An Analytical Model of Dynamic Power Losses in eGaN HEMT Power Devices

In this work, we present an analytical model of dynamic power losses for enhancement-mode AlGaN/GaN high-electron-mobility transistor power devices (eGaN HEMTs). To build this new model, the dynamic on-resistance (Rdson) is first accurately extracted via our extraction circuit based on a double-diode isolation (DDI) method using a high operating frequency of up to 1 MHz and a large drain voltage of up to 600 V; thus, the unique problem of an increase in the dynamic Rdson is presented. Then, the impact of the current operation mode on the on/off transition time is evaluated via a dual-pulse-current-mode test (DPCT), including a discontinuous conduction mode (DCM) and a continuous conduction mode (CCM); thus, the transition time is revised for different current modes. Afterward, the discrepancy between the drain current and the real channel current is qualitative investigated using an external shunt capacitance (ESC) method; thus, the losses due to device parasitic capacitance are also taken into account. After these improvements, the dynamic model will be more compatible for eGaN HEMTs. Finally, the dynamic power losses calculated via this model are found to be in good agreement with the experimental results. Based on this model, we propose a superior solution with a quasi-resonant mode (QRM) to achieve lossless switching and accelerated switching speeds.


Introduction
Enhancement-mode AlGaN/GaN high-electron mobility transistor power devices (eGaN HEMTs) are the most promising candidates for use as next-generation power devices.In such devices, III-V materials have several merits due to their wide bandgap energy, high critical breakdown electric field, high electron mobility and capability [1,2], and polarization effect [3].Due to these advantages, a high-frequency (high-fs) converter operating in the range of 1-5 MHz based on eGaN HEMTs can be readily realized.Although high-fs operation can help to reduce the converter size, it will generate more challenges with respect to dynamic power loss.Thus, building an analytical dynamic power loss model for an eGaN-based high-fs switch becomes important for prototype application in circuit design.
Recently, some state-of-the-art dynamic power loss models for eGaN HEMTs have been proposed.Wang et al. developed two analytical loss models based on detailed parasitic parameters for high-voltage and low-voltage GaN eHEMTs [4,5].In these models, the gate charge (Q g ) and output charge (Q oss ), instead of the voltage-dependent capacitance, were used to improve the non-linear characteristics.However, the loss caused by output capacitance is not separately discussed in terms of a hard switch and soft switch.Shen et al. fully accounted for the effects of parasitic parameters and transconductance [6].Hou et al. and Guacci et al. investigated the loss caused by the output capacitance in a hard switch and soft switch using simulation methods rather than experimental methods [7,8].However, these models did not take into account the impact on device loss from some aspects, instead of fully evaluating it; thus, the results accuracy is affected.For example, the problem of increased losses caused by dynamic on-resistance (R dson ) is not discussed.
Chen et al. presented a complete analytical loss model for low-voltage eGaN HEMTs, for which a piecewise model was employed [9].Piecewise models are also usually used to evaluate the dynamic power losses for Si-and SiC-based metal-oxide-semiconductor field-effect transistors (MOSFETs) [10][11][12][13][14][15].These models are carefully considered and allow accurate evaluation of device power losses.However, these models fail to include sufficient consideration of the parasitic elements and merely focus on Si-based MOSFETs, but not on GaN HEMTs.In addition, the effect of current operation mode on device transition time and loss is not considered in all known device loss models.Therefore, these analytical models need to be modified for use on eGaN HEMTs to make a more comprehensive and accurate model.
To improve the dynamic power loss model of eGaN HEMTs, we propose three experimental methods according to the practical application of devices in high-fs circuits, such as the double-diode isolation (DDI) method, the dual-pulse-current-mode test (DPCT) method, and the external shunt capacitance (ESC) method.Then, the dynamic R dson is accurately extracted in a high operating frequency (fs) of up to 1 MHz and a high drain voltage up to 600 V; the effect of current operation mode on the transition time is revealed, and the effect of current operation mode on the device loss is discussed from the shape of operating waveforms in the circuit.As the real channel current (Ich) is qualitatively modified compared to the drain current (I drain ), we can directly test in the device drain side.Afterward, the dynamic power loss of eGaN HEMTs is carefully described via a modified 12-segment piecewise model.Finally, we propose a quasi-resonant mode (QRM) with a low off-state drain voltage (V ds_off ), a zero turn-on current, and a relatively large on-state peak current for a lossless design and fast transit speed in power switches.

Traditional Power Loss Model
In the piecewise model, the operating sequence of the device is shown in Figure 1.In particular, the device was usually connected in series using a choke or transformer in power switches; thus, the value of I sta indicated the current mode of the device.(I sta = 0) denoted the device operating in discontinuous conduction mode (DCM), while (I sta > 0) denoted the device operating in continuous conduction mode (CCM).Whether the device operated in CCM or DCM depends on the choke in series.As we know, in a high-frequency circuit, chokes follow the volt-second balance principle, that is, the starting current of the choke in each cycle must be equal to the end current.During the t on time when the device was switched on, the choke current rose under an applied forward voltage V1, the rise slope was V1/L, and L was the inductance of the choke; during the t off time when the device was switched off, the choke current fell under an applied reverse voltage V2, and the fall slope was V2/L.Therefore, the peak value of the choke current in each cycle was V1•t on /L, and the end current value was (V1•t on − V2•t off )/L.Then, according to the known values of V1 and V2, we could design the required L to make the device operate in CCM or DCM.
A traditional calculation formula for high-f s power losses of device is given as follows [16]: where I dson_rms is the on-state drain-source current in the root mean square (RMS) value, and K th is the temperature coefficients related to R dson .The first term in Equation ( 1) occurs in the crossing area of I ds and the V ds , while the second term is the output capacitor energy dissipated in the device during the turn-on transition.Then, the third and fourth terms are the conductive loss and driving loss, respectively.Equation ( 1) is approximate, as it does not take into account the problem of a dynamic R dson increase, the impact of I drain on the transition time, or the discrepancy between I drain and the real channel current.
Micromachines 2023, 14, x FOR PEER REVIEW A traditional calculation formula for high-fs power losses of device is given [16]: where Idson_rms is the on-state drain-source current in the root mean square (R and Kth is the temperature coefficients related to Rdson.The first term in Equation in the crossing area of Ids and the Vds, while the second term is the output capaci dissipated in the device during the turn-on transition.Then, the third and fo are the conductive loss and driving loss, respectively.Equation ( 1) is approxi does not take into account the problem of a dynamic Rdson increase, the impact the transition time, or the discrepancy between Idrain and the real channel curren

Experimental Circuit and Method
A switching circuit with a floating buck-boost topology was employed to a switching processes, as shown in Figure 2a.In this circuit, an HEMT device wa shown with a simple three-capacitor model that included the parasitic capacit and Cds.The pulse width modulation (PWM) was produced via a pulse generato Keysight Technologies, Inc., Santa Rosa, CA, USA) with a maximum PWM of 12 amplified using a gate driver (SI8271GB), which had a 1.8-ampere peak sour and a 4.0-ampere peak sink current, and D1 was selected as a SiC diode (C3D100 at 15 A/650 V, which was used to reduce the reverse recovery problem.The p sistor and parasitic inductor were ignored to simply study the important role o sitic capacitors at a relatively high-fs that is smaller than 30 MHz.Then, variou and PWM in DCM and CCM were applied to elucidate the switching process production of dynamic power losses. The part of Figure 2b marked with the light-yellow area shows our nove Rdson extraction circuit based on a double-diode isolation (DDI) method; the deta to configure, test and calculate this circuit can be obtained from Refs.[17][18][19].sign, the model of the gate driver was SI8271GB, and D1 and D2 (1 A/1 kV UF used in series to isolate the high off-state voltage of the eGaN HEMTs.Then, th Rdson of the eGaN HEMTs could be easily extracted.Diodes in series made it test the real-time forward voltage drop (VF) of D2 in a low-voltage range and estimate the VF of D1 in the same forward current.In addition, the diodes in seri

Experimental Circuit and Method
A switching circuit with a floating buck-boost topology was employed to analyze the switching processes, as shown in Figure 2a.In this circuit, an HEMT device was used and shown with a simple three-capacitor model that included the parasitic capacitors C gs , C gd and C ds .The pulse width modulation (PWM) was produced via a pulse generator (81150A, Keysight Technologies, Inc., Santa Rosa, CA, USA) with a maximum PWM of 120 MH, and amplified using a gate driver (SI8271GB), which had a 1.8-ampere peak source current and a 4.0-ampere peak sink current, and D 1 was selected as a SiC diode (C3D10065E) rated at 15 A/650 V, which was used to reduce the reverse recovery problem.The parasitic resistor and parasitic inductor were ignored to simply study the important role of the parasitic capacitors at a relatively high-f s that is smaller than 30 MHz.Then, various voltages and PWM in DCM and CCM were applied to elucidate the switching processes and the production of dynamic power losses.We built the above switching circuit and extraction circuit using one printed circui board (PCB), as shown in Figure 2b.The part of Figure 2b marked with the light-yellow area shows our novel dynamic R dson extraction circuit based on a double-diode isolation (DDI) method; the details on how to configure, test and calculate this circuit can be obtained from Refs.[17][18][19].In this design, the model of the gate driver was SI8271GB, and D 1 and D 2 (1 A/1 kV UF4007) were used in series to isolate the high off-state voltage of the eGaN HEMTs.Then, the dynamic R dson of the eGaN HEMTs could be easily extracted.Diodes in series made it possible to test the real-time forward voltage drop (V F ) of D 2 in a low-voltage range and precisely estimate the V F of D 1 in the same forward current.In addition, the diodes in series reduced the parasitic capacitor by half, which was very helpful to the high-f s response of the extraction circuit.We called this method the DDI method.Moreover, ZD 1 and D 3 were free-wheeling diodes, and ZD 1 was also a positive clamping diode.These two diodes were a general 5-volt Zener ZD 1 and a general small signal diode D 3 (1N4148) with 75 V/150 mA.All of the functional diodes, including D 1 , D 2 , ZD 1 and D 3 , were specially selected to have a very low parasitic capacitance, which improved the high-f s response of the extraction circuit to several MHz.I 1 was a constant-current source of only several mA, meaning that it could not produce a temperature problem and have an extra self-heating effect.I 1 consisted of a constant-current diode, which was actually a junction field transistor with a gate-source short connection.Therefore, I 1 could achieve an excellent constant current over a wide operating voltage range.R t provided a minimum load for I 1 and suppressed the voltage spike at point B. An isolated low-voltage probe (P2221 from Keysight Inc.) with a 1:1 attenuation could be used to test the V F of D 2 and the voltage at point B. The low-voltage probe with a 1:1 attenuation did not amplify the background noise and operate in a low-voltage range, meaning that it could obtain an improved test accuracy.
We built the above switching circuit and extraction circuit using one printed circuit board (PCB), as shown in Figure 2b.

Qualitative Method Used to Discover the Channel Behavior
Since we could not directly perform the measurements inside of the HEMT device, we proposed an evaluation method that employed an extended parallel capacitor C ds , as shown in Figure 3, which we called the "external shunt capacitance (ESC)" method.In this lumped circuit, the intrinsic capacitor C ds was assumed not to exist, and the extended capacitor C ds outside of the device was assumed to be the intrinsic capacitor.Therefore, the channel current (I channel ) and I drain could be directly and separately measured using an oscilloscope and current probes.This method was different to the traditional simulation method [20], and the discrepancy between I channel and I drain could be visually observed.Although an extra parallel capacitor led to an increase in the measured I drain and I channel , this qualitative method could be used to assess the difference between these two currents, and, thereby, the cause of the discrepancy could be located.After understanding this reason, the resulting loss effect on the eGaN HEMT device could be further quantified via an analytical method.Using the analytical method, the additional C ds was no longer required; therefore, the C ds did not materially affect the device's losses.

Extraction of the Dynamic Rdson
It is well known that a high Vds_off will cause surface-and buffer-rela cesses, which will lead to a larger dynamic Rdson compared to the direct

Extraction of the Dynamic R dson
It is well known that a high V ds_off will cause surface-and buffer-related trapping processes, which will lead to a larger dynamic R dson compared to the direct current (DC) R dson (R dson_DC ) [21,22]. Figure 4 illustrates the mechanism of the increase in the dynamic R dson induced via the trapping effect.The high electric field helps the electrons to escape from the GaN well, and these electrons are then captured by traps or some of the surface states that are activated via a high electric field.When removing the electric field, these trapped electrons cannot be instantaneously released to the well.The reason for the slow return of electrons is that the trapping time of electrons in the off-state is in the order of ns, whereas the detrapping time of electrons in the on-state is in the order of second [23,24].Thus, trapped electrons accumulate and worsen the device's performance at a high f s .Meanwhile, electrons migrate from the gate to the gate-drain side's adjacent surface to form a virtue gate; hence, the number of electrons in the access region decreases.The decreasing number of electrons in the drift region will result in a large dynamic R dson [25,26].

Extraction of the Dynamic Rdson
It is well known that a high Vds_off will cause surface-and buffer-related trapp cesses, which will lead to a larger dynamic Rdson compared to the direct current (D (Rdson_DC) [21,22].Figure 4 illustrates the mechanism of the increase in the dyna induced via the trapping effect.The high electric field helps the electrons to esca the GaN well, and these electrons are then captured by traps or some of the surfa that are activated via a high electric field.When removing the electric field, these electrons cannot be instantaneously released to the well.The reason for the slow r electrons is that the trapping time of electrons in the off-state is in the order of ns, the detrapping time of electrons in the on-state is in the order of second [23,24 trapped electrons accumulate and worsen the device's performance at a high f while, electrons migrate from the gate to the gate-drain side's adjacent surface t virtue gate; hence, the number of electrons in the access region decreases.The de number of electrons in the drift region will result in a large dynamic Rdson [25,26].In the circuit of Figure 2a, the current I1 flows partly through Rt and partly the HEMT device, and the voltage of point B (VB) can be directly tested using the probe P2221.Then, the dynamic Rdson can be calculated as follows: , and I1 are the average voltages of point B and average currents through a resistive load and D2, and the current of the constant supply, respectively.Idrain, the voltage of point A (Vdrain), and VF_D2 of D2 are tested current probe (TCP0020), a high-voltage differential probe (THDP0200), and a l age differential probe with a 1:1 attenuation (TIVH02) and displayed using an osci (MDO3104).Finally, the calculated dynamic Rdson is normalized by Rdson_DC, whic mΩ , derived from an eGaN HEMT (GS66502B from GaN Systems Inc., Ottawa, [27]. Figure 5b-f show the results of the dynamic Rdson of the eGaN HEMT for vario fs, duty cycles, Idrain, and operating temperatures, which are extracted in the ontaking average values in the stable region marked in Figure 5a. Figure 5b shows dynamic Rdson increases as Vdrain increases under the conditions of an 80% duty c an fs of 100 kHz, meaning that the dynamic Rdson is voltage dependent.Figure 5c, the dynamic Rdson increases as fs increases and duty cycle decreases, respectively, f In the circuit of Figure 2a, the current I 1 flows partly through R t and partly through the HEMT device, and the voltage of point B (V B ) can be directly tested using the voltage probe P2221.Then, the dynamic R dson can be calculated as follows: where V B , V F_D2 , I drain , I D2 , and I 1 are the average voltages of point B and D 2 , the average currents through a resistive load and D 2 , and the current of the constant-current supply, respectively.I drain , the voltage of point A (V drain ), and V F_D2 of D 2 are tested using a current probe (TCP0020), a high-voltage differential probe (THDP0200), and a low-voltage differential probe with a 1:1 attenuation (TIVH02) and displayed using an oscilloscope (MDO3104).Finally, the calculated dynamic R dson is normalized by R dson_DC , which is 200 mΩ, derived from an eGaN HEMT (GS66502B from GaN Systems Inc., Ottawa, Canada) [27].Figure 5b-f show the results of the dynamic R dson of the eGaN HEMT for various V ds_off , f s , duty cycles, I drain , and operating temperatures, which are extracted in the on-state by taking average values in the stable region marked in Figure 5a. Figure 5b shows that the dynamic R dson increases as V drain increases under the conditions of an 80% duty cycle and an f s of 100 kHz, meaning that the dynamic R dson is voltage dependent.Figure 5c,d shows the dynamic R dson increases as f s increases and duty cycle decreases, respectively, for a 500-volt V drain condition, meaning that the dynamic R dson is also time dependent.Considering that the dynamic R dson is not only affected by the trapping effect, we further test the relationship between the dynamic R dson and I drain and temperature, as shown in Figure 5e,f, respectively.These two tests will help us to isolate the trapping effect caused by the increase in the dynamic R dson in a particular complex test condition.
In conclusion, the trend regarding the results of the extracted dynamic R dson of the eGaN HEMT is consistent with the mechanism of the trapping-effect-induced increase in the dynamic R dson .In Figure 6, we can obtain the real conduction resistance of the eGaN HEMT device under a certain working condition, and the conduction loss can then be corrected.
volt Vdrain condition, meaning that the dynamic Rdson is also time dependent.Considering that the dynamic Rdson is not only affected by the trapping effect, we further test the relationship between the dynamic Rdson and Idrain and temperature, as shown in Figure 5e,f, respectively.These two tests will help us to isolate the trapping effect caused by the increase in the dynamic Rdson in a particular complex test condition.In conclusion, the trend regarding the results of the extracted dynamic Rdson of the eGaN HEMT is consistent with the mechanism of the trapping-effect-induced increase in the dynamic Rdson.In Figure 6, we can obtain the real conduction resistance of the eGaN HEMT device under a certain working condition, and the conduction loss can then be corrected.

Discussion on the Effect of the Drain Current using a Double-Mode Test Technique
Based on the test circuit in Figure 1, a double-mode test technique, which included a DCM and a CCM, is proposed.In general, the electrical performance of a GaN device is  In conclusion, the trend regarding the results of the extracted eGaN HEMT is consistent with the mechanism of the trapping-effec the dynamic Rdson.In Figure 6, we can obtain the real conduction re HEMT device under a certain working condition, and the conduct corrected.

Discussion on the Effect of the Drain Current using a Double-Mode Test Technique
Based on the test circuit in Figure 1, a double-mode test technique, which included a DCM and a CCM, is proposed.In general, the electrical performance of a GaN device is characterized by either single-pulse or double-pulse mode.The typical "double-pulse" test is performed in three steps.The first step, which is represented by the turn-on pulse, is the initial adjusted pulse width.This pulse is adjusted to find the desired test current.The second step is to turn off the first pulse.The turnoff period is short to keep the load current as close as possible to a constant value.The third step is represented by the second turn-on pulse.The pulse width is shorter than the first pulse, meaning that that the device is not overheated, but it needs to be long enough for the measurements to be taken.Turn-off and turn-on timing measurements are then captured at the turning off of the first pulse and the turning on of the second pulse.This "double-pulse" technique only sends two pulses to the device, which is not periodically sustained, and the current in the third step is always higher than 0 A [28][29][30].In order to fully obtain the characteristics of the periodic operation of the device in the high-frequency circuit, we make the device continuously work periodically and stably in the CCM or DCM state by controlling the L value and the V ds_off [31,32].With the "double-pulse-current-mode" technique, we are able to focus on the impact of the starting current and peak current on the transition time of the device, which is not easy to do with the conventional "double-pulse" technique.Then, the tested waveforms during the turn-on and turn-off transitions for various voltage and PWM conditions are illustrated in the Figure 6.To ensure that the switching circuit operates in open-loop CCM and DCM, V Bulk is set to 400 V, and the V Load is set to 80 V in DCM and 20 V in CCM, meaning that the V ds_off values of the devices in the two modes are different.
The current I drain in DCM only exhibits one resonant waveform when the drain voltage decreases, as shown in Figure 6a, while I drain in CCM has an extra linear increase before the resonant waveform occurs, as shown in Figure 6b.The corresponding voltage fall time is approximately 14 ns in Figure 6a and approximately 42 ns in Figure 6b, meaning that that the extra linear increase in the current will increase the turn-on time and cause a high dynamic power loss.This linear increase in the current is caused by the high start current and the linear conduction of the eGaN HEM at this time.This finding means that DCM is a superior operating mode in terms of reducing the turn-on time.
In addition, the rise time of the drain voltage during the turn-off transition, which is approximately 10 ns, as shown in Figure 6d, is faster than that of approximately 30 ns shown in Figure 6c.This observation is true because I drain in Figure 6d is higher than that in Figure 6c, and the rise time of the drain voltage during the turn-off transition mainly depends on the charge time of C oss .Moreover, the peak current in DCM during the turnoff transition will be higher than that in CCM under the same output power conditions.This observation means that DCM is a superior operating mode in terms of reducing the turn-off time.
In conclusion, the drain current will significantly affect the turn-on and turn-off times, and DCM is better than CCM at reducing the crossover power losses.

Investigation of the Real Channel Current
According to the qualitative method shown in Figure 2, we can study the discrepancy between I drain and I channel .Figure 7a shows the tested I drain , I channel , V drain , and V drive values of the AlGaN/GaN HEMT in the turn-on transition for a V ds_off of 500 V, an f s of 100 kHz, and a duty cycle of 16.5%.It is shown that I channel is larger than I drain , while the drain voltage decreases.The current path in this time interval is shown in Figure 7b, where the channel current partially results from the discharging current of the parasitic output capacitor.
Figure 7c shows the tested I drain , I channel , V drain , and V drive values of the AlGaN/GaN HEMT during the turn-off transition for a V ds_off of 500 V, an f s of 100 kHz, and a duty cycle of 16.5%.It is shown that I channel is smaller than I drain , while the drain voltage increases.The current path in this time interval is shown in Figure 7d, where the channel current is partially diverted to the branch of the output capacitor.
In conclusion, I channel is not exactly equal to I drain , and, unfortunately, I channel cannot be directly tested.However, with the above test results and the current path analysis, we can acquire the reason for the discrepancy between I channel and I drain , meaning that the real I channel value can be obtained via a test of I drain and an analytical method, and the power losses of eGaN HEMTs can be correctly evaluated.7d, where the channel tially diverted to the branch of the output capacitor.
In conclusion, Ichannel is not exactly equal to Idrain, and, unfortunately, I directly tested.However, with the above test results and the current path a acquire the reason for the discrepancy between Ichannel and Idrain, meaning tha value can be obtained via a test of Idrain and an analytical method, and the p eGaN HEMTs can be correctly evaluated.

Modeling of Switching Power Losses
Figure 8 shows a detailed timing diagram of the switching period HEMTs in DCM or CCM.The operating period of the power devices can b 12-time intervals from t0 to t12 based on the status of the drain voltage and state, on-state, turn-on transition, and turn-off transition.To investigate th namic power loss, we reclassified the 12-time intervals into four stages (S1 their different contributions to the dynamic power loss.

Modeling of Switching Power Losses
Figure 8 shows a detailed timing diagram of the switching period [33] for eGaN HEMTs in DCM or CCM.The operating period of the power devices can be divided into 12-time intervals from t 0 to t 12 based on the status of the drain voltage and I drain in the off-state, on-state, turn-on transition, and turn-off transition.To investigate the detailed dynamic power loss, we reclassified the 12-time intervals into four stages (S1-S4) based on their different contributions to the dynamic power loss.In conclusion, Ichannel is not exactly equal to Idrain, and, unfortunately, Ich directly tested.However, with the above test results and the current path an acquire the reason for the discrepancy between Ichannel and Idrain, meaning that value can be obtained via a test of Idrain and an analytical method, and the po eGaN HEMTs can be correctly evaluated.

Stage 1 (S1)-Off-State with a High V ds
During the t 0 -t 1 and t 10 -t 11 time intervals and the time of the off-state, the device sustains a high V ds .Thus, the voltage-dependent leakage current (I lk ) will lead to an offstate power loss (P off ).We can no longer ignore this power loss, especially at a very high drain voltage and very high frequency.In general, the t 0 -t 1 and t 10 -t 11 time intervals can be neglected in comparison to the off-state time, meaning that P off can be written as follows: where T and D are the period and duty cycle, respectively.In addition, eGaN HEMTs have no reverse recovery problem because the 2DEG in the channel is naturally formed via the polarization effect.This outcome will reduce the power loss and mitigate the electromagnetic interference (EMI) problem, which is produced via the reverse recovery caused by ringing.

Stage 2 (S2)-On-State in Saturation Region
During the t 4 -t 7 time intervals, the device is in the on-state.The RMS value of the drain current (I drain_rms ) can be written as follows: To take the problem of the increase in the dynamic R dson into account, the traditional conductive power loss (P con ) can be modified as follows: where k dv , k d f , k dd , k cu , and k th_R are the dynamic coefficients of R dson related to the voltage, f s , the duty cycle, the current, and the temperature, respectively.

Stage 3 (S3)-Turn-on Transition
During the t 1 -t 4 time interval, the device is in the turn-on transition.In the t 1 -t 2 time interval, I drain increases, while V drain decreases slightly in CCM, but this time interval does not exist in DCM; in the t 2 -t 3 time interval, V drain decreases and leads to a resonant I drain .In the t 3 -t 4 time intervals, V drain decreases to a very low voltage, and the device starts to operate in an ohmic conducting state.These crossovers of V drain and I drain will cause power losses during the turn-on transition (P turn_on ): 1.
In the t 1 -t 2 time interval, I drain increases almost linearly from 0 to the I sta at t 2 , which is similar to a Si-based MOSFET [13,34], while V drain decreases slightly from V ds to V r due to the result of the parasitic inductance voltage drop caused by a high di/dt in the circuit.At t 2 , the current of the freewheeling diode D 1 decreases to zero.In this time interval, the gate voltage of the device slightly exceeds V th , meaning that the device is operating in a linear region.Meanwhile, the trapping effect of a high electric field will also lead to a large dynamic R dson in the linear region (R turn_on_cr ), which is similar to that in the on-state, as well as an extra gate lag.Thus, the coefficients of the dynamic R dson should be the same as those in Figure 4. Assuming that the heatsink is large enough and the self-heating effect is ignored, the t 1 -t 2 time interval, V r , and the power losses in this time interval (P turn_on_cr ) can be written as follows: 9) where L eff_Gate and W eff_Gate are the effective channel length and width, respectively.L s is the source inductor, which is in series with and between the source terminal and the ground.The coefficient of the gate lag(k lag) is a fitting parameter, which can be obtained by measuring the turn-on delay for various V ds_off , f s and duty cycles.2.
In the t 2 -t 3 time interval, the HEMT device takes over the total inductive load current, and V ds decreases to a boundary voltage of (V mr − V th ) at t 3 due to the discharging of C oss .The stray inductors in series around the circuit are resonant with C oss and the stray capacitors (C stray ) in this time interval.The current path through the device is illustrated in Figure 5b.It is assumed that V gs and i sta remain unchanged, and the reverse recovery of the D 1 is zero.In addition, the current in this time interval is usually large enough; hence, the charging time of C oss can be ignored.Moreover, voltage-dependent C oss is not suitable for the calculation of power losses in this time interval because V drain is always changing.Therefore, Q gd is used to replace C oss , and the time interval of t 2 -t 3 can then be written as follows: Then, the power losses in this time interval (P turn_on_vf ) can be written as follows [35]: where I v f is the average channel current during the t 2 -t 3 time interval.

3.
During the t 3 -t 4 time interval, the HEMT device operates in an ohmic conducting state.Then, V drain continues to decrease until it reaches a low on-voltage (V on ) from (V mr − V th ).Assuming that i sta and the Miller voltage V mr do not change, the t 3 -t 4 time interval, V on_r , and the power losses in this time interval (P turn_on_mr ) can be written as follows [36]: From the above analysis, Equation ( 6) can be modified as follows: P turn_on (measured) = P turn_on_cr + P turn_on_v f + P turn_on_mr We noticed that at this stage, i sta is a tested drain current instead of a real channel current, and they are actually different in the t 2 -t 3 time interval, as shown in Figure 5a.
However, I channel is the real factor that results in the power losses in this stage, and the real I channel is the combined current of I drain and the discharging current of C oss : Thus, Equation ( 18) can be finally modified as follows [12]: where Thus,

Stage 4 (S4)-Turn-off Transition
During the t 7 -t 11 time intervals, the device is in a turn-off transition.In the t 7 -t 8 time intervals, the drain voltage increases, while I drain stays almost constant; in the t 8 -t 9 time intervals, the drain voltage continuously increases, while I drain slightly decreases.In the t 9 -t 10 time intervals, I drain decreases, while the drain voltage stays almost constant.Finally, I drain decreases to zero, and the drain voltage becomes resonant in the t 10 -t 11 time intervals.These crossovers of V drain and I drain will cause power losses during the turn-off transition (P turn_off ) as follows: In the t 7 -t 8 time interval, the observations are very similar to those in the t 3 -t 4 time interval.The HEMT device moves into a linear region from an ohmic conducting state.V drain increases to a boundary voltage of V m f − V th .Assuming that the peak current is unchanged, and V m f = V mr , the t 7 -t 8 time interval, V on_f , and the power losses in this time interval (P turn_on_mf ) can be written as follows: In the t 8 -t 9 time interval, the observations are very similar to those in the t 2 -t 3 time intervals.V drain continues to increase more quickly towards the off-state V ds_off , while I drain decreases slightly to i r .This current drop is caused by a charging shunt to other peripheral devices [33], and the current path through the device is illustrated in Figure 5d.Assuming that the Miller voltage (V mf ) remains unchanged and the current-dependent charging time of C oss can no longer be ignored, we have the following equation: In the t 9 -t 10 time interval, the observations are similar to those in the t 1 -t 2 time interval.I drain decreases from i r to a low value because the current begins to divert from the HEMT device to D 1 .In this time interval, the drain voltage is in a state of resonance, while V gs decreases to (V mr − V th ), and the device channel current reaches zero at t 10 [20].Then, the t 9 -t 10 time interval and the power losses at this time interval (P turn_off_cf ) can be written as follows: During the t 10 -t 11 time interval, the device is turned off, but V drain ringing occurs due to the resonance between C oss and L stray .These fluctuations of the drain voltage will lead to a slight power loss, which depends on the ringing peak voltage (V ds_pk ).
Assuming that the reverse recovery of D 1 is zero, we have the following equation: From the above analysis, Equation ( 23) can be modified as follows: P turn_o f f (measured) = P turn_o f f _m f + P turn_o f f _vr + P turn_o f f _c f + P turn_o f f _vx (34) Instead of real channel currents, they are actually different in the t 8 -t 9 time interval, as shown in Figure 5c.However, I channel is the real factor that results in the power losses in this stage, and the real I channel is the diverted current of I drain and the charging current of C oss I channel = I drain − I Cds − I Cgd ≈ I drain − I Cds (35) Therefore, Equation ( 34) can be finally modified as follows [12]: where Thus, Finally, the total power loss (P total ) should be described based on the sum of Equations ( 3)-(38): In particular, the effects of I channel and I drain on P total can finally cancel out for a hard switch.However, in a soft switch application, such as a zero-voltage switch (ZVS), P turn_on_dis is zero; hence,P turn_o f f _char can no longer cancel out.This correction becomes very meaningful to the universality of the dynamic power loss model for eGaN HEMTs.
As can be seen, P total in Equation ( 39) is very different to that in Equation (1).Equation (39) has no power loss of reverse recovery, but it takes the trapping effect-induced dynamic R dson and the impacts of the I drain and the real I channel into account.

Model Verification via Experiments
To verify our dynamic power loss model, we adopt a floating buck-boost power converter with a light-emitting diodes (LEDs) operating in DCM and CCM.To maintain the operation mode and the output current (I o ) in an open-loop control system, some key parameters are adjusted (such as L 1 ) or tested (such as the output voltage V o , the peak operating current I pk , and the output power P o ) in the circuit, as shown in Figure 9, for an input voltage (V Bulk ) of 400 V, a duty cycle of 10%, and various f s and I o values.
switch.However, in a soft switch application, such as a zero-voltage switch _ _ P turn on dis is zero; hence, turn_ _char off P can no longer cancel out.This correction become meaningful to the universality of the dynamic power loss model for eGaN HEMTs.
As can be seen, Ptotal in Equation ( 39) is very different to that in Equation (1).Eq (39) has no power loss of reverse recovery, but it takes the trapping effect-induc namic Rdson and the impacts of the Idrain and the real Ichannel into account.

Model Verification via Experiments
To verify our dynamic power loss model, we adopt a floating buck-boost powe verter with a light-emitting diodes (LEDs) operating in DCM and CCM.To mainta operation mode and the output current (Io) in an open-loop control system, some k rameters are adjusted (such as L1) or tested (such as the output voltage Vo, the peak ating current Ipk, and the output power Po) in the circuit, as shown in Figure 9, for an voltage (VBulk) of 400 V, a duty cycle of 10%, and various fs and Io values.The power losses are then tested using a power analyzer (PW6001-03 from H Inc., Ueda, Nagano Prefecture, Japan).Figure 10a-c reveal that the analytical results total dynamic power losses generated via the proposed model are in good agreemen experimental results in both CCM and DCM, even for various Io, fs and VBulk value experimental results are slightly different from the analytical results, which may cause of the measurement accuracy of the power meter reduced at a high fs.The power losses are then tested using a power analyzer (PW6001-03 from HIOKI Inc., Ueda, Nagano Prefecture, Japan).Figure 10a-c reveal that the analytical results of the total dynamic power losses generated via the proposed model are in good agreement with experimental results in both CCM and DCM, even for various I o , f s and V Bulk values.The experimental results are slightly different from the analytical results, which may be because of the measurement accuracy of the power meter reduced at a high f s .
switch.However, in a soft switch application, such as a zero-voltage switch (ZV _ _ P turn on dis is zero; hence, turn_ _char off P can no longer cancel out.This correction becomes v meaningful to the universality of the dynamic power loss model for eGaN HEMTs. As can be seen, Ptotal in Equation ( 39) is very different to that in Equation (1).Equat (39) has no power loss of reverse recovery, but it takes the trapping effect-induced d namic Rdson and the impacts of the Idrain and the real Ichannel into account.

Model Verification via Experiments
To verify our dynamic power loss model, we adopt a floating buck-boost power co verter with a light-emitting diodes (LEDs) operating in DCM and CCM.To maintain operation mode and the output current (Io) in an open-loop control system, some key rameters are adjusted (such as L1) or tested (such as the output voltage Vo, the peak op ating current Ipk, and the output power Po) in the circuit, as shown in Figure 9, for an inp voltage (VBulk) of 400 V, a duty cycle of 10%, and various fs and Io values.The power losses are then tested using a power analyzer (PW6001-03 from HIO Inc., Ueda, Nagano Prefecture, Japan).Figure 10a-c reveal that the analytical results of total dynamic power losses generated via the proposed model are in good agreement w experimental results in both CCM and DCM, even for various Io, fs and VBulk values.T experimental results are slightly different from the analytical results, which may be cause of the measurement accuracy of the power meter reduced at a high fs.Figure 11a shows the relationship between the total dynamic power losses and I o in CCM and DCM.In the case of a small I o , the switching loss is dominant, while in the case of a large I o , the conduction loss is dominant.In addition, the dynamic power loss increases faster with the increase in I o in DCM than in CCM, indicating that DCM is not suitable for high current conditions.
higher than the rated device continuous operating current of 7.5 A. Generally, our should ensure that the operating current of the device does not exceed the rated certain margin should be designed, and the operating temperature of the device not exceed 120 °C.Although the high operating temperature may not have any e the GaN device, it will have a bad effect on other surrounding devices.To restrain the peak current and obtain a high operating efficiency, the QRM proposed.The reason for this proposal is that QRM works at the DCM boundary Vdrain will decrease to a minimum value at the beginning of the turn-on transition Idrain decreases to zero.In addition, the peak on-state current in DCM is usually larg that in CCM, and the current will be at a controllable high level, meaning that the time is fast in QRM.Therefore, QRM is more suitable for the achievement of a switch and even for the reduction in the turn-off transition time.

Conclusions
An improved 12-time-interval piecewise dynamic power loss model fo HEMTs is developed by specially quantifying the effects of the increase in the d Rdson, the impact of Idrain on the turn-on and turn-off times, and the real Ichannel; good ment with some experimental results is proven.
In this work, three methods or techniques are proposed, which are DDI meth double-mode test technique and qualitative method.Then, the dynamic Rdson is o by our new extraction circuit at a high operating fs of up to 1 MHz and high drain of up to 600 V, the drain current is found to significantly affect the turn-on and times via a switching circuit operating in DCM and CCM, and the real channel cu Figure 11b shows the switching loss during the turn-on and turn-off transitions in CCM and DCM.The results reveal that the switching loss is lower in DCM than in CCM during the turn-on transition, but larger during the turn-off transition when I o is larger than 1.25 A. This finding means that DCM is more suitable for a relatively small I o .In this case, according to Figures 10b and 11a, a 1.25-ampereI o is a moderate output current that is acceptable.
It also can be seen that all calculated results are a little bit higher than the experimental results, especially in a higher than 2-ampere I o condition and CCM mode.According to the analysis, the calculation model is not accurate enough to evaluate the self-heating effect of the device.Of course, in a high-frequency circuit, the peak current and the operating temperature of the device should be controlled by designing a suitable heat sink.In this case, when the I o is 2 A, the device peak current is as high as 10 A, which is higher than the rated device continuous operating current of 7.5 A. Generally, our design should ensure that the operating current of the device does not exceed the rated 7.5 A, a certain margin should be designed, and the operating temperature of the device should not exceed 120 • C.Although the high operating temperature may not have any effect on the GaN device, it will have a bad effect on other surrounding devices.
To restrain the peak current and obtain a high operating efficiency, the QRM is, thus, proposed.The reason for this proposal is that QRM works at the DCM boundary, where V drain will decrease to a minimum value at the beginning of the turn-on transition, while I drain decreases to zero.In addition, the peak on-state current in DCM is usually larger than that in CCM, and the current will be at a controllable high level, meaning that the turn-off time is fast in QRM.Therefore, QRM is more suitable for the achievement of a lossless switch and even for the reduction in the turn-off transition time.

Conclusions
An improved 12-time-interval piecewise dynamic power loss model for eGaN HEMTs is developed by specially quantifying the effects of the increase in the dynamic R dson , the impact of I drain on the turn-on and turn-off times, and the real I channel ; good agreement with some experimental results is proven.
In this work, three methods or techniques are proposed, which are DDI method, the double-mode test technique and qualitative method.Then, the dynamic R dson is obtained by our new extraction circuit at a high operating fs of up to 1 MHz and high drain voltage of up to 600 V, the drain current is found to significantly affect the turn-on and turn-off times via a switching circuit operating in DCM and CCM, and the real channel current is accurately calculated to distinguish it from the measured drain current.All of these parameters are included in the power loss model.
Moreover, the QRM has a low V ds_off , zero turn-on current, and relatively large peak current.Therefore, on the basis of the model, we propose the QRM to obtain a high efficiency and decrease the turn-off switching time required for the application of eGaN HEMTs.

Figure 1 .
Figure 1.Piecewise timing diagram of the power switching devices.

Micromachines 2023 ,
14, x FOR PEER REVIEW 4 of 1 gate-source short connection.Therefore, I1 could achieve an excellent constant curren over a wide operating voltage range.Rt provided a minimum load for I1 and suppressed the voltage spike at point B. An isolated low-voltage probe (P2221 from Keysight Inc. with a 1:1 attenuation could be used to test the VF of D2 and the voltage at point B. Th low-voltage probe with a 1:1 attenuation did not amplify the background noise and oper ate in a low-voltage range, meaning that it could obtain an improved test accuracy.

Figure 2 .
Figure 2. Lumped equivalent switching circuit with a floating buck-boost topology (a), and a pho tograph of the assembled printed circuit board (b).

Figure 2 .
Figure 2. Lumped equivalent switching circuit with a floating buck-boost topology (a), and a photograph of the assembled printed circuit board (b).

Figure 3 .
Figure 3.The lumped simulation circuit using an extra parasitic capacitor.

Figure 3 .
Figure 3.The lumped simulation circuit using an extra parasitic capacitor.

Figure 4 .
Figure 4. Mechanism of the dynamic R dson .

Figure 6 .
Figure 6.Experimental waveforms of the HEMT device during the turn-on transitions in 400-volt DCM with a VLoad of 80 V (a) and 400-volt CCM with a VLoad of 20 V (b), as well as during turn-off transitions in 400-volt DCM with a VLoad of 80 V (c) and 400-volt CCM with a VLoad of 20 V (d).

Freq5encyFigure 5 .
Figure 5. Dynamic R dson extraction waveforms at various f s (a) and the dynamic R dson normalized by R dson_DC for various V ds_off (b), fs (c), duty cycles (d), I drain (e), and temperatures (f).

Figure 6 .
Figure 6.Experimental waveforms of the HEMT device during the turn-on DCM with a VLoad of 80 V (a) and 400-volt CCM with a VLoad of 20 V (b), as transitions in 400-volt DCM with a VLoad of 80 V (c) and 400-volt CCM with a

Figure 6 .
Figure 6.Experimental waveforms of the HEMT device during the turn-on transitions in 400-volt DCM with a V Load of 80 V (a) and 400-volt CCM with a V Load of 20 V (b), as well as during turn-off transitions in 400-volt DCM with a V Load of 80 V (c) and 400-volt CCM with a V Load of 20 V (d).

Figure 7 .
Figure 7. Experimental results during the turn-on transition in 500-volt CCM (a) diagram of the corresponding current path (b), and the experimental results dur transition in 500-volt CCM (c) and a schematic diagram of corresponding current p

Figure 7 .
Figure 7. Experimental results during the turn-on transition in 500-volt CCM (a) and a schematic diagram of the corresponding current path (b), and the experimental results during the turn-off transition in 500-volt CCM (c) and a schematic diagram of corresponding current path (d).

Figure 7 .
Figure 7. Experimental results during the turn-on transition in 500-volt CCM (a) a diagram of the corresponding current path (b), and the experimental results duri transition in 500-volt CCM (c) and a schematic diagram of corresponding current pa

Figure 8
Figure 8 shows a detailed timing diagram of the switching period [ HEMTs in DCM or CCM.The operating period of the power devices can be 12-time intervals from t0 to t12 based on the status of the drain voltage and I state, on-state, turn-on transition, and turn-off transition.To investigate th namic power loss, we reclassified the 12-time intervals into four stages (S1 their different contributions to the dynamic power loss.

Figure 8 .
Figure 8. Timing diagram of the GaN HEMT devices.

Figure 9 .
Figure 9.The relationship between Io and Vo and Po, and Ipk (a), and the relationship between inductance of L1 for various fs (b) in an open-loop-controlled floating buck-boost power con

Figure 10 .
Figure 10.Comparison between the total dynamic power losses from the analytical and mental results in both CCM and DCM and for various Io (a), fs (b) and VBulk (c).

IFigure 9 .
Figure 9.The relationship between Io and V o and P o , and I pk (a), and the relationship between I o and inductance of L 1 for various f s (b) in an open-loop-controlled floating buck-boost power converter.

Figure 9 .
Figure 9.The relationship between Io and Vo and Po, and Ipk (a), and the relationship between Io a inductance of L1 for various fs (b) in an open-loop-controlled floating buck-boost power convert

Figure 10 .
Figure 10.Comparison between the total dynamic power losses from the analytical and exp mental results in both CCM and DCM and for various Io (a), fs (b) and VBulk (c).

IFigure 10 .
Figure 10.Comparison between the total dynamic power losses from the analytical and experimental results in both CCM and DCM and for various I o (a), f s (b) and V Bulk (c).

Figure 11 .
Figure 11.Experimental total dynamic power losses (a) and switching losses (b) as a functi output current in DCM and CCM.

Figure 11 .
Figure 11.Experimental total dynamic power losses (a) and switching losses (b) as a function of the output current in DCM and CCM. 2