Plinio Bau

Marc Cousineau

Bernardo Cougo

Frédéric Richardeau

Nicolas C Rouger

CMOS Active Gate Driver for Closed-Loop d v /d t Control of GaN Transistors

Keywords: Active gate driver, dv/dt, EMI, electromagnetic interference, GaN, HEMT Transistors, wide-bandgap semiconductor, closed-loop systems, driver circuits, feedback circuits, switching circuits, power electronics. I

whether they are published or not. The documents may come

problem is frequently observed with WBG devices because the threshold gate voltages and maximum gate voltage are lower than those in silicon. In addition, the threshold voltage for a SiC device decreases with temperature, which reduces its immunity, whereas some GaN devices are not affected by this property. Another disadvantage of high dv/dt is the use of volume-consuming EMI voltage common mode dv/dt filters [START_REF] Velander | An Ultralow Loss Inductorless dv/dt Filter Concept for Medium-Power Voltage Source Motor Drive Converters With SiC Devices[END_REF]. For aircraft applications, the size and weight of such filters are key parameters for the system design [START_REF] Santos | Trade-off between losses and EMI issues in three-phase SiC inverters for aircraft applications[END_REF]. Another disadvantage of high dv/dt values is a drain-source overvoltage during turn-off, mainly due to high related di/dt and the presence of parasitic inductors involved in the switching-loop. Finally, a fourth disadvantage is the high frequency induced common mode and differential mode current in the switching node [START_REF] Kim | Common Mode Noise Analysis for Cascaded Boost Converter With Silicon Carbide Devices[END_REF]. Consequently, the common mode transient immunity (CMTI) of isolation barriers must comply with higher dv/dt values [START_REF] Colin | High speed optical gate driver for wide band gap power transistors[END_REF].

Among all the possible ways to control the dv/dt of a power transistor, several options emulate a CGD external capacitance. In [START_REF] Park | Flexible dV/dt and di/dt control method for insulated gate power switches[END_REF], a method using discrete transistors was proposed to actively drive silicon IGBT devices. In [START_REF] Sun | Active dV/dt control of 600V GaN transistors[END_REF], a similar approach was adapted for GaN transistors, with discrete components. This solution has a lower bandwidth, and additional stray inductance between device's gate and source electrodes and therefore, cannot handle dv/dt's in the order of 100's of V/ns. Moreover, in the topology proposed in [START_REF] Sun | Active dV/dt control of 600V GaN transistors[END_REF], a higher delay is required for the biasing of the transistors involved in the feedback loop, limiting the capability to operate at higher dv/dt values. When increasing the dv/dt dynamic, the transient behavior of the feedback-loop becomes a key point to address. Indeed, one must avoid a prohibitive delay time to properly bias the several transistors involved in the feedback loop. With faster dv/dt values, it is also critical to limit the direct capacitor coupling between the drain and gate terminals of the power devices, to prevent detrimental effects through Miller coupling. Compared to [START_REF] Sun | Active dV/dt control of 600V GaN transistors[END_REF], it is then desired to increase the feedback loop gain and to further reduce the value of the high voltage capacitor required for the active gate drive technique. Due to a smaller capacitor, its integration can also be possible. This paper proposes a novel method with a faster and simpler topology to control the turn-on transient based on a full monolithic CMOS gate driver offering very large bandwidth analog circuits. An improved solution, where all required devices are integrated into one ASIC, following the trend of integration [START_REF] Wen | A Dual-Mode Driver IC With Monolithic Negative Drive-Voltage Capability and Digital Current-Mode Controller for Depletion-Mode GaN HEMT[END_REF]- [START_REF] Zhang | Very High Frequency PWM Buck Converters Using Monolithic GaN Half-Bridge Power Stages With Integrated Gate Drivers[END_REF], is presented, discussed and experimentally demonstrated.

II. ACTIVE GATE DRIVERS FOR SILICON AND WIDE BANDGAP POWER TRANSISTORS

The classical trade-off between dv/dt and the amount of switching energy (EON) is discussed in the following section. Then, the state-of-the-art for gate drivers with dv/dt control for power electronic applications is discussed. Our proposed method is then presented and compared to other approaches.

A. Proposed technique: turn-on control

The proposed active gate driver (AGD) technique is implemented only during turn-on. Indeed, the turn-off switching speed is mainly controlled by the load current amplitude and not directly by the gate driver when using high speed devices in high efficiency applications [25]. Nevertheless, our technique can be easily applied for the active control of the turn-off, should a hard turn-off be required by the application (the high dv/dt at turn off undergone at high load current can thus be limited by dynamically re-biasing the gate slightly higher than its threshold). The effects of temperature, load current and input voltage transients for the proposed technique are not discussed in this article. Without any active gate driving, a simplified expression for dv/dt during turn-on is introduced in (1). The derivative of the drain to source voltage (dvDS/dt) depends on the gate current M G i (gate current during the Miller plateau) and the gate to drain capacitance CGD:

d𝑣 DS d𝑡 = - 𝑖 𝐺 𝑀 𝐶 GD = - 𝑣 DRV -𝑣 M 𝑅 G 𝐶 GD (1)
where vDRV is the gate driver supply voltage, vM is the Miller plateau voltage (between external gate and source electrodes), and RG is the external gate resistance, neglecting physical effects for simplicity.

The main idea of the active gate driving is to control dv/dt by emulating an increase in the Miller capacitance (or CGD equivalent capacitance) of the power device only during the switching event and the dv/dt sequence. To do so, a current proportional to dvDS/dt has to be subtracted from the gate current during the turn-on event. Hence, a feedback loop is used to generate this current, which is directly connected to the gate of the power device to reduce the gate current amplitude during the Miller plateau. This feedback method has been previously proposed but with key limitations:

--With discrete components, only low switching speeds can be actively driven (e.g., fall time of tens or hundreds of nanoseconds, as in [START_REF] Sun | Active dV/dt control of 600V GaN transistors[END_REF].

--With integrated solutions in CMOS gate drivers, only low-voltage applications are addressed, where the maximum drain to source voltage is lower than the CMOS technology limit (e.g., <48 V, as in [START_REF] Chen | A 10MHz 5-to-40V EMI-regulated GaN power driver with closed-loop adaptive Miller Plateau sensing[END_REF]).

Fig. 1 shows a transistor-level diagram of the proposed method. A small value capacitor CS is used as a sensor of the derivative of the voltage vDS. A capacitor with a high breakdown voltage is required, since it has to sustain the high voltage of the DC bus.

To amplify the current generated into this sensor during the dv/dt, a large bandwidth gain current mirror is proposed, which is the core idea for this method. The main challenge in this approach is to propose a circuit that can simultaneously supply a high amplitude feedback current with a very small time-delay response.

Typically, this feedback current iFB may be higher than 1 A, and the delay in the feedback loop should be lower than 1 ns. This feedback current iFB is proportional to the derivative of the power transistor voltage vDS, current gain G and the value of the capacitor CS acting as a dv/dt sensor (as shown in ( 2)). Typical CS values are much lower than the GaN CRSS, leading to CS in the order of 0.7 pF to 2 pF. To reach these specifications, a CMOS integration with an optimal design is required. Note that the feedback circuit acts like an active equivalent gate-drain capacitor placed in parallel with CGD equal to G•CS. Due to the feedback current amplification through current mirrors, the sense capacitor CS can be downsized and further integrated on-chip. The feedback loop is composed of four low-voltage transistors, M1 to M4, and a high-voltage sensing capacitor CS. The current buffer, also called the main stage driver, is composed of a PMOS transistor M5 and a NMOS transistor M6 used to source and sink the high gate currents, respectively. This buffer has a split output architecture, making it possible to use different resistors to adjust the turn-on and turn-off switching losses separately. The capacitors CGD, CGS and CDS are intrinsic to the GaN power transistor. The diode DP is used only as a protection device at the input of the current mirror and is reverse biased during normal operation. In case the current in CS is too high, the diode DP will clamp the vinM voltage at -0.7 V, preventing the gate voltage for M1 and M2 will exceed more than the nominal maximum voltage value (5.5 V), therefore preventing breakdown destructive voltage in transistors M1 and M2. Fig. 2 introduces the waveforms for the main signals related to this approach that are used to actively control dv/dt. At the beginning of the dv/dt phase (at time t2), a delay TD is first required before the feedback loop starts to sink the current iFB. This delay is mainly due to the settling time of the feedback loop circuit. The current iFB quickly reaches its final value iFB_F, which is subtracted from the current iRG provided by the driver. When iFB_F increases, the gate current iG is decreased, leading to an increase in time t3 in order to provide enough time to transfer the overall charge required by the gate of the power transistor during the Miller plateau. As a result, the dvDS/dt is actively reduced. For the sake of simplicity, a constant Miller Plateau voltage was considered. During the turn-off transition, the sensing capacitor CS sources (instead of sinking) a current that flows through the body diode of M1. The width of M1 (W1) has to be sized correctly to handle the CS discharge current without breaking M1 or increasing the voltage at node vinM too much.

𝑖 FB = -𝐺 • 𝐶 S d𝑣 DS d𝑡 (2)
It can be noted that if the total subtracted current iFB_F increases too much, due to a high loop gain and overly fast feedback response, it can accidentally reach the value of the current supplied by the driver. In that case, the gate current iG in the power device during the Miller plateau is cancelled. Then, the vDS and vGS voltages start to oscillate and the closed-loop system becomes unstable. A limit of the method comes from the maximum amount of time TD required by the feedback current loop to operate. If this time delay is higher than the duration t3 -t2 observed in open-loop, the turn-on transition will be missed, and the feedback loop will have no effect on reducing dv/dt. It is important to ensure that the loop is able to operate as fast as possible. Finally, the time delay TD characterizes the system performance both in terms of time response and stability. In our case, we will optimize the integration and circuit design to have less than 1 ns delay and to actively control initial fall time of 3 ns and above (dv/dtpeak =-175 V/ns in the case of 400 V applications).

B. Benefits of the Active Gate Driver

When designing a half bridge, there is a trade-off between the switching losses (EON, EOFF) and switching speed (dv/dt, di/dt).

As long as the Miller effect is an active phenomenon (all turn-on or some turn-off transients at high load current), dv/dt is typically limited by the choice of the gate resistor RG. Fig. 3 introduces this classical trade-off (solid line) for the specifications detailed in the next sections (obtained with a Cadence™ simulation with a model of a GS66508T GaN device). This work proposes to reduce the dv/dt leading from the point A to the point C (dashed line) but with fewer switching losses compared to a simple change in the gate resistor value RG (from point A to B). This change in the EMI-loss trade-off can be further dynamically tuned while changing the AGD parameters. The amount of saved energy during turn-on is explained in Fig. 4. The proposed method reduces the amount of switching losses because the dv/dt value is reduced without modifying di/dt. As a consequence, the dissipated switching energy during the di/dt event (hatched area in Fig. 4 (d)) is canceled with our technique. The proposed method will not change di/dt because the proposed feedback loop will not be active during this phase. First, the di/dt value can be set by adjusting the value of RG, and then dv/dt can be separately adjusted to reduce the negative effects of the EMI. One has to note that the parasitic stray inductance is neglected in this section of the paper (to explain the method), which is reasonable for high-frequency applications of GaN power transistors with optimal PCB designs (e.g., power loop stray inductances in the range of 1 nH). As a positive consequence, both points B and C (Fig. 3) will also generate a lower drain current overshoot during the dv/dt sequence [t4, t2] (Fig. 4) than point A; i.e., the dv/dt generates an extra transient current proportional to the parasitic drain-source capacitors of the power transistors.

C. Summary/Benchmark

The proposed method has several advantages compared to other methods used to control dv/dt.

--Compared to an added constant external capacitor CGD, the emulated capacitance G•CS will not affect the device immunity through Miller coupling. The risk of a cross conduction fault is then mitigated. Another advantage is that the emulated capacitance can change through the feedback gain G. Moreover, the value of the required high-voltage CS capacitor can be reduced using our technique; hence, its integration within the CMOS circuit is possible.

--Compared to open-loop techniques, the closed-loop method adapts the response for different systems and power devices under different conditions, while an open-loop approach would have to be designed for each different application and power device [START_REF] Dymond | A 6.7-GHz Active Gate Driver for GaN FETs to Combat Overshoot, Ringing, and EMI[END_REF].

--Compared to other previously demonstrated closed-loop techniques, our approach is simple, extremely fast and highly integrated. While other closed-loop methods convert analog signals to digital signals using an ADC, their speed is limited to tens or hundreds of nanoseconds. Very high switching speeds and/or very short switching times cannot be controlled by the solutions presented today in the literature [START_REF] Krishna | Closed loop analog active gate driver for fast switching and active damping of SiC MOSFET[END_REF].

--Compared to other integrated solutions [START_REF] Wen | A Dual-Mode Driver IC With Monolithic Negative Drive-Voltage Capability and Digital Current-Mode Controller for Depletion-Mode GaN HEMT[END_REF], [START_REF] Chen | A Smart IGBT Gate Driver IC With Temperature Compensated Collector Current Sensing[END_REF], our solution offers both low (e.g., 48 V) and medium voltage (e.g., 400 V) applications, while using only low voltage CMOS devices and technology (e.g., 10 V, 20 V). Only a small (pF range) high-voltage sense capacitor is required, which is easily integrated with standard low-voltage CMOS technologies.

III. CMOS ULTRA-FAST ACTIVE GATE DRIVER

The best way to implement the proposed method is by the use of an integrated analog circuit designed to minimize the delay TD of the feedback loop, while allowing high gain and large feedback currents.

A. Overall design approach and CMOS Active Gate Driver performance

As introduced in Fig. 1, two stages of current mirrors are cascaded. Therefore, the total response time is defined by several consecutive phenomena. This time delay results from a succession of several events. During the turn-on of the power transistor and the dv/dt sequence, the voltage vDS drops down from the voltage of the DC bus to a value close to zero. This transient is shown in Fig. 5(a). This signal, vDS(t), is the input signal of the feedback loop. Because the terminal vinM of the sensing capacitor CS is at a quasi-constant voltage with respect to the voltage range of vDS, the derivative of vDS(t) will generate a proportional quasi-constant current flowing through CS, the iCs(t) current, as shown on the second waveform Fig. 5(b). This current will charge the parasitic capacitor CGP present on node vinM, involving the gates of the PMOS transistors M1 and M2, and change the biasing-voltage of the first current mirror, as shown in Fig. 5(c). As soon as this voltage crosses the PMOS threshold voltage vTh_p, a current will start to flow through the channel of M2, as shown in Fig. 5(d). This current charges the gates of the transistors M3 and M4, leading to an increase in the voltage vGSn(t), as shown in Fig. 5(e). Finally, when vGSn reaches the NMOS threshold voltage vth_n, the output current iFB of the second current mirror starts to rise, as shown in Fig. 5(f). As soon as this current iFB is no longer equal to zero, after time tD, the feedback loop starts to operate and dv/dt is reduced and controlled. In practice, the gain G of the feedback loop will vary according to the desired reduction in dv/dt. For instance, the higher the gain G is, the larger the iFB_F is, leading to a reduced dv/dt during turn-on. One can also note that tE will be larger when large gain values G are set. Since the current mirror is composed of two stages, the gain G is the product of the two intermediate gains of each stage (Gp and Gn in Fig. 1). Based on simulations in Cadence™ with the design kit provided by the CMOS foundry, total delay times tE-t2 in the range of 290 ps to 640 ps can be achieved (see Table II in [START_REF] Wen | A Dual-Mode Driver IC With Monolithic Negative Drive-Voltage Capability and Digital Current-Mode Controller for Depletion-Mode GaN HEMT[END_REF] for more details). These values are functions of the gain G, which is proportional to the sizes of the current mirror transistors, with lower gains leading to shorter delay times. Fig. 6(a) shows the dvDS/dt reduction for the system operating at point A (open-loop) and C (closed-loop), as defined in Fig. 3 and 4. Fig. 6(b) shows the extension of the Miller plateau due to the added virtual capacitance effect and closed-loop control. Fig. 6(c) shows the gate current iG that is going to the power device gate terminal, and Fig. 6(d) shows the drain current iD of the power transistor and a beneficial reduction in overcurrent, while keeping the same initial di/dt.

A current biasing circuit is connected to the vinM node. Compared to the iCs amplitude, a small current is sinked from this node that helps to precharge the intrinsic capacitances of the 4 transistors in the current mirrors, allowing a faster response. It should be noted that, in practice, both the feedback loop delay TD(50%) and its bandwidth are affected both by the sizing of the several transistors involved in the current mirrors and the choice of the sensing capacitor CS value. The final transistor sizes implemented are the results of an optimization process involving both theoretical analysis and simulation validations using accurate CADENCE TM SPECTRE transistor models of the CMOS technology. The CS sense capacitors are integrated with the CMOS AGD. Since CS must have a breakdown voltage higher than the GaN power device, five different designs were considered that used different metal layers and inter layer dielectrics (Fig. 7). Integrated capacitance values of 0.7 pF, 1 pF and 1.5 pF have been implemented and tested. The breakdown characterization was performed under high vacuum, whereas the capacitance measurement was carried out with a HIOKI IM3570 using probe tips and calibration.

As presented in Fig. 7, there is a common-mode parasitic capacitance between the LV node and the CMOS substrate that needs to be taken into consideration, which will add common mode current and a voltage divider effect to the sensing capacitor CS.

B. PCB Design

The analog circuits were implemented in 0.18 µm CMOS technology (AMS H18A6), and the fabricated test chip was packaged in a 6 mm × 6 mm QFN with 24 pins. Two PCB versions (Fig. 8) were realized with layout considerations to minimize the parasitic inductances of both the power and control loops of the power transistor. The PCB uses 4 layers for the prototypes for the EPC2001C transistors and 6 layers for prototypes with GS66508T transistors. Two low-voltage decoupling capacitors with a capacitance of 1 µF are placed close to the gate driver to supply the peak current required during the switching transients, in addition to decoupling the capacitors integrated on-chip. The sensing capacitor CS was integrated either on-chip or externally. Attention is made to minimize the PCB parasitic capacitance between drain and source of the power device.

A CMOS gate driver was implemented for the low-side power transistor, while the gate of the high-side transistor was shorted to its source. The output power load is an air inductor with a low parasitic capacitance.

Please notice that our AGD topology can be adapted to any WBG power transistor, but due to the limit of vDS of integrated current mirror and main buffer MOSFETs (5.5 V), the built prototype is limited to driving transistors from 0 to 5 V.

Consequently, this PCB is only used for double pulse tests with our CMOS AGD driving EPC GaN HEMTs or GaN System devices, with the active control implemented at the low-side transistor. Neither the drain nor the gate currents are probed to comply with extremely low parasitics both for the power loop and the driving loop. The parameters are summarized in Table II. In the case of GaN System devices, the gate driver supply voltage is not optimal to achieve a low ON-state resistance after turn-on. This result occurs due to the 5 V CMOS transistors used for M1 to M6 (Fig. 1), which were chosen for the first CMOS AGD prototype.

Nonetheless, it is possible to drive such GaN devices under these conditions and to achieve a high switching speed, as demonstrated hereinafter.

C. Impact of the proposed method on the total gate charge

The emulated gate-to-drain capacitor (CGD+G•CS) leads to an extended Miller plateau, which will have an impact on the total amount of gate charge provided by the gate driver supply. Since charge is subtracted during a turn-on event through transistor M4, the amount of charge required to turn-on the power device will increase. Indeed, in the proposed improved gate driver circuit, the amount of charge subtracted by the current mirror has to be provided by the driver power supply vDRV. This additional amount of gate driver energy EDRV_SUP is given by:

𝐸 DRV_SUP = 𝑣 HVdc • 𝐺 • 𝐶 S • 𝑣 DRV (4)
Eq. ( 4) shows that the extra energy supplied by the driver will increase proportionally to the gain of the internal current feedback circuit G. A decrease of 58% (from -15 V/ns to -6.3 V/ns) in dvDS/dt will produce an increase of 58% in the energy provided by the driver EDRV_SUP. Since the switching energy of the power device is considerably higher than the energy required by the driver, this increase in driver energy has a limited impact. For the 400 V application, the gate charge is increased by 44% from point A to B. One can note that this additional gate driver energy is inherent to the proposed close-loop control, and other previously demonstrated approaches are subject to such an energy increase [START_REF] Park | Flexible dV/dt and di/dt control method for insulated gate power switches[END_REF], [START_REF] Sun | Active dV/dt control of 600V GaN transistors[END_REF].

D. Application to a 100 V GaN power commutation cell

Using the fabricated CMOS AGD with the integrated buffer, Fig. 9 shows experimental waveforms obtained during the turn-on with and without the closed-loop control, with the same gate resistor and driving voltages for the same test parameters as previously described in Table II. For the closed-loop, a prebiasing current of 20 µA was applied at the input of the current mirror (vinM node) using a sourcemeter unit Keithley 2612B. Without the closed-loop control, the fall time is 4.36 ns (90%-10% vDS(t)), with a peak dv/dt of -15 V/ns. Even with this fast switching event, the AGD is able to actively control the dv/dt sequence from the beginning, without modifying di/dt. It is possible to see the di/dt sequence in the vGS signals because it is the interval between vTH (around 1.7

V from the datasheet) and the beginning of the dv/dt phase, the second line marked in Fig. 9. The iL is not measured in our circuit to reduce the power loop inductance. However, the vGS(t) signal with and without the closed-loop control clearly shows that the di/dt sequence remains almost identical in both cases (Fig. 9 and Fig 10 marked as di/dt sequence). One can also note that the reduced dv/dt with the closed-loop feedback allows the reduction of the drain current overshoot and subsequent gate overvoltage before the Miller plateau. Due to the AGD, the fall time is increased from 4.36 ns to 7.37 ns (90%-10% vDS) without affecting the gate charge before the Miller plateau. This increase in fall time corresponds to the reduction in peak dvDS/dt from -15 V/ns to -6.3 V/ns as shown in Fig. 7. One must note that all the analog circuits are integrated within the CMOS AGD; only the driver supply decoupling capacitors, HV-sensing capacitor (for some tests) and gate resistors are external devices. It should also be emphasized that due to the high speed and large gain of the integrated current mirrors, the HV-sensing capacitor CS is designed in the pF range, allowing its further integration within the CMOS chip (please see table II for values).

Fig. 10 shows the measured vGS waveforms in open-loop and in closed-loop with gains of 10 and 50 for the same value of sensing capacitor CS = 2 pF (external). The duration of the Miller plateau is successfully increased with higher feedback gain values ("effect 1" in Fig. 10). It is also clear that the diD/dt phase is not affected by the closed-loop control. The di/dt value is estimated to be approximately 1A/ns, since the vGS signal changes from vTH to vM in approximately 1 ns. Please note that measurements are carried out with iL=2 A to obtain higher values of dv/dt to explore the speed limits of the method. In addition to the reduction of the dvDS/dt with higher closed-loop gains, the drain overcurrent during turn-on is also reduced. This effect can be seen in Fig. 10 To compare the implementation of the AGD with a gain of 50, Fig. 11 shows a comparison between the experimental results and simulated waveforms. Increasing the feedback gain of the current mirrors decreases dvDS/dt while maintaining an identical di/dt sequence. 175 V/ns is therefore reduced to V/ns with our CMOS AGD. A biasing current of 320 µA is applied, and one can observe that dv/dt starts to be attenuated in less than 1 ns. All the parameters for the results are described in Table II. Without an integrated analog feedback loop, such a result would not be possible. This experimental result shows, for the first time, the active control of 650 V GaN devices with extremely high switching speeds, both in open-and closed-loops. Fig. 13 shows a similar result, where the high-voltage capacitor is integrated on the same CMOS chip as the gate driver (1 pF, 3.5 kV breakdown, see section IV). The small differences in switching speeds between Fig. 12 and Fig. 13. can be explained by the use of a different PCB board, albeit from the same design (typical dispersion in power devices, CMOS gate driver and PCB parasitics). Nonetheless, this result clearly shows that the AGD can be fully functional, even with the high-voltage sense capacitor CS monolithically integrated within the CMOS AGD. Please note that the effect of a biasing current improving the feedback response time can be seen comparing Fig. 12 (ibias=320 µA) and Fig. 13 without biasing current. The attenuation in dv/dt occurs latter in Fig. 13 compared to Fig. 12, as predicted and discussed before.

F. Benefits for the EON vs. dv/dt trade-off

Table III shows the simulated values in Cadence™ related to the points presented in Fig. 3 and Table II according to the experimental results obtained with the closed-loop systems. EON is calculated by simulations using the SPICE-compatible model of the transistor provided by the manufacturer for each GaN power device. Comparing points A, B and C, the maximum value of dvDS/dt was reduced by 61% with our technique, while increasing EON by only 46% (point C, closed-loop), whereas it would have increased by 100% with a larger gate resistor (point B) for the same dvDS/dt. This balance sheet must be further confirmed by EON measurements in our prototype. In this work, the drain current of the GaN transistor was not measured, as it would have increased the power loop parasitic inductance and therefore limited our capability to show a very fast active gate control.

G. Effect of the closed-loop control in the frequency domain

The experimental data for vDS(t) for the turn-on, turn-off, ON and OFF-states measured with the double pulse method are merged into a periodic signal, with a 1 MHz switching frequency and a duty cycle of 0.5. The Fourier transform of such a vDS(t) signal is shown in Fig. 14 and Fig. 15 for 48 V and 400 V applications, respectively, for both the open-loop and closed-loop controls. An analytical expression for the expected attenuation KdB(G20) at high frequency is provided by [START_REF] Kim | Common Mode Noise Analysis for Cascaded Boost Converter With Silicon Carbide Devices[END_REF]. Consequently, for the reduction in the peak dv/dt during turn-on with the closed-loop control, the vDS spectrum is reduced at high frequency, e.g., 13 dBµV lower at 100 MHz (48 V application, Fig. 14) or 7.6 dBµV at 100 MHz (400 V application, Fig. 15). This is a clear advantage of the AGD for reducing the high-frequency voltage content of the switching nodes with fewer switching losses compared to a classical adjustment of the gate resistor. II.

IV. CONCLUSION

While the typical fall times for GaN HEMTs are as low as a few nanoseconds in 48 V and 400 V applications, it is quite challenging to achieve a closed-loop feedback from the high- *Similar points as defined in Fig. 3 and Fig. 4 for peak dv/dt values. or variable gate resistors), switching losses are reduced for the same level of dv/dt reduction. The AGD showed a clear reduction in the peak dv/dt in 400 V and 48 V applications from -175 V/ns to -120 V/ns and from -15 V/ns to -6.3 V/ns, respectively.

To achieve this active control with extremely fast GaN devices, the response time of the feedback loop ranges between 290 ps and 640 ps (gain and bias dependent). Since the technique used here is based on the use of active devices, the feedback gain can be further adapted to comply with system-level considerations (e.g., best trade-off between switching losses vs. EMI). As a future work, EMI radiative measurements will be considered to confirm the benefits of the AGD.

V. APPENDIX Fig. 18. Measurement of the feedback loop delay (TD) for a current mirror with a gain of 10 and without a biasing current (ibias) (case GS66508T vHVdc=300 V).

Fig. 1 .

 1 Fig. 1. Transistor-level schematic of the CMOS gate driver with a dv/dt feedback control loop for turn-on control.Applying Kirchhoff's law at the gate node, the dvDS/dt reduction is proportional to the feedback current iFB. The following expression is obtained (valid as long as there is a current flowing through CS with iFB < iRG for stable operation, and a constant vM voltage on the dv/dt sequence:

Fig. 2 .

 2 Fig. 2. Theoretical waveforms showing the influence of the feedback loop time delay TD. iRGM is the current provided by the driver to the power transistor during the dv/dt event.

Fig. 3 .

 3 Fig. 3. Trade-off EON vs dv/dt as a function of RG (solid line) or closed-loop gain G (dashed line) values for a constant bus voltage, load current and temperature.The proposed method aims to reach the point C without increasing the external gate resistor RG.

Fig. 4 .

 4 Fig. 4. Waveforms with different values of dv/dt and di/dt for the operating points A, B and C. The saved energy is due to the reduction of dv/dt without changing di/dt.

Fig. 5 .

 5 Fig. 5. Waveforms for the voltages and currents of the current mirrors between times t2 and t3 (where CGp and CGn are respectively the total amount of parasitic capacitance viewed at the gate of M1 and M3). The feedback loop delay is detailed and expressed as TD(50%)=tE-t2.

Fig. 6 .

 6 Fig. 6. Simulation waveforms for (a) vDS, (b) vGS, (c) iG and (d) iD with (case C) and without (case A) the proposed method, including estimated PCB parasitic elements; (d) also shows a benefical effect of reduction in overcurrent (iD) during turn-on that is also provided by the proposed method. Case study for the 48 V application.

Fig. 7 .

 7 Fig. 7. Schematics and optical microscope pictures of the CMOS-integrated pF-range HV capacitors.

Fig. 8 .

 8 Fig. 8. Prototypes for a double-pulse test-bench with the proposed dv/dt control circuit.

  ("effect 2") where iD(t) and vGS(t) are linked by the transconductance of the GaN transistor in this operation state. Reducing the drain overcurrent and gate overvoltage before the Miller plateau is a clear proof of the ultrafast closed-loop control. Due to the AGD, the classical design trade-offs in operating conditions and reliability issues are clearly pushed forward.

Fig. 9 .

 9 Fig. 9. Measured vDS(t) and vGS(t) waveforms for open-loop (without the proposed method) and closed-loop (with the proposed method) controls.

Fig. 10 .

 10 Fig. 10. Measured vGS(t) for open-loop (without the proposed method) and closed-loop controls with mirror gains equal to 10 and 50.

Fig. 11 .

 11 Fig. 11. Measured and simulated waveforms vDS(t) and vGS(t) for open-loop and closed-loop controls using a current mirror with gain of G=50. A prebiasing current of 150 μA is used in this measurement.

Fig. 12 .

 12 Fig. 12. Measured vDS(t) waveforms for open-loop (without the proposed method) and closed-loop (with the proposed method) controls for 650 V GS66508T GaN transistors. ibias=320 µA.

Fig. 13 .

 13 Fig. 13. Measured vDS(t) waveforms with an embedded sensing capacitor CS and without an ibias current for this measurement.

Fig. 14 .

 14 Fig. 14. vDS spectrum with open and closed-loop during turn-on calculated from data measured for the EPC transistor with all the parameters in TableII.

Fig. 15 .

 15 Fig. 15. vDS spectrum with open and closed-loop during turn-on calculated from data measured for the GaN Systems 650 V transistor with all the parameters inTable II.voltage drain to the low-voltage gate node. In this context, an ultrafast method to actively control the dv/dt rate of the GaN HEMT drain-source voltage during turn-on is proposed and experimentally demonstrated. The key challenges are to achieve a subnanosecond delay for the feedback loop and to integrate all active and passive devices within a CMOS gate driver. Here, a CMOS AGD was designed, characterized and further implemented with 100 V and 650 V GaN transistors.The CMOS AGD is based on a standard low-voltage CMOS technology. Due to the AGD, the dv/dt sequence can be actively tuned, without modifying the di/dt sequence. The Miller plateau is then extended, with benefits on reliability consideration with a lower capacitive drain overcurrent and gate overvoltage during the active gate driving. Compared to classical methods (e.g., fixed

Fig. 16 and

 16 Fig.[START_REF] Reusch | Evaluation of gate drive overvoltage management methods for enhancement mode gallium nitride transistors[END_REF] and Fig 17 shows that the system proposed in this paper will not affect the turn-off behavior because the discharge current of CS will pass through the body diode of M1. Fig.18shows the feedback loop delay measured by connecting the current mirror input to the drain of the power device (for normal operation) and its output to a 14.7 Ω resistor to vDRV. The potential at the output of the current mirror (M4 Drain potential) is referred to as vout_M in the figure.

Fig. 16 .

 16 Fig. 16. Measured vDS(t) and vGS(t) waveforms for open-loop (without the proposed method) and closed-loop (with the proposed method) for a turn-off event (case EPC2001C vHVdc =50 V).

Fig. 17

 17 Fig. 17. The behavior of the system during the turn-off event. (a) Theoretical waveforms during turn-off, (b) the discharge path of CS capacitor during turn-off

  Fig. 17. The behavior of the system during the turn-off event. (a) Theoretical waveforms during turn-off, (b) the discharge path of CS capacitor during turn-off event and (c) simulation showing the feedback system will not source a current (iFB) during a turn-off event.

TABLE I DIMENSIONING

 I OF CMOS TRANSISTORS WIDTH

		Type	Key consideration to fix Width/Length
	M1	PMOS	W1 fixed by minimum vinM voltage at
			the highest iCs= Cs*Max(dvDS/dt), saturation
			regime
	M2	PMOS	W2=Gp × W1
	M3	NMOS	W3 is fixed to obtain vGSn=vdrv/2 for
			the highest iCs, saturation regime
	M4	NMOS	W4=Gn × W3, where G=Gp × Gn
	M5	PMOS	W5 is fixed by the maximum source current for
			the GaN transistor, saturation regime
	M6	NMOS	W6 is fixed by the maximum sink current for the
			GaN transistor, saturation regime
	*Note all PMOSs and NMOSs used have a vDSmax and vGSmax = 5 V
	and a length set to minimum.

ACKNOWLEDGMENTS

The authors would like to thank B. Lantin, D. Flumian, S. Vinnac, M.L. Locatelli and S. Dinculescu from Laplace lab for their contribution to the experimental results.

This research is partially funded by IRT Saint Exupéry grant EPowerDrive.


Aurore Voldoire

River to ocean models interpolation

, the method used to interpolate river discharges simulated by the river routing CTRIP model to the NEMO ocean model is not conservative locally. This document explains the reasons of non-local conservation and proposes a new interpolation method that ensures local conservation. The consequences of this new interpolation are assessed in long term piControl type simulations in which forcing are fixed to preindustrial levels. In these simulations, we observe a strong impact on sea-ice extent and volume in both hemispheres. This in turn impacts the large-scale ocean mass transport (AMOC and ACC). Nevertheless, the resulting Arctic sea-ice extent is unrealistically large and it raises the need to tune the model ones the new interpolation method is included. More investigations would require such a tuning to be done.

The new interpolation method can be applied to any other models given that the models ocean and river grids are dealt with in the OASIS coupler. This interpolation method could also be used for other quantities: biogenic fluxes, calving, etc. To this aim, it will be made available directly in OASIS future versions.

Root Causes of non local conservation

In CNRM-CM6-1 [START_REF] Voldoire | Evaluation of CMIP6 DECK Experiments Journal of Advances in Modeling Earth Systems[END_REF] and in its derived versions CNRM-ESM2-1 [START_REF] Séférian | Evaluation of CNRM Earth System Model , CNRM -ESM2 -1 : Role of Earth System Processes in Present -Day and Future Climate Journal of Advances in Modeling Earth Systems[END_REF] and CNRM-CM6-HR, the interpolation method used to interpolate river discharge from the river routing model TRIIP to the ocean model NEMO has been chosen among the available methods in OASIS [START_REF] Craig | Development and performance of a new version of the OASIS coupler, OASIS3-MCT 3.0[END_REF]. There was not any interpolation method very appropriate for this type of remapping, so we used the simple method of distance-weighted interpolation. The conservative remapping was not appropriate since river discharge does not span the entire NEMO ocean grid points. The distance weighted interpolation method was thought to be less erroneous since outflow were distributed to ocean grid point closed to the river bank and since it takes into account the distance between source and target grid points.

Respective model areas of grid points are not taken into account

However, the area of TRIP (0.5 • resolution) and NEMO (ORCA1 grid, 1 • resolution) grid points are one order magnitude different (Fig. 1). Given that distance-weighted does not take into account the area of source-target grid points, this remapping method does not conserve the amount of water exchanged that are provided by TRIP in kg/m 2 . The integral of this quantity should be conserved (ie flux * area).

The total area of river discharge grid points in TRIP is 7 106 km 2 , whereas it is spread over 64 106km 2 on the NEMO grid. There is a large mismatch in between these quantities. We could reduce the mismatch by increasing the number of masqued grid points on the ocean NEMO grid. The mismatch would also been reduced if the resolution of the two grids were closer. Such methods would reduce the local non conservation but would not ensure a perfect conservation.

Non coastal river bank

In the TRIP grid, there are river bank that are not closed to the sea. For instance, there are many river bank over central Eurasia. These river discharges correspond to river discharges to small lakes. The water mass budget of these lakes is not dealt with in the current version of CNRM-CM6-1. In the OASIS distance-weighted interpolation algorithm, these grid points does not have an identified neighbour in the target ocean grid (Fig. 2), even if 10 neighbours are searched for (Fig 2b). This problem would also appear for bilinear or conservative interpolations. Thwater mass should be taken into account in the CNRM-CM6-1 system to properly close the water budget.

Therefore, in CNRM-CM6-1, there are 2 steps for the interpolation:

• remapping following a distance-weighted interpolation (DISTWGT OASIS) with only one neighbour

• global conservation procedure to ensure a global conservation of the water mass coming from the TRIP river model.

As we only take one neighbour in the first step, the number of river discharge point not taken into account during the first step is large (Fig. 2a). Note that even if we had taken 10 neighbours, the number of unused grid points would remain important.

Effects on local conservation

The TRIP simulated mean river outflow over the Amazon region (Fig. 3a, green bars) is systematically larger than the river outflow received by the ocean model (blue bars), whatever month considered. This is reversed over the south Greenland region (Fig. 3b). If we consider the globe (Fig. 3c), the amount of water received by the ocean model corresponds to the amount of water sent by the TRIP river model. However, due to the difference in mean area, the amount of water on the ocean grid after the first step, ie, the distance-weighted interpolation is dramatically overestimated. This is partly compensated by the non coastal river outflow not taken into account during this first step. This means that the error would have probably been larger if all river discharge grid points were taken into account. The ratio applied to conserve the global mean is thus large and the resulting regional outflow is severely modified. This ratio is indeed the same for all regions but depending on the error made during the first step of interpolation, this results in regions of underestimation and regions of overestimation of the river discharge.

OASIS interpolate these water masses as fluxes, ie the local values are relatively consistent between the two grids (figure 4). However, the total water mass is very different depending on the grid : 98 tons are simulated by TRIP over the Amazon and only 35 tons are received on the NEMO grid over the same region.

2 New method proposed

Description of the interpolation method

The interpolation should consider the water mass integrated over each grid points rather than the water mass flux and there is the need to take into account properly the "inland" river outflow. In general, interpolations in OASIS are written so as to provide a value on each unmasked target grid points. The idea is that the target model needs a value on each unmasked grid points. Here, to be appropriate, the new interpolation method should consider all input grid points and we do not need absolutely to get a value on each unmasked target grid points. The question is thus reversed: we take the interpolation links from a reverse interpolation distance-weighted from the ocean grid to the river grid. This allows to know for each river discharge grid points one (or several neighbours) in the ocean grid and there is no river discharge grid points unsused. Note that this means that there can be several ocean grid points associated to one river grid point, the resulting water mass flux to the nemo grid points can be written :

F nemo = i F trip (i) * area trip (i)/area nemo (1)
and the new weights are calculated following :

ww(i) = aire(i)/aire nemo (2)
In the case of using a n-neighbours distance weighted interpolation, then the effective area should take into account the number of neighbours effectively used for each river grid points :

area ef f trip (i) = area trip (i)/nneighbours ef f (3)

Offline application to CNRM-CM6-1 outputs

Here, the new interpolation method is applied to TRIP outputs taken from a piControl CMIP6 simulation, and provides a new field on the NEMO ocean grid. As expected, the total mass of water over the domain is conserved. Over the amazon region, the results is close to 98 tons (figure 5). The small differences obtained arise from the fact that the domains considered are not "closed", ie there are river banks close to the northern border of the domain (Orinoco river) that partly spread over ocean grid points of the region. This also explains that the mismatch is larger when more neighbours are taken into account which means that more neighbours of the Orinoco river are in the region considered and thus more water from this river ends in the local domain. By looking at a closed domain like the Island coast, we have assessed that the local conservation is obtained (not shown). Figure 6 confirms the local conservation over the annual cycle for both regions. The choice of the number of neighbours remains subjective, more neighbours are taken, more the flux is spread over the ocean and less there is a risk of numerical explosion in the ocean model in case of strong outflow.

Inland river discharge management

The new interpolation method remains problematic for inland river outflows. For these points, the closer ocean grid point can be very far from the river outflow and it would be unrealistic to discharge this water mass on such localised places. In the TRIP river atlas, the river outflow grid points are provided following two categories, the second one corresponds to these inland outflows. To limit the problem, we can thus apply a different treatment to these outflow regions. Figure 7 is an updated version of figure 2 in which inland outflow grid points which do not have any neighbours are coloured green. In this new figure, the number of red grid points, ie coastal river outflow according to TRIP but no neighbour using the old method, is drastically reduced and most of them are closed to the ocean so we can rely on the new interpolation method to deal with them correctly. Note however, that there are still few inland grid points (over east Africa for instance). This means that we may not avoid totally some spurious effects where these inland outflow will be spread on ocean coastal grid points.

Concerning inland river discharge, as the objective is mainly to close the water budget of the coupled system and not to spread this amount of water in spurious regions, we can spread the total amount of water provided by these grid points over the whole ocean, as is already done for the lake water budget. Spread over the ocean, this represent a very small water flux locally that should have a negligible effect. This allows to close the water budget without introducing a spurious spatialisation. 3 Impact of the new method 3.1 Experiments performed 3 sensitivity experiments have been performed based on the CMIP6 piControl simulation with CNRM-CM6-1 to assess the impact of the new treatment of the coupling between rivers and ocean:

• interp n10: new interpolation method using 10 neighbours (each river grid points has 10 neighbours in the ocean)

• interp n1: new interpolation method using 1 neighbour

• all changes: apply a different treatment for river discharge depending on its location (inland or coastal) and interpolation with the new method with one neighbour for the coastal discharge. In this simulation, there is also a new land-sea mask introduced in the atmospheric-surface model to better match the ocean model land-sea mask and avoid mismatches. This feature has been developped for CMIP6 but was not valided anough to be activated in CNRM-CM6-1, it is only activated in CNRM-CM6-HR.

For all these experiments, the reference simulation is the piControl CNRM-CM6-1 simulations published for CMIP6 in which there is no local conservation (old interpolation method). All simulations use constant greenhouse gases and aerosol forcings representative of the preindustrial era as provided for CMIP6 and all share the same equilibrated initial state.

Simulation interp n10 was the first test done and has allowed to validate the interpolation method ensuring no numerical explosion would happen. Using one neighbour appeared less questionable scientifically. As there was not any numerical problem using only one neighbour, it has been decided to extend only interp n1. Finally, interp n10 has been run over 150 years, whereas interp n1 and all changes experiments are 300 years long.

Results

Impact on the global mean climate

Figure 8 shows the time series of several key quantities summarising the global mean climate of these simulations. The impact of the change in river-ocean coupling on global mean temperature (Fig. 11a) is similar in all three sensitivity experiments. There is a decrease of temperature over the first 50 years then a weak warming tendency is observed but the mean temperature remains colder than in the reference simulation even after 300 years for interp n1 et all changes. interp n10 is shorter but its evolution is similar to the others. The Arctic sea-ice volume is larger in all three sensitivity experiments (Fig. 11b). On the contrary, the impact on the Antarctic sea-ice volume is negligible in interp n1 and interp n10 whereas there is a net increase in all changes. The origin of this difference are further explained in section 3.2.3. The impacts on the large-scale ocean circulation are consistent with the sea-ice changes. In all three sensitivity experiments, we observe a strong weakening of the mean Atlantic Meridional Overturning Circulation (AMOC, Fig. 11d) that stabilizes after 70 years of simulation to 11.5 Sv. The large AMOC low-frequency variability observed in the reference experiment nearly disappears. The AMOC seems less stable in all changes, but a longer simulation would be necessary to confirm this feature. The impact on the Antarctic Circumpolar Circulation (ACC, Fig. 11e) differs in between the sensitivity experiments. Consistently with the southern hemisphere sea-ice volume changes, there is a large increase of the ACC only in all changes where it reaches 117Sv on average over the last 50 years whereas it is 110Sv in the other experiments and in the reference experiment. In the following, we focus on the all changes experiment in which there are impacts on the sea-ice volume in both hemispheres.

Impacts on the Arctic region

Figure 9 shows the sea-ice volume in the Arctic in march (the month of maximum extension). The sea-ice cover is now over-estimated over northern Atlantic and Pacific. Such an extension limits the deep water formation in these regions. The change is even drastic in the Labrador Sea (Fig. 9d-e) where in the all changes experiment, the annual maximum mixed layer depth is reduced from more than 500 m to 100 m. The change in sea-ice and mixed layer depth are very similar in interp n1. Thus, this reduction in deep water formation in the region probably explains the large AMOC weakening obtained in the sensivity experiments. As seen on figure 6b, the impact of the new interpolation method on the local river discharge is large particularly in winter. This probably explains a larger sea-ice extent. As the Arctic sea-ice extension obtained is unrealistic, this points out that sea-ice tuning made for the reference experiment to reach a realistic sea-ice extent is not appropriate in the sensitivity experiment. A new tuning would be necessary to better match with the observed sea-ice extent.

Impact on the Antarctic region

The impact on the Antarctic sea-ice volume is more realistic than the Arctic sea-ice change, as is the increase in ACC. However, in this region, the impact is not similar in all three sensitivity experiments.

a) b) c) d) e) f)
Figure 10: Same as Fig. 9 for the Antartic with sea-ice volume in september.

As there is no impact in interp n1 and interp n10, this indicates that it is not the interpolation method which is at play to explain the different sea-ice cover.

To better understand what happens in the austral ocean, Figure 11 shows the evolution of the water fluxes south of 60S. On coastal grid points, the river discharge simulated by TRIP is weaker in the all changes experiment than in other experiments mainly due to a reduction of TRIP river runoff on Antarctica (Fig. 11a). On this figure, the dashed line indicates the amount of water that originates from inland river discharge (a uniform value applied all over the ocean that originates from all inland river discharge grid points). This flux is much weaker than the coastal discharge around Antarctica and does not greatly impacts the coastal runoff. Now, if we consider the budget over all ocean grid points south of 60S (Fig. 11b), the water flux from rivers is higher in the all changes experiment than in the others. This is due to the integration of the global inland river discharge over this large domain which results in a large contribution relative to the regional coastal runoffs that are very weak aroud Antarctica. Indeed, in all other experiments, the river discharge flux is zero over non coastal grid points. Even if the value is very weak on all grdi points in the all changes experiment (7.5.10 -3 kg.m -2 .d -1 ), integrated over the whole ocean surface, this flux is higher than the regional coastal river discharge. However, this remains a small contribution to the surface water budget over open ocean south of 60S since the iceberg flux represents 0.3kg.m -2 .d -1 in the same region, this is one order of magnitude higher.

The net water flux received at the ocean surface (Fig. 11c) is not significantly changed over the region. This means that the difference comes from the geographical distribution of the river water fluxes. Figure (11d) shows the difference in annual mean river discharge between interp n1 and all changes experiments and picture the reduction in coastal water flux around Antarctica, without a clear regional pattern. To summarize, the difference between interp n1 and all changes comes from the way the inland river outflow are distributed over the ocean. In interp n1, it is concentrated on coastal grid points whereas in all changes it is spread out over a large region. This raises the sensitivity of the Antarctic sea-ice and ACC to fresh water fluxes treatment in the region.

It could be raised that the change in behavior is due to the land-sea mask change. The land-sea mask change could impact the all changes simulation via an initial chock that would modify irreversibly the large-scale ocean circulation. In the all changes experiment, the ocean is in equilibrium and a shock could only reflect a disequilibrium in the land surface water content. To check this possibility, an additional experiment has been run in which the initial land water (including snow) reservoirs are better initialised. In this experiment, the large-scale ocean circulation is similarly impacted as in the all changes experiment, confirming the role of the design of the river-ocean coupling in explaining the difference in Antarctic seaice cover.

Conclusion

A new way to couple river discharges to ocean is proposed and rely on two new features:

• implementation of a new interpolation method from the TRIP river model grid to the NEMO ocean grid to ensure local conservation of water. This new method is independent of the models used so can be useful in other models and applied to other coupling fields (such as calving or geochemical fluxes). The method can be adapted to any model grid supported by the OASIS coupler. The OASIS development team will include this new interpolation method in a future version of OASIS. This feature is very easy to implement, there is only to change the interpolation weights file without model code change.

• separate treatment of coastal river discharges and inland river discharges from TRIP: use of the new interpolation method for coastal river discharges and uniform spreading over the ocean for inland river discharges. This second feature requires modification of TRIP and NEMO codes as well as the addition of a new coupling field to be indicated in the OASIS nameliste file.

Using the new interpolation method, the local conservation of river discharges is assessed on long term control simulations. These changes have large impacts on the sea-ice volume and large-scale ocean circulation. The new interpolation method modifies significantly the extent of the Arctic sea-ice and the deep water formation in the northern Atlantic. The separate treatment of coastal and inland river discharges has a clear impact on the Antarctic sea-ice by limiting the amount of fresh water entering the ocean along the coast. These sensitivity experiments confirm that the treatment of river discharge is an important feature in climate models that has a large impact on the mean climate. This coupling should be implemented carefully. This new method will be implemented in future versions of CNRM-CM along with a new tuning of the sea-ice properties.

Figure 1 :

 1 Figure 1: Area of non masqued points for the river model TRIP grid (left) and for the NEMO ocean model grid (right) in 10 3 km 2

Figure 2 :Figure 3 :

 23 Figure 2: Number of neighbours in the NEMO ocean grid for each river bank grid point. In blue, the TRIP grid point has a neighbour in the target ocean grid, in red, no neighbour is found. a) Left panel is when interpolation is based on only one neighbour, b) right panel is based on 10 neighboors interpolation.

Figure 4 :

 4 Figure 4: Water mass flux sent at each TRIP river discharge grid points (top) and water mass received by the ocean NEMO model (bottom) over the Amazon region (left) and the south Greenland region (right). The title of each plot indicates the total water mass (in kg) integrated over the region considered.

Figure 5 :Figure 6 :Figure 7 :

 567 Figure 5: Water mass flux sent at each TRIP river discharge grid points (top) and water mass received by the ocean NEMO model using the new interpolation method with one neighbour (middle) and 10 neighbours (bottom) over the Amazon region (left) and the south Greenland region (right). The title of each plot indicates the total water mass (in kg) integrated over the region considered .

Figure 8 :Figure 9 :

 89 Figure 8: Evolution of the annual mean a) global temperature, b) Arctic sea-ice volume, c) Antarctic sea-ice volume d) Atlantic Meridional Overturning Circulation (AMOC) at 26 • N and e) Antarctic Circumpolar Circulation (ACC) for the reference piControl CMIP6 experiment (black) and sensitivity experiments interp n10 (orange), interp n1 (blue) and all changes (red). The bold line represents the low-pass filtered time series with 10 years cut-off.

Figure 11 :Figure 13 :Figure 15 :

 111315 Figure 11: Evolution of a) the river discharge (kg.m -2 .d -1 ) received on the NEMO ocean grid averaged along coastal points south of 60S b) the river discharge received on the NEMO grid averaged over all ocean grids points south of 60S, on a) and b) the dashed line indicates the flux received from non coastal grid points as a uniform value over the ocean surface for the all changes experiment, c) net water flux received at the ocean surface averaged south of 60S for the reference piControl CMIP6 experiment (black) and sensitivity experiments interp n10 (orange), interp n1 (blue) and all changes (red). The bold line represents the low-pass filtered time series with 10 years cut-off. d) Annual mean river discharge anomaly between simulations all changes and interp n1 averaged over 2100-2149 (the last 50 years of each simulation). Dots indicate significant changes at the 95% significance level. 13


Jean-Yves Hogrel
email: jy.hogrel@institut-myologie.org

PhD Valérie Decostre

PhD Isabelle Ledoux

MSc Marie De Antonio

MSc Erik H Niks

MD Imelda De Groot

MD Volker Straub

MD Francesco Muntoni

PhD Valeria Ricotti

MD Thomas Voit

PhD Andreea Seferian

MD Teresa Gidaro

PhD Laurent Servais

Normalized grip strength is a sensitive outcome measure through all stages of Duchenne Muscular Dystrophy

Keywords: Duchenne muscular dystrophy, grip strength, outcome measures

Objective The main aim was to explore the changes in hand-grip strength in patients with Duchenne muscular dystrophy (DMD) aged from 5 to 29 years. Secondary aims were to test the effect of mutation, ambulatory status and glucocorticoid use on grip strength and its changes over time and to compute the number of subjects needed for a clinical trial to stabilize grip strength.

Methods

The analysis was performed on data collected during five international natural history studies on a cohort of DMD patients. Two hundred and two patients with genetically proven DMD were pooled from five different natural history studies. Excepting 13 patients with only one visit, the mean duration of follow-up was 2.2 ±1.6 years. A total of 977 measurement points were collected.

Grip strength was measured on the dominant side with a high precision dynamometer. The analysis was performed using absolute values and normalized values expressed in percentage of predicted values for age.

Results

For absolute values, grip strength typically increased in ambulatory boys and decreased in non-ambulatory patients. However, when normalized, grip strength was already reduced at age 5 years and thereafter continued to fall away from normal values. The weaker the patients, the less strength they are prone to lose over again.

Interpretation Grip strength constitutes a sensitive and continuous outcome measure that can be used across all stages of DMD. Its measurement is easy to standardized, can be used in ambulatory and non-ambulatory patients and does not present any floor or ceiling effect. It is thus attractive as an outcome measure in therapeutic trials.

Introduction

Duchenne Muscular Dystrophy (DMD) is a degenerative genetic muscle disease in which mutations in the dystrophin gene lead to muscle fiber degeneration and gradual replacement of muscle by fat and connective tissue. The clinical onset of symptoms usually appears in the lower limbs of boys before 4 years of age. DMD weakness typically affects proximal muscles first, with loss of distal muscle strength and function later. Muscles of the hands are thus affected later in the disease course, however also become progressively weakened and eventually paralyzed in the second and third decades of life. Despite the importance in maintaining strength and independent function as long as possible for young men with DMD [START_REF] Wagner | Assessment of hand function in Duchenne muscular dystrophy[END_REF], only few recent studies have focused on the upper limbs of DMD patients [START_REF] Hogrel | Longitudinal functional and NMR assessment of upper limbs in Duchenne muscular dystrophy[END_REF][START_REF] Mayhew | Development of the Performance of the Upper Limb module for Duchenne muscular dystrophy[END_REF][START_REF] Pane | Upper limb function in Duchenne muscular dystrophy: 24 month longitudinal data[END_REF][START_REF] Pane | Reliability of the Performance of Upper Limb assessment in Duchenne muscular dystrophy[END_REF][START_REF] Pizzato | Longitudinal assessment of grip strength using bulb dynamometer in Duchenne Muscular Dystrophy[END_REF]. Hand and arm function is indeed associated with many domains of daily life activities (physical performance such as holding a glass, writing, turning a door knob, but also psychological and social functioning), so a key element in improving these may be to preserve arm function [START_REF] Klingels | Development of a patient-reported outcome measure for upper limb function in Duchenne muscular dystrophy: DMD Upper Limb PROM[END_REF][START_REF] Lue | Quality of life of patients with Duchenne muscular dystrophy: from adolescence to young men[END_REF].

Grip strength can be impaired from a young age in DMD, even long before the loss of ambulation [START_REF] Pizzato | Longitudinal assessment of grip strength using bulb dynamometer in Duchenne Muscular Dystrophy[END_REF][START_REF] Wagner | Assessment of hand function in Duchenne muscular dystrophy[END_REF]. It is correlated with the degree of physical disability [START_REF] Mattar | Hand weakness in Duchenne muscular dystrophy and its relation to physical disability[END_REF][START_REF] Seferian | Upper limb strength and function changes during a one-year follow-up in non-ambulant patients with Duchenne Muscular Dystrophy: an observational multicenter trial[END_REF], is sensitive to change in the nonambulatory DMD population [START_REF] Seferian | Upper limb strength and function changes during a one-year follow-up in non-ambulant patients with Duchenne Muscular Dystrophy: an observational multicenter trial[END_REF] and presents excellent reliability [START_REF] Servais | Innovative methods to assess upper limb strength and function in non-ambulant Duchenne patients[END_REF]. Maximal grip strength (MGS) measured with an appropriate handgrip dynamometer is a continuous variable that does not present any floor or ceiling effects in DMD [START_REF] Servais | Innovative methods to assess upper limb strength and function in non-ambulant Duchenne patients[END_REF]. However, these results have been observed on a rather limited number of patients and on a limited age range. Furthermore, reporting MGS as an absolute value rather than as a percentage of predicted values induces a confounding interference with physiological growth [START_REF] Hogrel | Longitudinal functional and NMR assessment of upper limbs in Duchenne muscular dystrophy[END_REF]. Indeed stature has been shown to be the main predictor of muscle strength during normal childhood development [START_REF] Hogrel | Stature is an essential predictor of muscle strength in children[END_REF], with a smaller stature yielding lower strength. As height influences stride length, hence the distance walked within 6 minutes. We hypothesized that expressing MGS in percentage of predicted values rather than in absolute values could increase sensitivity to change by reducing the confounding factors of growth and maturation.

The main aim of this study was to explore the progression of maximal grip strength during the course of DMD over a large range of age. Secondary aims were to test the effect of ambulatory status, glucocorticoid use and mutation on MGS and to compute the number of subjects needed for a clinical trial aiming to stabilize grip strength.

Methods

Study design

The results of MGS were gathered from five Ethical Review Board-approved natural history studies in DMD conducted between 2010 and 2019 ( All patients or legal guardians for patients younger than 18 years of age gave written informed consent prior to participation in the studies.

Measurement procedure

MGS was measured using the MyoGrip device [START_REF] Servais | Innovative methods to assess upper limb strength and function in non-ambulant Duchenne patients[END_REF] (Figure 1) every 6 or 12 months depending on the study protocol. The Myogrip dynamometer is an electronic device specifically developed for measuring isometric grip strength in very weak patients, but which can also be used in healthy subjects. It measures forces in kilograms (kg) from 0 to 90 kg with a resolution of 0.01 kg and an accuracy of 50 g over the whole range of measurement. Handle size is adjustable in a continuous way in order to fit at best the hand size of the subjects.

The physiotherapists of all centers were trained to use the same standardized operating procedure.

All tests were performed with patients seated on a chair or in their wheelchair facing a table with the forearm placed on the table or on the wheelchair shelf. Before each test, patients were given a description of the grip task, a demonstration of the movement required and advice on maintaining correct practice. If standard upper limb position described by the protocol could not be maintained because of patient contractures, alternative positions were allowed. Trials were carried out with strong verbal encouragement asking the patients to provide maximal voluntary isometric contractions for 3 seconds. A rest period of about 30 seconds was respected between the trials. The trials were considered valid or not by the physiotherapist relying on several factors (compensations, motivation, understanding, positioning...). If the difference between two measurements was lower than 10% of the highest, the highest was accepted. If not, a subsequent measurement was made until two trials were within 10% with a maximum of 5 trials. The maximal value of all valid trials was kept for further analyses.

In two of the protocols (ULENAP and pre-Acti), two visits were performed within 14 days in order to assess the test-retest reliability of grip measurements.

Statistical analysis

MGS on the dominant side (defined as the writing/drawing hand) was analyzed using both absolute values (in kg) and normalized values (in % of predicted values for age). Equations of predictive models using chronological age were computed from previous data collected in healthy controls [START_REF] Hogrel | Grip strength measured by high precision dynamometry in healthy subjects from 5 to 80 years[END_REF][START_REF] Li | Predicting maximal grip strength using hand circumference[END_REF][START_REF] Servais | Innovative methods to assess upper limb strength and function in non-ambulant Duchenne patients[END_REF] as following: before the age of 17 years: MGS = 3.40 EXP(0.1527 x age) and after the age of 17 years: MGS = 45.66 EXP(-0.001 x age). Patients were classified according to their genotype, ambulatory status at the time of inclusion and glucocorticoid status.

Test-retest reliability was assessed using an intraclass correlation coefficient (ICC) and a Bland-Altman representation.

Linear mixed effects models were used to assess trends in grip changes over time. Interactions were included separately in the model as fixed effects between time and ambulatory status, glucocorticoids use or mutations. Models were adjusted for age at inclusion. Sample size was calculated by simulation study in order to determine the number of subjects required for a placebo-controlled clinical trial in which stabilization of the MGS in the treated group over one year should be detected, with an alpha risk of 5%, and a power of 80%. Grip values were simulated using linear mixed model included age, time, group and the interaction between age and group. We assumed no differences of grip value at baseline, so the coefficient value for the group where equal to 0. Beta parameters were simulated from a Gaussian distribution using results provided by the linear mixed model. When grip strength was expressed in kg, the stabilization meant that the grip evolution over time of treated patient was equal to the grip evolution of healthy controls. When grip strength was expressed in % predicted values, the stabilization meant that the change was 0%. We assumed than the variability of the treated group was the same than the DMD population presented in this study.

Analyses were performed using R 3.3.1 software (R Foundation for Statistical Computing, Vienna, Austria). Statistical significance was set at 0.05.

Results

Population description

A total of 202 subjects (5.0-28.7 years) were included in this cohort study (see Table 1). At baseline, 92 patients were ambulatory and 110 were non-ambulatory. With the exception of 13 subjects who had only one visit, the mean follow-up duration was 2.2 ± 1.6 years (range: 0.04-6.53 years). A total of 977 measurement points was collected. Eighty-six ambulatory patients (93%) were treated with glucocorticoids, whilst only 53 non-ambulatory patients (48%) were. Fifty-nine patients had mutations amenable to exon skipping for exon 53, 28 for exon 44; 15 for exon 45, 25 for exon 51, 74 patients had other deletions (4 mutations amenable to exon skipping for exon 8, 3 for exon 43, 8 for exon 50, 3 for exon 52, 8 for exon 55 and 23 others) or other mutations (7 duplication, 2 insertion, 4 missense, 12 nonsense mutations), and 1 had an unknown mutation.

Grip strength measurement reliability

Test-retest reliability was assessed on 104 independent measurements (Figure 2). The intraclass correlation coefficient was 0.977.

Grip strength change during the life of DMD patients

Absolute values of MGS increased by 0.23 kg/year on average in ambulatory boys and decreased by -0.34 kg/year in non-ambulatory patients (Figure 3.A). When expressed as percentage of predicted values for age, MGS decreased in both groups (Figure 3.B). This decrease was significantly more important in ambulatory patients compared to non-ambulatory patients (-4.95 % points per year vs. -2.53 % points per year; p<0.001).

Effect of DMD mutation, corticosteroid treatment and ambulatory status on grip strength

Glucocorticoids had a positive effect on muscle strength since the subjects without glucocorticoids were 6.3% weaker than patients treated with glucocorticoids (p<0.001). However patients treated with glucocorticoids lost significantly more strength (significant difference of -2.84 % points per year, p<0.001).

Patients amenable to exon skipping 45, 51 and 53 were significantly weaker than patients amenable to exon skipping 44 (significant difference of 13.7%, 9.3% and 13.9%, respectively, p<0.05). However the latter group lost significantly more strength per year (-5.8 % points per year) than patients amenable to exon skipping 45 and 53 (significant difference of 3.0 % points per year and 2.7 % point per year, respectively).

Computation of the patient number needed for stabilizing grip strength during a therapeutic trial

Following the methodology specified in the Methods section, the number of patients per arm needed for a clinical trial is presented in Table 2.

Discussion

We showed that maximal grip strength expressed in percentage of predicted value counterbalances the cofounding effect of growth during childhood and can be used as continuous variable to measure the functional decline due to Duchenne muscular dystrophy across all stages of the disease. The analyses demonstrated the decrease of grip strength in a large population of DMD patients aged from 5 to 30 years compared to normal values. It is often suggested that upper limb function begins to deteriorate in DMD around the age of 9-12 years when assessed using scales [START_REF] Janssen | Patterns of decline in upper limb function of boys and men with DMD: an international survey[END_REF][START_REF] Jung | The correlation analysis of functional factors and age with duchenne muscular dystrophy[END_REF][START_REF] Pane | Reliability of the Performance of Upper Limb assessment in Duchenne muscular dystrophy[END_REF]. This statement is partly due to the ceiling effect of scales. The use of high precision dynamometry and normalized values clearly demonstrates that grip strength decline can be captured at a younger age, as early as 5 years of age, as already underlined in the CINRG longitudinal study cohort [START_REF] Bushby | Clinical outcome measures for trials in Duchenne muscular dystrophy: report from International Working Group meetings[END_REF] or other studies [START_REF] Pizzato | Longitudinal assessment of grip strength using bulb dynamometer in Duchenne Muscular Dystrophy[END_REF][START_REF] Wagner | Assessment of hand function in Duchenne muscular dystrophy[END_REF]. The changes in grip strength described in the present study are perfectly in line with those recently published on a part of the cohort by Ricotti et al [START_REF] Ricotti | Respiratory and upper limb function as outcome measures in ambulant and non-ambulant subjects with Duchenne muscular dystrophy: A prospective multicentre study[END_REF]. However, the clinical meaningfulness of these changes has yet to be established; for example, upper limb functional limitations are most likely not clinically significant at 5 years of age, since DMD boys have sufficient strength for daily tasks, as well as full range of motion and ability to compensate for their strength deficit. In the context of a clinical trial, the relatively well-preserved muscles could offer the opportunity to study the effect of disease modifying drugs by way of measuring a stabilization (or even an improvement) in strength in response to therapies, where scales may suffer from a ceiling or a floor effect.

The age-dependence of MGS changes suggests that its decline was inversely proportional to age. The weaker the patients, the less strength they are prone to lose over again. Similar exponential-like decrease have already been observed for other variables. For example, forced vital capacity, which is a variable generally expressed in percentage of predicted values, was also described as exponentially decreasing in DMD patients of equivalent ages [START_REF] Connolly | Outcome reliability in non-ambulatory boys/men with Duchenne muscular dystrophy[END_REF][START_REF] Kohler | Disability and survival in Duchenne muscular dystrophy[END_REF]. Outcome measures are generally presented in absolute values. The six-minute walk test (6MWT) has been the most widely used primary endpoint in therapeutic trials. The distance (in m) of the 6MWT is generally described as improving up to age of 7 due to maturation effect, before reaching a plateau and then declining [START_REF] Mazzone | 24 month longitudinal data in ambulant boys with Duchenne muscular dystrophy[END_REF]. This inversed Ushaped curve was also observed in MGS absolute values, where patients improved up to roughly 12 years and then decreased afterwards. A powerful way of minimizing the cofounding factors of growth and maturation is to express performance in percentage of predicted values for the considered variables [START_REF] Mcdonald | The 6-minute walk test and other endpoints in Duchenne muscular dystrophy: longitudinal natural history observations over 48 weeks from a multicenter study[END_REF]. This is particularly critical in children as they are growing [START_REF] Hogrel | Stature is an essential predictor of muscle strength in children[END_REF].

In this report, we chose to express the model only in terms of age, since it avoids a possible error of measurement in a multicenter setting, but more powerful predictive equations were obtained in controls using hand circumference. Further studies should include a consistent estimate of stature such as height, ulnar length or hand circumference, which has been shown to be a strong predictive determinant of MGS [START_REF] Hogrel | Grip strength measured by high precision dynamometry in healthy subjects from 5 to 80 years[END_REF]. It can be easily assessed even in wheelchair-bound patients with contractures using strict measurement procedures.

Many factors influence muscle strength measurement and may act as confounding factors: genetics (mutation, genetic modifiers), developmental factors (chronological age, growth, pubertal status, stature), symptomatology (contractures, cognitive status), neural factors (compensation abilities, motor strategy, neural plasticity), behavioral factors (psychological status, motivation, self-esteem), environmental factors (social and cultural background) and obviously standards of care and assessors. These factors may explain, at least partly, the large variability between DMD subjects. Indeed, grip strength can be very heterogeneous among patients (see for instance Figure 3 in Seferian et al [START_REF] Seferian | Upper limb strength and function changes during a one-year follow-up in non-ambulant patients with Duchenne Muscular Dystrophy: an observational multicenter trial[END_REF] or Figures 3 and4 in Connelly et al [START_REF] Connolly | Outcome reliability in non-ambulatory boys/men with Duchenne muscular dystrophy[END_REF]). The decline in MGS appeared however sensitive enough to detect a difference between exon 44 and exon 53 skippable patients, two genotypes that are known to be slightly less and more severe, respectively [START_REF] Servais | Non-Ambulant Duchenne Patients Theoretically Treatable by Exon 53 Skipping have Severe Phenotype[END_REF][START_REF] Van Den Bergen | Prolonged Ambulation in Duchenne Patients with a Mutation Amenable to Exon 44 Skipping[END_REF].

The European Medical Agency reported in their guidelines that "for total evidence of clinical efficacy an effect on motor function should be supported by an effect on muscle strength" [START_REF] Ema | Guideline on the clinical investigation of medicinal products for the treatment of Duchenne and Becker muscular dystrophy[END_REF]. Indeed the main function of a muscle is to contract, to produce a mechanical force, to make the movement possible and translate it into an action. This function is primarily impaired in neuromuscular disorders. The assessment of strength is thus a direct measure of the muscle capacity and is a key feature to follow during the natural course of the disease but more importantly during the possible recovery of the muscle capacity to generate force. Due to the fact that the data were gathered from several protocols, there was unfortunately no common functional scale to use before MGS, which is a limitation of the present work.

The constant relative decline of MGS in both ambulatory and non-ambulatory DMD subjects, the absence of floor and ceiling effects, the good reliability of the measurements, the possibility to standardize data acquisition and finally the direct link between muscle function and strength production [START_REF] Seferian | Upper limb strength and function changes during a one-year follow-up in non-ambulant patients with Duchenne Muscular Dystrophy: an observational multicenter trial[END_REF] makes maximal grip strength an attractive outcome measure for DMD trials. In particular the authors wish to personally thank Geneviève Laforet and Elisabeth Thomson (from Sarepta) and Géraldine Honnet (from Généthon). This research was also supported by the NIHR Great Ormond Street Hospital Biomedical Research Centre.

  Further work is needed to quantify minimally clinically meaningful change using functional scales and demonstrate positive changes during interventional studies. Acknowledgements: Grip strength data in Duchenne muscular dystrophy (DMD) using the MyoGrip device were gathered through several natural history studies in several sites (London, Newcastle, Leiden, Nijmegen and Paris). The ULENAP study was sponsored by the Institute of Myology and funded by the Association Française contre les Myopathies. The pre-U7 study was sponsored by Genethon. This project was supported by the AFM (Association Française contre les Myopathies) and by ADNA (Advanced Diagnostics for New Therapeutic Approaches), a program dedicated to personalized medicine, coordinated by the Institut Mérieux and supported by research and innovation aid from the French public agency, OSEO. The pre-Acti study was sponsored by the Institute of Myology and funded by the Association Française contre les Myopathies. The iMDEX natural history study was sponsored by each participating center and funded by the Association Française contre les Myopathies. The SRP-4053 study was sponsored by Sarepta. No funders were involved in data collection, analyses or interpretation or in the preparation of this paper. They all gave their agreement for the use of data.

Figures captionsFigure 1 .

 1 Figures captions

Figure 2 .

 2 Figure 2. Test-retest reliability assessed using ICC (A) and Bland-Altman plot (B).

Figure 3 .

 3 Figure 3. Grip strength change with age either expressed in absolute values (A) or in percentage of

Figure 1 Figure 2

 12 Figure 1

Figure 3

 3 Figure 3

Table 1 )

 1 in Paris (Institute of Myology), London (NIHR Great Ormond Street Biomedical Research Center), Newcastle (John Walton Muscular Dystrophy Research Center), Nijmegen (Radboud University Medical Center) and Leiden (Leiden University Medical Center). Molecular diagnosis of DMD was the only common inclusion criteria to all protocols.

We thank the patients and their families for their participation in the studies used in the present meta-analysis. The grip strength data have been acquired in different protocols by several physiotherapists. We acknowledge the dedicated work of Gwenn Ollivier, Aurélie Canal, Charlotte Lilien and Stéphanie Gilabert (Paris), Merel Jansen, Maaike Pelsma and Anke Langelaan (Nijmegen), Menno van der Holst (Leiden), Vic Selby and Jordan Butler (London), Michela Guglieri, Alexander Murphy and Anna Mayhew (Newcastle). We are also grateful to Amélie Moraux and Pauline Hivert for the management of the MyoGrip database and to Simone Birnbaum for thorough proofreading of the manuscript and text improvement.

The authors would like to pay tribute to the memory of Joana Pisco Domingos, suddenly deceased in early January 2018.

Author contributions:

Ethical standards

All studies have been approved by the appropriate ethics committee and have, therefore, been performed in accordance with the ethical standards laid down in the 1964 Declaration of Helsinki and its later amendments. All patients or legal guardians for patients younger than 18 years of age gave written informed consent prior to participation in the studies.