses generation power transformer is only 8pF (characterization at 1MHz using a Vector Network Analyzer). The design of the planar transformer used will not be more detailed in the present paper because any type of transformer can be used for the proposed method.

For experimental needs, data frames were implemented on two FPGA boards using VHDL programming. Due to the FPGA board, the logic levels are in CMOS 3.3V compatibility.

The experimental waveforms are shown in Fig. 11 demonstrating the data exchange using the proposed circuit. A low logic level is applied during 11µs on the 'Enable' signal every 1ms (f=1kHz) which opens Q1 and Q3 and enables the primary load resistance. VSEC represents the differential voltage at the secondary winding of the transformer as described in Fig. 5 and6. On the Fig. 11, the TxD and RxD signals represent the data after decoding at the primary side (RxD) and at the secondary side (TxD). A maximum bit rate of 1Mb/s for TxD and 16kb/s for RxD was observed. These characteristics can be The same result could be obtained with Q7 and a logic inverter. The synthetized clock signal is obtained by synchronization with the first rising edge of the TxD signal (phase A).

An output voltage dropout of ΔVOUT=-0.8V can be observed on the Fig. 11, which corresponds to VOUT=27.5V at the end of the phase B. This value is highly dependent on the circuit consumption. In this case, a 330Ω-load resistance (RLOAD) was used to simulate a static power consumption of 2.5W. The output voltage drop depends on 4 parameters: the duration of the demagnetized period, the power consumption of the circuit, the value of the capacitor COUT and the number of changes in the RxD logic levels as explained in the previous section. The circuit was tested with a nominal capacitance of 14.1µF for the output capacitor. However, a voltage derating behavior was observed on this capacitor. In the board presented in Fig. 10, the output capacitor consists of 3 ceramic capacitors of 4.7µF (=14.1µF) in X7R material (MC1206B475K500CT).

Considering that the capacitance depends on the voltage applied, the equivalent capacitor at VOUT=28.8V was about 2µF and the observed ΔVOUT was much more than expected with the nominal value (14.1µF). The voltage drop could be reduced by the use of NP0/C0G capacitors or the increase of the nominal voltage. In this design, a 1206 package with 50V rated voltage has been chosen in order to reduce the bank capacitors size.

A post-regulation is then realized by a Buck converter which can regulate the supply voltage at 25V as long as VOUT is greater than 25.7V. The demagnetized duration and the capacitor COUT

B. High dv/dt susceptibility tests

The gate driver boards are always implemented as close as possible to the power modules in order to guarantee a correct switching of the power device. Indeed, the parasitic inductances of wires are sensitive to the common-mode currents. The power circuit is often composed of several power devices in series or parallel. In a half-bridge configuration, two power devices are associated in series (HS and LS). During a fast switching of the power component, a high dv/dt can be observed in the switch node. In the gate driver boards, the secondary ground potential is imposed by the source voltage which is a floating potential as the source voltage of the HS component varies when the LS power device is used. As a result, the gate drivers are submitted to a severe environment with high EMI constraints.

In order to test the dv/dt susceptibility, high voltage pulsed signals were applied between the primary ground and the floating secondary ground [START_REF] Weckbrodt | Short Pulse Transmission for SiC Communicating Gate Driver Under High dv/dt[END_REF], as shown in Fig. 12. In this experiment, a battery-powered oscilloscope was used with caution as high voltage transients were applied on the secondary ground potential. The TxD signal was monitored during this process in order to detect the perturbations on the internal signals. The monitored signal is taken at the input of a Schmitt triggered logic gate. The Schmitt triggers are very important in this design as it can provide a reliable digital signal at the output using the hysteresis principle. The tests were performed up to ±125kV/µs applied across the isolation barrier. The signals presented in Fig. 13 were taken at the secondary side using a RF probe to minimize the noises due to the ground loop. In this configuration, the oscilloscope must be referred at a floating potential due to the fast pulses of 1.5kV applied on the isolation barrier. The results presented in Fig. 13 demonstrate the reliability of the proposed DATA communication system in the worst case. The observed noise on the signals is the addition of the real perturbation and the noise due to the probe. Since the EMI noises are monitored in the worst case of study, the threshold voltages of the Schmitt-triggered logic gates were used to verify the integrity of the TxD signal when the EMI noise occurs.

C. Implementation in a driver board design under real switching conditions

As described in Fig. 14, a gate driver board was connected to a 1.2kV SiC MOSFET module (Cree CAS300M12BM2) in a double pulse test bench. The proposed solution was implemented in a smart driver board which integrates Spartan-7 FPGA boards on the primary and secondary circuits, as shown in Fig. 15 (b). This circuit was tested in a DC-DC Buck configuration using an inductance of 700µH connected to the busbar. An external gate resistance of 2.4Ω was implemented on the gate driver board presented in Fig. 15. This board was specifically designed for health monitoring and integrates the proposed method as a communication channel in addition to conventional features (galvanic isolation, short-circuit detection, soft shut-down…). The design of this board will not be more detailed in the present paper.

In the experimental setup, a differential probe and a Rogowski coil were used to monitor the drain-source voltage and the drain current of the power SiC MOSFET. As shown in Fig. 16, a 400V/200A switching did not affect the RxD signal at the primary side as no undesirable logic level change occurred during the switching. The resulting dv/dt is about 15kV/µs which correspond to an optimal switching at 400V considering the switching characteristics provided in the CAS300M12BM2 datasheet (rise time of 68ns and fall time of 43ns).

IV. DISCUSSION AND PERSPECTIVES

As mentioned in the introduction, the targeted application is health monitoring for power SiC MOSFET transistors. In this case, the RxD data are monitoring parameters that can be measured using the secondary circuit of a smart driver board such as the on-state voltage, the gate leakage currents, temperature values or others ageing indicators… The RxD data could also be used for fault transmission by sending a more detailed error message to the primary side. It could even replace the traditional error pulse transmission but this solution is not recommended as the latency of the proposed communication method is not guaranteed. Another application is the reparametrizing of the gate driver in real time which could be achieved by exploiting the TxD flux. For example, switching slope control, blanking time setting or gate-source voltage variation could be realized using the proposed method. Other applications such as the implementation of sensors on high voltage lines could also be addressed.

Nowadays, gate drivers integrate more and more features and FPGA/CPLD are already integrated on the primary circuit in some designs. The addition of measurement and communicating features on the gate drivers increases the complexity, the cost and the size of the board which could be a major constraint to the development of such technology. However, the Fig. 15 demonstrates that it is possible to integrate the proposed solution in a 120x70mm² design for driving a 62mm power module. Moreover, the FPGA integration is the first step in the prototyping process as most of the circuitry presented in the Fig. 6 could be integrated in mixed analog/digital chip designs.

V. CONCLUSION

A new structure for bidirectional DATA communication using a low-power supply circuit was proposed and investigated. The presented results show the relevance of the proposed method in highly constraints gate driver designs. The proposed structure was simulated and experimental results are provided. Careful consideration should be given to the choice of the output capacitors throughout the implementation of this topology. In the implemented solution, bit rates of 1Mb/s for TxD and 16kb/s for RxD were demonstrated. Fast transient voltages were also applied on the designed board in order to verify its dv/dt immunity up to 125kV/µs. The method was also implemented in a smart gate driver board and confronted to a 400V/200A switching using a 1.2kV SiC module. The proposed solution requires the integration of digital circuits on the gate driver board but offers new perspectives for on-line monitoring using the gate drivers in power electronics. A specific serial protocol based on UART can be implemented for complex

Fig. 2 .

 2 Fig. 2. Open loop Push-Pull converters with fixed duty cycle -State of the art on the power supply circuits in commercially available gate driver boards: (a) Infineon 2ED300C17; (b) Semikron SkyperPro32; (c) Cree PT62SCMD12; (d) Power Integration 2SC0650.

Fig. 1 .

 1 Fig. 1. Isolated Push-Pull DC-DC converter with regulation loop

Fig. 4 .Fig. 3 .

 43 Fig. 4. Proposed principle based on the topology presented in Fig. 2 (d)

Fig. 5 .

 5 Fig. 5. Proposed communicating power supply circuit for gate driver application

Fig. 6 .

 6 Fig. 6. Proposed communicating power supply circuit: (a) phase A and (b) phase B

Fig. 8 .Fig. 7 .Fig. 9 .

 879 Fig. 8. Simulations using SPICE models (VOUT=28.8V)

Fig. 11 .Fig. 12 .Fig. 13 .

 111213 Fig. 11. Experimental waveforms

Fig. 14 .Fig. 16 .Fig. 15 .

 141615 Fig. 14. Experimental setup for evaluation under real switching conditions

A c c e

  p t e d M a n u s c r i p t

DATA communication across the isolation barrier of the gate driver boards. Due to the complexity and the cost of the health monitoring using the gate driver, this technology might make sense only for high power converters (>50kW) in which the reliability is the priority.


Tosi

B Rousseau

) A Raponi

M Ciarniello

E Ammannito

F G Carrozzo

M C De Sanctis

S Fonte

A Frigeri

F Tosi

Correction of the VIR-visible data set from the Dawn mission

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

I. INTRODUCTION

The targets of the NASA Dawn mission were the asteroid Vesta and the dwarf planet Ceres 1 . In September 2012, after one year of observations, the spacecraft left Vesta and started the exploration of Ceres in 2015, ending at the end of October 2018. The scientific payload of Dawn was made of three instruments designed to characterize the surface: the Visible and InfraRed mapping spectrometer 2 (VIR), the Framing Camera 3 (FC) and the Gamma Ray and Neutron Detector 4 (GRaND).

This study is focused on the correction of the data acquired by VIR, which is composed of two spectral channels: the visible channel (VIS), which is a twodimensional Charged Coupled Device (CCD) covering the wavelength range 0.25-1.07 µm and the infrared channel (IR), which is a two-dimensional HgCdTe array covering the range 1.02-5.09 µm with a nominal spectral sampling of 1.8 nm/band (432 bands) and 9.8 nm/band (432 bands) respectively. VIR channels may work together or independently (mainly according to the scientific planning), sharing the same optical path while using two different sensors close to each other 2 . However, while the CCD sensor of the VIS channel works at a temperature ranging from 165K to 195K, the HgCdTe array of the IR channel has to work at a stable but adjustable temperature close to 80-85K during the acquisitions. The data produced by VIR are called hyperspectral images a) batiste.rousseau@inaf.it (or cubes) due to their structure: two spatial dimensions and one spectral dimension.

In the following Section II we present the main characteristics of the VIR visible data set during the journey of Dawn around Ceres. Section III describes the VIS and the IR sensor temperatures behavior during the VIR acquisitions and how they affect the data. In Section IV, we present the VIR Arcturus observation and we address the question of the strategy adopted to define the correction as well as its application on the data. In Section V, results of the correction are reported and the conclusions are presented in Section VI.

II. THE VIR DATA SET AT CERES

The observations of Vesta and Ceres are grouped in different phases depending on the altitude of the spacecraft and/or of the scientific goals. Table I describes the timeline and some characteristics of the ten mission phases during the Dawn mission at Ceres and for which visible data were acquired. Here we briefly describe the different mission phases in a chronological order. All the resolutions provided corresponds to across-track resolutions, which can differ to the along-track resolutions because of the exposure time and the spacecraft movement.

The CSA (Ceres Science Approach) phase corresponds to the Ceres approach and offers a full coverage of the surface at low resolution. The CSR (Ceres Science RC3 -Rotational Characterization 3) phase, aiming at study the rotation of Ceres, provides a complete coverage of the surface at intermediate resolution. CTS (Ceres Trans-TABLE I. Mission phases of Dawn at Ceres, chronologically sorted and during which VIR visible data were acquired. The fourth column presents the number of cubes processed and available in each phase. Differences are due to the occurrence of sky observation or corrupted data. The approximate minimum and maximum across-track resolutions are provided in the fifth column. The range of temperatures experienced by the visible and the infrared channel are reported in columns 6 and 7. The last column reports the correction factor used to correct the data set (see section IV C). Asterisks in the first column indicate which phases have been used to compute a correction factor.

Mission Phase phase, with a resolution of 2000 m/pixel and mostly devoted to GRaND acquisitions. This was followed by the CXO (Ceres Opposition) phase, with a lower resolution, that allowed the observation of the opposition effect on the Ceres surface [START_REF] Ciarniello | Lunar and Planetary Science Conference, Lunar and Planetary Science Conference[END_REF][START_REF] Ciarniello | [END_REF] . Finally, VIR acquired the last VIS spectra during C2E (Ceres X2 Elliptical), the second extended mission phase. In that final phase, data with a resolution ranging from 230 m/pixel to 15m/pixel were acquired.

The data acquired by VIR are converted through the calibration pipeline 2,7 from raw digital numbers (DN) to physical units of radiance. Then, they are converted in radiance factor following:

I /F = π × d 2 × I F (1)
Where I is the calibrated radiance in units of W.m -2 .µm -1 .sr -1 , F is the solar flux at 1 astronomical unit and d is the heliocentric distance of Ceres at the time of the acquisitions.

The data used in this study are available on the PDS archive and corresponds to the LEVEL 1B version of the VIR data (https://sbn.psi.edu/pds/resource/dawn/ dwncvirL1.html). A multiplicative factor related to the ground observation of Ceres and Vesta as well as a correction matrix is applied to all the data used here in order to correct the original deviation of the spectra and to reduce the spectral artifacts [START_REF] Carrozzo | [END_REF] . For the purpose of this investigation, the data are also photometrically corrected 9 to minimize the effects caused by the variations of the observation geometry.

III. INSTRUMENTAL EFFECTS ON THE VIR VIS DATA

The visible data acquired at Ceres were used to study the characteristics of the surface using the map of the albedo distribution, the spectral slopes and other spectral parameters. However, in the data acquired during the different mission phases unexpected variations in spectral slopes and overall spectral shape occur independently of the scene observed, or the observational conditions in terms of geometrical factors, illumination conditions or temperature of the surface.

This behavior could have an instrument cause. Here we investigate the reasons of the unexpected changes in the VIS spectra in order to correct the data set.

A. The visible detector temperature dependency on the visible data

During a mission phase, the VIR observations are organized in sequences composed of hyperspectral cubes acquired in succession, without interruption. The acquisition schemes depend on the mission phase, thus mainly on the spacecraft orbit. Normally, during a sequence of acquisitions, the CCD detector of the VIS channel operates for hours consecutively. This effort leads to a temperature increase, while the cooling down is only possible when the detector is not operative, i.e. between two sequences. The range of temperatures experienced by the VIS sensor varies from 168K to 195K in the overall mission phases but may experience a smaller range within a single phase (see Table I). Panel A of the Figure 1 shows the map of the VIS sensor temperatures (VIS temperature hereafter) of the CSH phase providing an example of the typical effects experienced by the detector during a series of observation sequences. Along the first sequence of six cubes, numbered from 1 to 6 in black in Figure 1, the VIS temperature increases monotonically (also represented in the panel B of the Figure 1). When a new sequence starts after several hours (red arrow and numbering, panel A Figure 1), the VIS sensor has cooled down and the temperature increases until the last cube of the sequence.

It has been observed that the changes of the VIS temperature has a strong impact on the global spectral slope. Figure 2 represents the normalized median spectra of the CSH phase at different VIS temperatures. The spectral slope is regularly evolving from strongly negative to less negative or flatter while the VIS temperature is ranging from 168K to 184K respectively. In the CSH case, the variation of the radiance factor at 950 nm (after normalization at 550 nm) reaches 11% between 168K and 184K. It represents 0.68%/K, which is close to the average value (0.67%/K ± 0.04) observed for the most representative mission phases of the VIR VIS data set (CSL, CSR, CXL and CSH). Such spectral variations -presented here in CSH but also observed during the other mission phases -cannot be linked to the spatial distributions of these observations or to the diversity of composition across the Ceres' surface [9][10][11][12][13] .

B. The infrared channel temperature effect on the visible data

The VIS and IR channels composing the VIR instrument are decoupled and may observe independently, depending on the science objectives. During its operation, the IR channel is cooled down actively by a crycooler at a stable temperature close to 80-85K 2 . On the contrary, the VIS channel is cooled down passively thanks to a

Normalised I/F 184K 183K 182K 181K 180K 179K 178K 177K 176K 175K 174K 173K 172K 171K 170K 169K 168K FIG. 2.
Median spectra of the CSH mission phase for the different VIS temperatures. The spectra are normalized at 550 nm. The reference spectrum (see Section IV B) is indicated in blue.

radiator and operates at higher temperatures 2 , typically from 165K to 195K as indicated in Table I. When the IR channel is not in use, the cryocooler is switched off in order to preserve it. In that case, the IR temperature, as measured by the platinum resistors placed on the back side of the detector 2 , increases to reach progressively an equilibrium temperature around 175K (see also Table I).

As illustrated by Figure 3, we noticed different spec-tral behaviors for different mission phases (CSH and CSL, blue and red spectra of Figure 3). The difference between the two spectral shapes cannot be explained by local variability across the surface or by different observation geometries, given that observations sampling the same region were selected under the same conditions. Looking at different spatial scales (global comparison between the mission phases or between different cubes), we tried to identify possibly relevant parameter(s) affecting the spectral response among different ones such as: the exposure time, the DN level, the spatial resolution, the local solar time and the instrumental temperatures measured during the acquisitions (telescope, radiator, spectrometer and IR detector temperatures). It seems that only the IR temperature is linked with the unusual spectral behavior observed.

In Figure 3, we report the two median spectra of the same area (longitudes from 288.5 • E to 291 • E and latitudes from 3.9 • S to 0.4 • N). The blue spectrum is a median of 216 spectra coming from the cube 494868787 acquired during the CSH mission phase, while the red spectrum is a median of 3414 spectra of the cube 521987329 acquired during the CSL mission phase. As reported in Table I, the IR temperature during CSH is 85K and 175K during CSL. In order to minimize photometric effects induced by observation geometry and the spectral ones, related to the above mentioned VIS temperature, we selected data acquired at the same VIS temperature (between 182K and 183.5K) and at the same phase angles (between 38 • and 41.5 • ). In addition, to further reduce the impact of these effects, we used photometrically corrected data 9 and we applied the correction for the VIS temperature effect (see Section IV below).

The main differences among the blue and the red spectra of Figure 3 is the spectral slope which gets globally more negative as the IR temperature increases (CSL case, red spectrum). The shape is also modified: the CSL spectrum seems to be distorted, having a higher amplitude, especially in the range around 700-900 nm. While this spectral interval corresponds to a lower responsivity of the sensor, to date, it is not possible to establish whether it affects the resulting shape. According to the two CSL spectra of Figure 3, the effect of the high IR channel temperature on the radiance factor measured at 950 nm is of the order of 4%.

With an equivalent number of spectra, the median spectra of CSH is less noisy than the one of CSL. We may suppose that the higher IR temperature, the more noise affects the VIS spectra. In addition, we also note an inversion of the spikes visible in the two spectra (e.g. between 460 nm and 530 nm and at 585 nm, 655 nm, 675 nm and 850-860 nm for the main ones). The later effect is indirectly due to the denoising procedure 8 which corrects the data following an average trend. The spectra, once corrected, can be different in such structures depending on their initial shape. Finally, based on the comparison of Figure 3, we exclude a systematic and major effect on the absolute albedo. Median of CSH (blue) and CSL (red and green) spectra (216 and 3414 respectively) acquired at the same location and under the same conditions of observation geometry and VIS temperature. The red CSL spectrum, which is not corrected for the high IR temperature effects, exhibits the distortion induced by this instrumental issue. The green spectrum is corrected for the IR temperature effects and is discussed in Section V.

Having checked the influence of the parameters described above, we think that the main cause of the spectral distortion in the VIR VIS spectra is the thermal input coming from the IR sensor on the visible channel. Under this assumption, in the next section, we define an empirical correction that is designed to minimize the effects of the VIS and IR temperatures on the VIS channel, by adjusting the visible spectra to a common reference.

IV. CORRECTION OF THE DATA

We showed that the spectral modifications observed in the VIR VIS data came from a) the VIS temperature variations during a sequence of acquisitions (Figure 1 and 2) and b) the IR channel temperature (Figure 3), which varies whether the IR channel is used or not. We illustrated that an increase of the VIS temperature implies a more negative spectral slope while a high IR temperature increases the amplitude of the spectral features and makes a slightly more negative spectral slope. Here we address the correction of the data, first by defining reference VIS and IR temperatures, then by calculating a correction factor, and finally by describing how to apply it.

A. Absolute calibration and reference for the correction processes

While several in-flight observations of stars have been performed during the Dawn mission, only one observation of Arcturus is suitable for the VIS channel calibration, being acquired at full spectral resolution. Figure 4 reports this observation compared to three Arcturus' spectra acquired from Earth [14][15][16] 4. Comparison between Arcturus' spectra from VIR and different ground-based measurements from [14][15][16] . The spike around 675 nm in the VIR spectrum is due to an order sorting filter. Below 425 nm and after 975 nm, the signal in the VIR observation is below 60 DN and consequently too low to be reliable.

observations have been chosen because their spectral resolutions are close to the one of VIR, therefore facilitating the comparison. In the ranges below 425 nm and above 975 nm (grey areas in Figure 4), the raw signal of the VIR observation is too low (below 60 DN) to be evaluated correctly. Consequently, those ranges are not considered here. In terms of absolute level, the agreement between the different ground-based observations and the VIR spectrum is very good. We only note a slight disagreement in the range 760-870 nm which could be explained by the presence of a minimum in the CCD responsivity in that range (see sec. III B). However, as previously mentioned, the impact of this minimum in the CCD responsivity on the spectral shape in that range is not confirmed to date. The good match provided through this comparison validates the instrumental absolute calibration. This agreement implies that the VIS and IR temperatures of this observation can be used as a reference for the correction processes detailed in the next section. We then consider the two following assumptions:

1. The VIS temperature -of 177K during this acquisition -will be considered as a reference for calculating the correction factor. 2. The IR temperature -around 80K at that time and indicating that the cryocooler is in operation -will be also considered as a reference.

B. Definition of the correction factors

Due to the complexity of the VIR data set in terms of instrumental effects and observation parameters as well as for computational reason (see section IV C), it was not possible to derive a unique correction factor (CF) to be applied to the entire data set. At the same time, it was not possible to compute one correction for each mission phase, mainly due to lack of data for some of them. Given this, a minimum number of correction factors has been derived and applied to the different mission phases.

As shown in Figure 2, we have grouped the observations by bin of 1K (VIS temperature) to build the correction factor. This correction factor, illustrated for the CSH mission phase in Figure 5, is defined as the ratio between the normalized median spectra at a given bin of VIS temperature and the normalized median spectrum as derived from the CSH data set, at the VIS temperature of 177K and at the IR temperature of 85K, i.e.:

CF λ,T V IS ,T IR = ( I /F ) λ,T V IS ,T IR ( I /F ) CSH,λ,T V IS =177K,T IR =85K (2)
Where I/F at the numerator is the median radiance factor normalized at 550 nm and for a given bin of VIS temperature of the mission phases for which a correction factor is computed; (I/F ) CSH at the denominator is the median radiance factor normalized at 550 nm at a VIS temperature of 177K and an IR temperature of 85K of the CSH mission phase; λ is the wavelength; T V IS is the VIS temperature and T IR is the IR temperature.

The CSH spectrum acquired at 177K (T V IS ) and 85K (T IR ), colored in blue in the Figure 2, is considered as the reference spectrum because the 285319 spectra used to build it are distributed across the whole range of longitudes and at mid-latitudes (between 60 • S to 30 • N). This insures a good representation of Ceres' surface composition, avoiding both bias from uneven sampling and extreme observation geometries. Also, even if the IR temperature of reference is 80K while the one of the CSH is 85K, we note that no differences are observed between the median spectra of the whole data of CSH (IR temperatures around 85K) and CSR (IR temperatures around 80K), which makes possible the choice of CSH as a reference despite the slightly different IR temperature.

The production of the correction factor relies on the following hypotheses:

1. Since the spectra grouped in bins of VIS temperature come from different locations of the surface with possibly different albedos due to variations of composition or residuals of the photometric correction, they have been normalized at 550 nm. The implication of this first hypothesis is that the radiance factor at 550 nm will have the same value before and after the correction, independently from the VIS temperature. It implies also that around this wavelength, the correction will be lower than potentially needed and prevent us to correct for effects on the radiance factor absolute level. 2. A normalization relative to the VIS temperature is also needed since we have to assume that at a given temperature, the spectrum does not need correction. As described in the section IV A, the temperature of 177K has been chosen in light of the absolute calibration tested with Arcturus' observation. 3. In the same way, we assume that during the VIR regular operating mode, the cryocooler is switched FIG. 5. Correction factor corresponding to the CSH mission phase. Its computation is based on the spectra of the Figure 2 and Equation 2. These data are normalized at 550 nm and 177K which is the temperature of reference.

on, which implies that the IR temperature is close to 80K-85K. This assumption appears to be solid thanks to the quality of the VIR Arcturus observation, performed when also the IR was operating, in comparison to the ground based ones.

Following Equation 2, the correction factor for a single mission phase (e.g. CSH, CSS. . . ) describes a set of vectors, one for each VIS temperature bins, covering the VIR VIS spectral range. Figure 5 represents the CSH correction factor based on the spectra of Figure 2.

In Section III B we described the effect of an IR temperature around 175K and we explained the choice of the reference at 80-85K. While the VIS temperature continuously evolves during the acquisition sequences, the IR temperature does not change and is constant during each mission phase. The only exceptions are CXO and a part of CSS, for which the IR channel was operating at the beginning of the sequences and then switched off at the end, as described later. By definition, the use of the reference spectrum of CSH within the correction factor allows us to correct the distortion induced by high IR temperature when present (e.g. CSL) while it will have no effect for other mission phases acquired with an IR temperature of 80-85K (e.g. CSR).

Finally, this correction factor is adequate to correct both the VIS temperature effect and the IR temperature distortion while conserving the relative variability of each individual spectrum. It allows the comparison and mapping of different cubes acquired under variable instrumental conditions and provides a relatively homogeneous result.

C. Application of the correction factors

The correction factor to be applied for each spectrum must take into account the VIS temperature measured at the time of the acquisition. Those VIS temperatures, as well as the IR temperature, are provided by the house-keeping parameters of VIR. As an example, for a given pixel, the VIS temperature can be 172.34k, while the correction factor is available for 172K and 173K. We then calculate an interpolation -made with the IDL routine INTERPOLATE -which allows us to determine the value of the correction factor for this effective VIS temperature. Then, the correction of the data is performed by dividing each spectrum by the correction factor interpolated at the corresponding VIS temperature.

As indicated in Table I, different correction factors have been computed for the CSR, CSS, CSH and CSL mission phases. Given the VIS temperature ranges and CSS IR temperatures distribution (see below), this is the minimal number of correction factors that can be used. To correct the CSA, CTS, CXL, CXG and C2E mission phases, the correction factor of other mission phases has been used. The choice is based on the VIS temperature range spanned in the different sequences and the corresponding IR temperature. In order to apply the correction factor properly, the VIS temperature range from which it is derived should encompass the one of the mission phase that has to be corrected. Simultaneously, the IR temperature of the data to be corrected must match the data used to compute the correction factor. For example, the CSL correction factor will be used to correct the CXL, CXG and C2E data, for which IR temperature of 175K corresponds to a spectral shape similar to the red spectrum of the Figure 3. On the other hand, we cannot use the CTS or the others mission phases, which have IR temperature of 80K and a spectral shape similar to the blue spectrum of the Figure 3. The Table I indicates also which correction factor must used to correct a given mission phase. Some exceptions or particular cases are nonetheless worthy to be detailed below, because if they are ignored, they can lead to imprecise correction causing artifacts on final maps.

(a) The CXL mission phase is corrected with the CSL correction factor, because both have a high IR temperature. However, the CXL VIS temperature range is larger than the one of CSL since the CXL's starts at 169K while the CSL's at 171K (see Table I). The CXL data with a VIS temperatures comprised between 169K and 171K are then corrected by the CSL correction factor at the VIS temperature of 171K, without extrapolation. Because it impacts only 0.2% of the VIS CXL data set, this can be neglected. We also note that a fraction of the CXL data are acquired while the IR temperature is comprised between 160-172K. Therefore, the CSL correction may not be fully adequate in that case and some residuals may be observed even after the application of the correction. While this subset of data represents 18% of the CXL mission phase, it represents only 1.3% of the whole VIR VIS data set and then can be discarded for mapping purposes, if necessary. (b) The CSS data set represents a peculiar case. One part of the corresponding data set has been acquired with an IR temperature around 80K (IR channel/cryocooler switched on), and the other part has been acquired around 175K (IR channel/cryocooler switched off). However, for ∼ 92% of the observations acquired at an IR temperature of 80K the VIS temperature was below 182K (which represents ∼ 66% of CSS data), while the rest of the data, acquired at an IR temperature of 175K, the VIS temperature were higher than 182K. Consequently, a part of the CSS data shows a CSH-like spectrum and the other part exhibits a CSL-like spectrum (blue and red spectrum of Figure 3 respectively). Following the definition of the correction factor, the spectrum of reference, acquired at a VIS temperature of 177K, is not affected by the high IR temperature effect and the CSS correction factor is then behaving well for the two parts of its data set. However, the particularity of the CSS mission phase implies that its correction factor cannot be used to correct the others missions phases.

(c) For the CXO mission phase, which represents only 0.6% of the whole VIR VIS data set, the IR temperature increased progressively from 90K to 175K during all the acquisitions because the IR cryocooler has been turned off just before the VIS channel started to operate. This configuration could have provided a chance to characterize the variation of the spectral response as a function of the IR temperature. However, this mission phase has been dedicated to the study of the opposition effect, and during the VIS sequence, while the IR temperature was raising, the phase angle of the observations progressively increased from ∼ 0 • to ∼ 6.6 • . This introduced an unwanted correlation between the phase angle and the IR temperature. Phase angle variations may in principle introduce spectral variability, thus, in this case, we are not able to disentangle intrinsic spectrophotometric effects from the spurious ones introduced by the IR temperature variability (which is of the order of 4%, see Section V). Given this, we choose to not apply or fix any correction factor for this mission phase.

V. RESULTS

Because the changing VIS temperature affects mostly the spectral slope, we define the following slope parameter in order to illustrate the effectiveness of the correction:

S max(620|650)-950nm = ( I /F ) 950nm -( I /F ) max(620|650)nm ( I /F ) max(620|650) × (9500 Å -max(6200|6500) Å) (3)
Where S max(620|650)-950 (S hereafter) is the spectral slope, computed between the radiance factor at 950 nm ((I/F ) 950nm ) and the position at which the maximum occurs in the interval 620-650 nm ((I/F ) max(620|650nm) ). Figure 6 presents the maps and the distributions of the spectral slope as defined in Equation 3 before (panels A and B) and after (panels C and D) the application of the correction factor for the CSH mission phase. The maps presented were obtained by projecting the footprint of each single pixel on an equidistant cylindrical projection. All overlapping footprints are merged by calculating the median.

After correction, for 98.2% of the 3 219 440 CSH processed spectra the spectral slope is distributed between S = -3.10 -5 k Å-1 and S = 0k Å-1 (with a median at S = 1.26 × 10 -5 k Å-1 ). This range is chosen for the color scale of the Figure 6 even if some locations such as Haulani (longitude ∼10 • E -latitude ∼10 • N), and Occator crater (longitude ∼240 • E -latitude ∼20 • N) or some pixels at high incidence angles and at southern latitudes show values exceeding these limits. Panels B and D of Figure 6 show a linear fit (least square) across the distribution of the spectral slope against the VIS temperature. The fit is calculated in the restricted spectral slope range -10 -4 -10 -4 k Å-1 in order to exclude a minority of outliers identified by their very low DN level and extreme slope values. After correction, the two excluded subsets represent only 1684 pixels over more than 3 million for the fit of the panels B and D in Figure 6. The computed slope of the distribution is reduced from -1.76 × 10 -4 %k Å-1 .K -1 to -7.16 × 10 -10 %k Å-1 .K -1 , indicating that the correction works well. The final value of the spectral slope is S = -1.29 × 10 -5 k Å-1 , which is very close to the median of the distribution.

The correction makes it possible to analyse specific regions or features, using different mission phases and resolutions. This is illustrated by the maps of Figures 7 and8 centered in the South region of Dantu. The maps are orthographic projections of the data available in CSH, CSS, CSR and CTS mission phases. As opposed to Figure 6, the pixels are represented as points and not as polygons of their surface footprints. However, the density of pixels as well as their spatial resolution in that region guarantees good coverage (except in few locations, e.g. ∼ 160 • E of longitude and 5 • S of latitude) and avoid artifacts in the map due to this mapping technique [START_REF] Rousseau | EPSC-DPS2019[END_REF] . As in Figure 6, overlapping pixels are merged by calculating the median. The data used in the panel A of the Figures 7 and8 are already photometrically corrected but not corrected for the temperature effect. In the temperature-corrected observations of the radiance factor at 950 nm, a small, although significant improvement can be noted with respect to the non-corrected ones (panel B in Figure 7). For the spectral slope, the improvement is more substantial (panel B in Figure 8). For example, the region around Dantu crater (longitude ∼ 140 • E, latitude ∼ 20 • N) was not distinguishable before the correction and it is clearly visible after. In addition, the ejecta ray coming from the Occator crater 18 can be recognized in the map of the corrected spectral slope (panel B Figure 8) and it can be followed across the map on the whole range of longitudes and from latitude 0 • N to about 15 • S.

In Figure 3, the CSL green spectrum is corrected with the correction factor based on the CSH reference. It allows the removal of the distortion caused by the high IR temperature and the retrieval of the right spectral slope and shape. A homogeneous behavior in the noise is also retrieved between CSH and CSL, which was not the case without the IR correction as explained in section III B. However, due to the normalisation in the correction process (see Section 2), a systematic difference in albedo is observed between the CSH and CSL spectra of Figure 3 (blue and green respectively), which we do not expect here since the data has been corrected and, in particular, acquired on the same area. This systematic residual cannot be corrected -by definition of the correction factor -and points out the limit of our correction when the IR channel temperature is high. However, in the range 460-950 nm, this residual is constant and of the order of ∼ 1% (by comparing the CSH spectrum and the CSL green spectrum). It is consequently a minor side effect compared with the original distortion induced by the high IR temperature which is around ∼ 4% at 950 nm (by comparing the CSL red and green spectra before and after the IR correction).

VI. CONCLUSION

Data acquired at Ceres by the visible channel of the VIR imaging spectrometer are affected by the VIS temperature variations during different sequences of acquisitions. In addition to the variation of the spectral slope induced by this first parameter, the IR temperature, linked to the use of the IR channel/cryocooler, plays a secondary role on the spectral slope but also on the global shape of the spectra. We developed an empirical correction and we applied it to the whole Ceres data set. The correction uses a unique spectral reference, chosen to be representative of the surface of Ceres and in the optimum ranges of the VIS and IR temperatures. The spectral reference has been defined according to the quality of the match existing between the VIR and ground-based observations of Arcturus. This consistency allowed to define the VIS and IR temperatures of reference and to highlight the accuracy of the absolute calibration. The correction applied to the VIR visible data of Ceres proved necessary to interpret and compare different set of observations and perform mapping. The spectral slope and shape are also more reliable because the spurious spectral variability has been minimized, both at global and local scale. In this respect, the final corrected data set of the VIR visible channel is now homogeneous within a single mission phase and also among different ones.

Data acquired at Vesta by the VIS channel of VIR are also affected by the VIS temperature variations. However, because the IR channel/cryocooler was always turned on during the VIS channel acquisitions (except for a very limited part of the data set), the Vesta data are not affected by the spectral distortion due to high IR channel temperature.

SUPPLEMENTARY MATERIAL

See supplementary material for the figures of the median spectra and correction factors of the CSR, CSS and CSL mission phases.

ACKNOWLEDGMENTS

VIR is funded by the Italian Space Agency-ASI and was developed under the leadership of INAF-Istituto di Astrofisica e Planetologia Spaziali, Rome-Italy (Dawn ASI INAF I/004/12/0). The instrument was built by Selex-Galileo, Florence-Italy. The authors acknowledge the support of the Dawn Science, Instrument, and Operations Teams. The author made use of TOPCAT (Tools for OPerations on Catalogues And Tables) [START_REF] Taylor | Astronomical Data Analysis Software and Systems XIV[END_REF] for a part of the data analysis and figure production. We are grateful for the anonymous reviewers for their constructive suggestions that helped improve this manuscript. 4. Correction factor corresponding to the CSS mission phase. Its computation is based on the spectra of the Figure 3 of the supplementary materials and Equation 2 of the main manuscript. These data are normalized at 550 nm but, contrary to the Figure 5 of the manuscript, not normalized at 177K since the reference spectrum is the one of CSH as indicated by Equation 2 of the manuscript. As described in the manuscript, it is possible to observe in this figure the change in the spectral behavior after 182K when the IR channel has reached a higher temperature. 6. Correction factor corresponding to the CSL mission phase. Its computation is based on the spectra of the Figure 5 of the supplementary materials and Equation 2 of the main manuscript. These data are normalized at 550 nm but, contrary to the Figure 5 of the manuscript, not normalized at 177K since the reference spectrum is the one of CSH as indicated by Equation 2 of the manuscript.

FIG. 1 .

 1 FIG. 1. Panel A: temperature map of the CSH mission phase. Two sequences of acquisitions are marked by black arrows, with the beginning of the second indicated by a red arrow. Numbers indicate the acquisition order. Panel B: Evolution of the temperature for the two sequences pointed in Panel A. The total duration of each sequence is around 2 hours and 30 minutes. The VIS temperature is increasing from the beginning to the end of each sequence from 169K to 184K. The second sequence, indicated by the red arrow on the panel A, starts almost 17 hours after the end of the first one. During this time, the CCD sensor is able to cool down and temperature drops.

  FIG. 3.Median of CSH (blue) and CSL (red and green) spectra (216 and 3414 respectively) acquired at the same location and under the same conditions of observation geometry and VIS temperature. The red CSL spectrum, which is not corrected for the high IR temperature effects, exhibits the distortion induced by this instrumental issue. The green spectrum is corrected for the IR temperature effects and is discussed in Section V.

5 FIG. 6 .

 56 FIG. 6.Panel A: map of the spectral slope (630-950 nm) for the CSH mission phase without the correction of the VIS temperature effect. Panel B: distribution of the spectral slope (630-950 nm) as a of the VIS temperature for the data of Panel A. A clear trend is visible in both cases due to the increase of the VIS temperature (see also Figure1). The interpretation of the map is not possible without a correction of the data. Panel C: map of the spectral slope after the correction of the VIS temperature effect. Panel D: distribution of the spectral slope in function of the VIS temperature after the correction. Once the correction is applied, no trend can be noted in the distribution of panel D. Intrinsic spectral variability of Ceres' surface relevant morphological features can be clearly recognized in the map of the panel C, e.g.: Haulani close to the longitude 0-20 • E, latitude 0-20 • N; Dantu around the longitude 140 • E, latitude 20 • N; Occator on longitude 240 • E, latitude 20 • N.

FIG. 7 .

 7 FIG. 7. Orthographic projection of the Dantu region using the radiance factor at 950 nm, before the correction of the VIS and IR temperature effects (panel A) and after the correction (panel B). In panel A, the data are already photometrically corrected. The data used come from the CSH, CSS, CSR and CTS mission phases.

FIG. 8 .

 8 FIG. 8. Orthographic projection of the Dantu region using the spectral slope (see the text for the definition), before the correction of the VIS and IR temperature effects (panel A) and after the correction (panel B). In panel A, the data are already photometrically corrected. The data used come from the CSH, CSS, CSR and CTS mission phases.

FIG. 2 .

 2 FIG.2. Correction factor corresponding to the CSR mission phase. Its computation is based on the spectra of the Figure1of the supplementary materials and Equation 2 of the main manuscript. These data are normalized at 550 nm but, contrary to the Figure5of the manuscript, not normalized at 177K since the reference spectrum is the one of CSH as indicated by Equation 2 of the manuscript.

  400

  . These ground-based

		5×10	-8
		4×10	-8
	Flux (W/m²/µm)	1×10 2×10 3×10	-8 -8 -8		Kiehling et al. 1987 Alekseeva et al. 1996 Rayner et al. 2009 VIR
		0	400	600 Wavelength (nm) 800	1000	1200
	FIG.

  FIG. 1. Median spectra of the CSR mission phase for the different CCD temperatures. The spectra are normalized at 550 nm.

	400 0.80 0.85 0.90 0.95 1.00 1.05 1.10 Normalised I/F	500	600	700 Wavelength (nm) 800	900	1000 1100	187K 186K 185K 184K 183K 182K 181K 180K 179K 178K 177K 176K 175K 174K 173K 172K 171K 170K 169K
	400 0.85 0.90 0.95 1.00 1.05 1.10 Correction factor	500	600	700 Wavelength (nm) 800	900	1000 1100	187K 186K 185K 184K 183K 182K 181K 180K 179K 178K 177K 176K 175K 174K 173K 172K 171K 170K 169K

  FIG. 3. Median spectra of the CSS mission phase for the different CCD temperatures. The spectra are normalized at 550 nm.

	0.85 0.90 0.95 1.00 1.05 1.10 1.15 Normalised I/F	500	600	700 Wavelength (nm) 800	900	1000 1100	195K 194K 193K 192K 191K 190K 189K 188K 187K 186K 185K 184K 183K 182K 181K 180K 179K 178K 177K 176K 175K 174K 173K 172K 171K 170K 169K 168K
	400 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Correction factor	500	600	700 Wavelength (nm) 800	900	1000 1100	195K 194K 193K 192K 191K 190K 189K 188K 187K 186K 185K 184K 183K 182K 181K 180K 179K 178K 177K 176K 175K 174K 173K 172K 171K 170K 169K 168K
	FIG.

  FIG.5. Median spectra of the CSL mission phase for the different CCD temperatures. The spectra are normalized at 550 nm. Note the different spectral shape between this set of spectra, which are affected by the high IR channel temperature, and the CSH or CSR mission phase.

	400 0.85 0.90 0.95 1.00 1.05 1.10 1.15 Normalised I/F	500	600	700 Wavelength (nm) 800	900	1000 1100	193K 192K 191K 190K 189K 188K 187K 186K 185K 184K 183K 182K 181K 180K 179K 178K 177K 176K 175K 174K 173K 172K 171K
	400 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 Correction factor	500	600	700 Wavelength (nm) 800	900	1000 1100	193K 192K 191K 190K 189K 188K 187K 186K 185K 184K 183K 182K 181K 180K 179K 178K 177K 176K 175K 174K 173K 172K 171K

FIG.

Supplementary materials of "Correction of the VIR-Visible data set from the Dawn mission"

Frigeri, 1 and F. Tosi 1 1) IAPS-INAF, via Fosso del Cavaliere 100, 00133, Rome, Italy 2) Italian Space Agency (ASI), Via del Politecnico snc, 00133, Rome, Italy a) batiste.rousseau@inaf.it