Minimum Power Input Control for Class-E Ampliﬁer Using Depletion-Mode Gallium Nitride High Electron Mobility Transistor

: In this study, we implemented a depletion (D)-mode gallium nitride high electron mobility transistor (GaN HEMT, which has the advantage of having no body diode) in a class-E ampliﬁer. Instead of applying a zero voltage switching control, which requires high frequency sampling at a high voltage (>600 V), we developed an innovative control method called the minimum power input control. The output of this minimum power input control can be presented in simple empirical equations allowing the optimal power transfer efﬁciency for 6.78 MHz resonant wireless power transfer (WPT). In order to reduce the switching loss, a gate drive design for the D-mode GaN HEMT, which is highly inﬂuential for the reliability of the resonant WPT, was also produced and described here for circuit designers.


Introduction
Class-E power amplifiers perform well in wireless power transfer (WPT) applications [1] because of their simple topology as well as high efficiency under zero voltage switching (ZVS) and zero voltage derivative switching (ZVDS) conditions. Thus, they have been used in various applications, such as battery charging [2], drones [3], LED lighting [4], and biomedicine [5]. Many studies have demonstrated the excellent performance of class-E power amplifiers [6,7], particularly when gallium nitride high electron mobility transistors (GaN HEMTs) are used [7][8][9][10][11]. GaN HEMTs provide high efficiency and performance due to their exceptional characteristics, such as low gate charge loss [7] and gate-source capacitance, which almost produce an ideal ZVS [8,9].
However, the performance of class-E power amplifiers is affected by load variation in addition to various non-ideal factors [12]. In response, different strategies have been proposed to optimize class-E amplifiers to increase operating efficiency and extend the transfer distance. These strategies involve a tuning couple [13]; the tuning duty ratio and frequency in relation to inductors and capacitors [14]; the control and compensation of variations in coupling and load impedance [10,11]; the coupling structure [15]; and the addition of transmitters [16,17]. In addition, a study proposed an analytical method that accounts for non-ideal factors (such as the inductance resistance, on resistance, and leakage current) in order to reduce the difference between calculated and actual values [18]. Moreover, although the use of GaN HEMTs in class-E power amplifiers improves efficiency and performance, a compatible and suitable gate driver must be designed to drive the GaN HEMT [19,20]. To this end, the charge pump gate drive presented by Ishibashi [20] is useful for driving the depletion (D)-mode GaN HEMT in a class-E amplifier.

Materials and Methods
In our previous paper [23], the mathematical derivation of the ZVS control of a class-E WPT unit was proposed. As stated in [23], one of the critical issues for WPT is dealing with the switching loss of the GaN HEMT transistor. The switching loss is mainly caused by GaN HEMT characteristics, including the output parasitic capacitance Coss and the input parasitic capacitance Ciss. Hence, the D-mode GaN HEMT characteristics, which are provided in Section 2.1, must be carefully studied and examined before and after the packaging. Nevertheless, the parasitic capacitance variations between turn-on and turn-off are the dominant factor for the switching loss. Hence, the gate driver design methodology is provided in Section 2.2. The design of the charge pump gate drive for the D-mode GaN HEMT is critical for class-E WPT efficiency. With regard to the maximum power transfer, we need to understand how the impedance matching mechanism is adjusted through the resonant frequency ω o , which is discussed in Section 2.4. Finally, we introduce a method called minimum power input control that functions by controlling the duty ratio δ, given in Section 2.5, to ensure the best power transfer efficiency (PTE), which implies the high PDL associated with a low switching loss. Figure 1 shows a flowchart of the key characteristic parameters for achieving the minimum power input control which is introduced in the following sections.  Figure 1. Flowchart of key characteristic parameters, which may also refer to [23], for achieving the minimum power input control. Figure 2a illustrates the transfer characteristics of the fabricated D-mode GaN HEMT device when V G = −10 to 1 V, with V D = 10 V in Figure 2b. The threshold voltage given by the tangent of the I D -V G was found to intersect at −7 V. Therefore, the turn-on voltage of the D-mode GaN HEMT, v GS,ON , was recorded at −7 V. The maximum allowable gate voltage V GS,max was tested under the condition of |V GS,max | < 30 V. According to the leakage current due to different voltages, C OSS = C GD + C DS varied, albeit only slightly, in the turn-on and turn-off periods. Furthermore, as the D-mode GaN HEMT had no body diode, the leakage current only flowed when v DS was negative. Table 1 summarizes the  characteristics of the D-mode GaN HEMT. gies 2021, 14, x FOR PEER REVIEW 3 of 17 Figure 1. Flowchart of key characteristic parameters, which may also refer to [23], for achieving the minimum power input control. Figure 2a illustrates the transfer characteristics of the fabricated D-mode GaN HEMT device when VG = −10 to 1 V, with VD = 10 V in Figure 2b. The threshold voltage given by the tangent of the ID-VG was found to intersect at −7 V. Therefore, the turn-on voltage of the D-mode GaN HEMT, vGS,ON, was recorded at −7 V. The maximum allowable gate voltage VGS,max was tested under the condition of |VGS,max| < 30 V. According to the leakage current due to different voltages, COSS = CGD + CDS varied, albeit only slightly, in the turn-on and turn-off periods. Furthermore, as the D-mode GaN HEMT had no body diode, the leakage current only flowed when vDS was negative. Table 1 summarizes the characteristics of the D-mode GaN HEMT.  The main reasons that the GaN HEMT is well-suited for WPT applications are that (1) it can perform high frequency switching with low switching loss; (2) it possesses no body diode; and (3) it involves low Ciss and Coss variation. The characteristic of have no body diode can ease the ZVS control and provide low energy loss during class-E switching operations. The Ciss and Coss variations of MOSFET can be as high as several hundred times between turn-on and turn-off. As for the GaN HEMT, Table 2 summarizes the parasitic capacitance of the D-mode GaN HEMT before packaging. The parasitic capacitances were nearly one-third of the MOSFET. The parasitic capacitance value and its variation were different for different packaging. For instance, the TO247, as shown in Figure 3b, yielded smaller capacitance than the TO220 shown in Figure 3a. Both types of packaging showed that the capacitance variation between turn-off at low V DS and turn-on at high V DS becomes smaller as the switching frequency increases. This is very good for resonant WPT in which the switching frequency is targeted at 6.78 MHz. In this study, the GaN HEMT in the TO220 packaging was used as it resulted in a smaller size than the TO247 packaging.    The design of the D-mode GaN HEMT gate drive for the wireless power transfer is sensitive to parameters including the gate-drain parasitic capacitance Crss (=CGD) and the gate input parasitic capacitance Ciss (=CGD +CGS). It is preferable for these parasitic capacitances to be as small as possible to enable higher frequency switching without much switching loss. On the other hand, the drain-source parasitic capacitance CDS incorporated with C2 and L2 forms a useful LC tank for the power transfer unit (PTU), which needs to be as constant as possible during the time the transistor is switching on and off. All the parasitic capacitances are closely related to the GaN HEMT design, including the thickness of the epitaxial structure of the GaN device. The resulting output characteristic in Figure 2b determines the RD,on related to the efficiency of the wireless The design of the D-mode GaN HEMT gate drive for the wireless power transfer is sensitive to parameters including the gate-drain parasitic capacitance C rss (=C GD ) and the gate input parasitic capacitance C iss (=C GD +C GS ). It is preferable for these parasitic capacitances to be as small as possible to enable higher frequency switching without much switching loss. On the other hand, the drain-source parasitic capacitance C DS incorporated with C 2 and L 2 forms a useful LC tank for the power transfer unit (PTU), which needs to be as constant as possible during the time the transistor is switching on and off. All the parasitic capacitances are closely related to the GaN HEMT design, including the thickness of the epitaxial structure of the GaN device. The resulting output characteristic in Figure  2b determines the R D,on related to the efficiency of the wireless power transfer. The transfer characteristic in Figure 2a shows the preferable v GS control range. It is preferable for the turn-on voltage v GS,ON to be as near to zero as possible to reduce the voltage level of the power supply for the gate drive.

Design of Charge Pump Gate Drive for D-Mode GaN HEMT
In order to design the D-mode GaN HEMT gate drive for class-E amplifiers, Ishibashi's [20] charge pump gate drive was adopted in this study. The leakage current is critical to the charge pump reservoir dynamics, which result from the reverse saturation current of the Schottky barrier diodes (SBD), which is preferably kept as small as possible. The disadvantage of the charge pump circuit-the current leaking through the diode reverse saturation current-causes no harm to the high frequency switching. However, the class-E amplifier has the additional disadvantage of C GD being connected to the high voltage switching of v DS .
In a p-n junction diode, two types of capacitance occur: transition capacitance (C T ) and diffusion capacitance (C D ): In a forward-biased diode, C D , which is the focus of the following derivation, is much larger than the C T . Furthermore, the gate drive v s is high, and the current i G passes from V GH to V SS , which, for simplicity, is taken as the ground. The current i G passes from V GL to V SS when v s is low. As shown in Figure 4, we first assumed that V DS is floating and that R G,p = R G . In the gate drive state, v s is high and v G,h = 0.7 V, according to the diode forward-threshold voltage (built-in potential). The charge on the gate and diode side is:     The charge on the capacitor side is: The steady state gate voltage when the gate is turning off is: Assuming that The leaking current in the charge pump occurs due to the diode reverse saturation current. When v DS is connected to a half sine voltage such that the charge pump requires some amount of negative charge, which must be quickly supplied, because of C GD (the Miller capacitor) when v DS is increasing to a high voltage and the gate is turning off. The charge pump must also retract the same quantity of negative charges when the gate is turning on. Thus, in such dynamic behavior, the resulting effect is the Miller plateau: a low voltage surge occurs when the gate is turning on, and the period in the Miller plateau increases when the gate is turning off. As shown in Figure 5, when R G,p is too high (as indicated by the dotted line), R G,p causes a negative voltage surge due to the rapid retraction of negative charges through C GD and C C to R G,p . The negative voltage can potentially surge down to lower than −V GS,max and cause the gate source to break down. In such cases, R G,p must be reduced to prevent a large voltage drop in v G,h when the gate is turning on; the corresponding design parameters for the gate drive are shown in Table 3. The ideal gate source voltage for 6.78 MHz switching is also indicated by a dark solid line in Figure 5. Using the D-mode GaN HEMT as the switching device, the resonance mechanism for proper resonant frequency is a function of the duty cycle settings based on the hypotheses of zero voltage control and zero current control for the class-E amplifier [23]. ZVS and ZCS are achieved by adjusting both the duty cycle and resonant frequency to comply with the known phenomenon in GaN HEMT control, including the Miller plateau and current clamp in the gate drive design.

Class-E Amplifier Circuit
Class-E amplifiers, as shown in Figure 6, have been used in 6.78 MHz resonant WPT applications. In this study, the actual load Z L for a wireless power transfer system was considered to be the mutual inductance in parallel with the equivalent impedance of the receiver side. For simplicity in exposition, we let the load R L be purely resistive. In the circuitry, the capacitor C DS is the parasitic capacitor of the D-mode GaN HEMT. As the GaN HEMT contains no body diode, (1) a current path where v DS is negative is impossible and (2) the resonant current i 2 can be sinusoidal with low total harmonic distortion (THD). In the equivalent circuit, the input and output power of the class-E amplifier are defined as P in = i 1 V DD and P out = i 2 v L , respectively. The WPT experimental layout is shown in Figure 7a, and the charge pump gate driver for the D-mode GaN HEMT is shown in Figure 7b. The circuit parameters are shown in Table 4.
GaN HEMT contains no body diode, (1) a current path where vDS is negative is impossible and (2) the resonant current i2 can be sinusoidal with low total harmonic distortion (THD). In the equivalent circuit, the input and output power of the class-E amplifier are defined as Pin = i1VDD and Pout = i2vL, respectively. The WPT experimental layout is shown in Figure 7a, and the charge pump gate driver for the D-mode GaN HEMT is shown in Figure 7b. The circuit parameters are shown in Table 4.  GaN HEMT contains no body diode, (1) a current path where vDS is negative is impo and (2) the resonant current i2 can be sinusoidal with low total harmonic dist (THD). In the equivalent circuit, the input and output power of the class-E amplif defined as Pin = i1VDD and Pout = i2vL, respectively. The WPT experimental layout is s in Figure 7a, and the charge pump gate driver for the D-mode GaN HEMT is sho Figure 7b. The circuit parameters are shown in Table 4.

PWM Control and Circuit Response
In this study, the class-E amplifier circuit was considered in terms of two aspects: the switching power supply and impedance loading. The duty cycle of switching is denoted δ (i.e., the pulse width is δT (Figure 8a)). The SPICE analysis is shown in Figure 8b.

PWM Control and Circuit Response
In this study, the class-E amplifier circuit was considered in terms of two aspects: the switching power supply and impedance loading. The duty cycle of switching is denoted δ (i.e., the pulse width is δT (Figure 8a)). The SPICE analysis is shown in Figure 8b. The switch was operated at a frequency of ωo = 2π/T. In the steady state, the output current is i2 = I2 sin(ωot + β) + I2,a cos(2ωot + β). The higher order terms I2,a << I2 cause the sinusoidal output to be asymmetric on its upswing and downswing wave forms. An example in which β = −180°, I2 = 1, and I2,a = 0.15, which are often seen in experiments, is shown in Figure 9a. The SPICE analysis is shown in Figure 9b. In practice, the vGS signal of the class-E amplifier, as shown in Figure 10, is different from that of the SPICE analysis simulation. The output signal from the gate drive was no longer a square wave when the gate driver input signal from the PWM was a square wave between 0 and 5 V. The distortion of the gate drive output vGS is due to the input parasitic capacitance Ciss. Since the Ciss is relatively small at the high drain-source voltage vDS, as shown in Figure 3, compared to the Ciss at the low drain-source voltage, The switch was operated at a frequency of ω o = 2π/T. In the steady state, the output current is i 2 = I 2 sin(ω o t + β) + I 2,a cos(2ω o t + β). The higher order terms I 2,a << I 2 cause the sinusoidal output to be asymmetric on its upswing and downswing wave forms. An example in which β = −180 • , I 2 = 1, and I 2,a = 0.15, which are often seen in experiments, is shown in Figure 9a. The SPICE analysis is shown in Figure 9b. Equivalent.

PWM Control and Circuit Response
In this study, the class-E amplifier circuit was considered in terms of two aspects: the switching power supply and impedance loading. The duty cycle of switching is denoted δ (i.e., the pulse width is δT (Figure 8a)). The SPICE analysis is shown in Figure 8b. The switch was operated at a frequency of ωo = 2π/T. In the steady state, the output current is i2 = I2 sin(ωot + β) + I2,a cos(2ωot + β). The higher order terms I2,a << I2 cause the sinusoidal output to be asymmetric on its upswing and downswing wave forms. An example in which β = −180°, I2 = 1, and I2,a = 0.15, which are often seen in experiments, is shown in Figure 9a. The SPICE analysis is shown in Figure 9b. In practice, the vGS signal of the class-E amplifier, as shown in Figure 10, is different from that of the SPICE analysis simulation. The output signal from the gate drive was no longer a square wave when the gate driver input signal from the PWM was a square wave between 0 and 5 V. The distortion of the gate drive output vGS is due to the input parasitic capacitance Ciss. Since the Ciss is relatively small at the high drain-source voltage vDS, as shown in Figure 3, compared to the Ciss at the low drain-source voltage, In practice, the v GS signal of the class-E amplifier, as shown in Figure 10, is different from that of the SPICE analysis simulation. The output signal from the gate drive was no longer a square wave when the gate driver input signal from the PWM was a square wave between 0 and 5 V. The distortion of the gate drive output v GS is due to the input parasitic capacitance Ciss. Since the Ciss is relatively small at the high drain-source voltage v DS , as shown in Figure 3, compared to the Ciss at the low drain-source voltage, the turn-off delay time t d,off is therefore larger than the turn-on delay time t d,on . The actual duty ratio is larger than the designed duty ratio. Thus an emperical result, and not just the SPICE model simulation result alone, was required to compensate in the design. Knowledge about the device characteristics, especially the parasitic capacitance variation resulting from different packaging and different switching frequencies, is essential to control resonant WPT via a class-E amplifier.

Maximum Power Transfer
The equivalent circuit of the wireless power transfer for a single PTU transferring power to a single PRU is shown in Figure 11. The resonant frequency ω o was selected to yield the best impedance matching between Z PTU (jω o ) and Z PRU (jω o ) in order to obtain the maximum power transfer, which is also referred to as the maximum amount of power delivered to the load (PDL). The equivalent turn ratio a within the equivalent circuit for the wireless power transfer is a function of the distance between PTU and PRU. Hence, ω o must be controlled from time to time to achieve the impedance matching condition when the PRU is moving. In a closed loop control, to tune the resonant frequency ω o , the Airfuel the turn-off delay time td,off is therefore larger than the turn-on delay time td,on. The actual duty ratio is larger than the designed duty ratio. Thus an emperical result, and not just the SPICE model simulation result alone, was required to compensate in the design. Knowledge about the device characteristics, especially the parasitic capacitance variation resulting from different packaging and different switching frequencies, is essential to control resonant WPT via a class-E amplifier.

Maximum Power Transfer
The equivalent circuit of the wireless power transfer for a single PTU transferring power to a single PRU is shown in Figure 11. The resonant frequency ωo was selected to yield the best impedance matching between ZPTU(jωo) and ZPRU(jωo) in order to obtain the maximum power transfer, which is also referred to as the maximum amount of power delivered to the load (PDL). The equivalent turn ratio a within the equivalent circuit for the wireless power transfer is a function of the distance between PTU and PRU. Hence, ωo must be controlled from time to time to achieve the impedance matching condition when the PRU is moving. In a closed loop control, to tune the resonant frequency ωo, the Airfuel Alliance recommends obtaining the required feedback of the actual power reading of the PRU via a 2.4 GHz communication network.
The PDL is also a function of VDS,max of the switching power supply circuit shown in Figure 6. We need a high VDS,max to enable linkage travel for the magnetic flux in the air, linking it to the PRU antenna coil. From [23], the VDS,max is derived into a function of the duty ratio δ, as shown in Figure 12. Theoretically, the VDS,max is a monotonically increasing function in terms of the duty ratio δ. On the other hand, while the switching loss of the D-mode GaN HEMT also increases with the VDS,max, the power transfer efficiency degrades due to the high VDS,max. The reason that the switching loss of the D-mode GaN HEMT increases is that the GaN HEMT has no body diode. There is really only one disadvantage of the GaN HEMT having no body diode: a higher reverse voltage drop. The reverse voltage drop of a GaN HEMT includes a resistive element arising from the channel resistance and threshold voltage. The voltage drop in a high voltage GaN HEMT can be as much as several volts when conducting large currents, which is larger than the equivalent drop in a MOSFET. Thus, we have a situation in which there is a trade-off between a high PDL and a high switching loss in terms of the duty ratio δ.
In practice, when we monitor the power input of the PTU, we see the power input increase due to either the mismatching of the impedances, resulting in low PDL in the low duty ratio δ region, or the high switching loss from the high VDS,max in the high duty ratio δ region. The minimum power input, which trades off both deficiencies, is the optimal solution. In the following section, we introduce an empirical technique to locate the optimal duty ratio δ and achieve the best power transfer efficiency, which implies the high PDL associated with a low switching loss.

Minimum Power Input Control
The minimum power input control of a class-E amplifier can be obtained experimentally. A specific power transmitter unit, with its equivalent parameters, is detailed in The PDL is also a function of V DS,max of the switching power supply circuit shown in Figure 6. We need a high V DS,max to enable linkage travel for the magnetic flux in the air, linking it to the PRU antenna coil. From [23], the V DS,max is derived into a function of the duty ratio δ, as shown in Figure 12. Theoretically, the V DS,max is a monotonically increasing function in terms of the duty ratio δ. On the other hand, while the switching loss of the D-mode GaN HEMT also increases with the V DS,max , the power transfer efficiency degrades due to the high V DS,max . The reason that the switching loss of the D-mode GaN HEMT increases is that the GaN HEMT has no body diode. There is really only one disadvantage of the GaN HEMT having no body diode: a higher reverse voltage drop. The reverse voltage drop of a GaN HEMT includes a resistive element arising from the channel resistance and threshold voltage. The voltage drop in a high voltage GaN HEMT can be as much as several volts when conducting large currents, which is larger than the equivalent drop in a MOSFET. Thus, we have a situation in which there is a trade-off between a high PDL and a high switching loss in terms of the duty ratio δ.

Minimum Power Input Control
The minimum power input control of a class-E amplifier can be obtained experimentally. A specific power transmitter unit, with its equivalent parameters, is detailed in Table 4. We completed a set of 70 experiments and interpolated the results (Figure 13). In the experiments, VDD = 108 V, nominal resonant frequency = 4.12 MHz, and δ% (nominal duty ratio) = 30%. We calculated the minimum power points, which are indicated by red dots in Figure 13 and corresponded to the lowest power loss from Coss to the ground in the switching. The experiment was extended to different input voltages VDD. The results are shown in Figure 14. In WPT applications, higher input voltages VDD are required for greater power transfer distances. Conversely, power input Pin increases with the distance between the PTU and power receiver unit (PRU). Furthermore, in cases of multiple PRUs, the power input Pin must be increased accordingly to supply sufficient power to the PRUs. We thus formulated our minimum control strategy according to the following steps: (1) Due to the power transfer query issued by the PRU, we determined the input voltage VDD according to the measured distance between the PTU and PRU. In practice, when we monitor the power input of the PTU, we see the power input increase due to either the mismatching of the impedances, resulting in low PDL in the low duty ratio δ region, or the high switching loss from the high V DS,max in the high duty ratio δ region. The minimum power input, which trades off both deficiencies, is the optimal solution. In the following section, we introduce an empirical technique to locate the optimal duty ratio δ and achieve the best power transfer efficiency, which implies the high PDL associated with a low switching loss.

Minimum Power Input Control
The minimum power input control of a class-E amplifier can be obtained experimentally. A specific power transmitter unit, with its equivalent parameters, is detailed in Table 4. We completed a set of 70 experiments and interpolated the results (Figure 13). In the experiments, V DD = 108 V, nominal resonant frequency = 4.12 MHz, and δ % (nominal duty ratio) = 30%. We calculated the minimum power points, which are indicated by red dots in Figure 13 and corresponded to the lowest power loss from C oss to the ground in the switching. The experiment was extended to different input voltages V DD . The results are shown in Figure 14. In WPT applications, higher input voltages V DD are required for greater power transfer distances. Conversely, power input P in increases with the distance between the PTU and power receiver unit (PRU). Furthermore, in cases of multiple PRUs, the power input P in must be increased accordingly to supply sufficient power to the PRUs. We thus formulated our minimum control strategy according to the following steps: (1) Due to the power transfer query issued by the PRU, we determined the input voltage V DD according to the measured distance between the PTU and PRU.
(2) Due to the immediate power input P in required for all PRUs, we determined the duty cycle δ (or duty ratio) according to the empirical data in Figure 14.
(3) From the duty ratio δ % calculated in step 2, we determined the resonant frequency f 0 according to the empirical data in Figure 15.
The minimum power input P in is supplied to the WPT based on the empirical data or equations in Figures 14 and 15, which guarantees optimal power transfer efficiency. The minimum power input control is equivalent neither to conventional ZVS nor to zero current switching because of the absence of a body diode in the D-mode GaN HEMT. The energy stored in the C DS is not released to ground when v DS is negative. However, the minimum power input control minimizes the energy stored in the C DS when the gate is turned on, which is like the ZVS control. A more important feature of our design is that almost all energy loss in the class-E amplifier is due to switching loss. Thus, the power loss on the transistor switched-off time, which is the product of the drain current with the v DS , is the key factor affecting the minimum power input control. The power loss is related to the gate drive design and the parasitic capacitance of the D-mode GaN HEMT; it is also absent in conventional ZVS control derivations.
The minimum power input Pin is supplied to the WPT based on the empirical data or equations in Figures 14 and 15, which guarantees optimal power transfer efficiency. The minimum power input control is equivalent neither to conventional ZVS nor to zero current switching because of the absence of a body diode in the D-mode GaN HEMT. The energy stored in the CDS is not released to ground when vDS is negative. However, the minimum power input control minimizes the energy stored in the CDS when the gate is turned on, which is like the ZVS control. A more important feature of our design is that almost all energy loss in the class-E amplifier is due to switching loss. Thus, the power loss on the transistor switched-off time, which is the product of the drain current with the vDS, is the key factor affecting the minimum power input control. The power loss is related to the gate drive design and the parasitic capacitance of the D-mode GaN HEMT; it is also absent in conventional ZVS control derivations.

Resonant WPT Results
As shown in Figure 16, a single PTU for the resonant WPT based on the D-mode GaN HEMT class-E amplifier was capable of transferring 1 W of power to a PRU 140 cm away. In the experiment, the load comprised 44 LEDs in series, each of which had a nominal power of 0.06 W. The maximum voltage VDS,max was 700 V, and the maximum current iD was 2.5 A. The radii of the coils for both PTU and PRU were approximately 25 Figure 15. Resonant frequency f 0 vs. the duty ratio δ % under the minimum power input control.

Resonant WPT Results
As shown in Figure 16, a single PTU for the resonant WPT based on the D-mode GaN HEMT class-E amplifier was capable of transferring 1 W of power to a PRU 140 cm away. In the experiment, the load comprised 44 LEDs in series, each of which had a nominal power of 0.06 W. The maximum voltage V DS,max was 700 V, and the maximum current i D was 2.5 A. The radii of the coils for both PTU and PRU were approximately 25 cm. When the PRU was 50 cm from the PTU, the PRU received 5 W power from the PTU (Figure 17). Due to the different distances between the PTU and PRUs in the WPT application, the maximum voltage V DS,max , which is proportional to the duty cycle δ, must be adjusted to send power at an optimal efficiency. The minimum power input control was applied for this purpose according to the look-up table. The maximum voltage V DS,max is typically triple the input voltage V DD in practice. Hence, the breakdown voltage of the D-mode GaN HEMT had to be higher than 1000 V for the application of 220 V AC , which was rectified to 310 V DC . Figure 18 shows the performance comparison of the PTE (%) in terms of transmission distance (cm). The method proposed in this paper yields performance comparable to the WPT with NIC method [24] with, however, no additional impedance transformation network circuit. cm. When the PRU was 50 cm from the PTU, the PRU received 5 W power from the PTU ( Figure 17). Due to the different distances between the PTU and PRUs in the WPT application, the maximum voltage VDS,max, which is proportional to the duty cycle δ, must be adjusted to send power at an optimal efficiency. The minimum power input control was applied for this purpose according to the look-up table. The maximum voltage VDS,max is typically triple the input voltage VDD in practice. Hence, the breakdown voltage of the D-mode GaN HEMT had to be higher than 1000 V for the application of 220 VAC, which was rectified to 310 VDC. Figure 18 shows the performance comparison of the PTE (%) in terms of transmission distance (cm). The method proposed in this paper yields performance comparable to the WPT with NIC method [24] with, however, no additional impedance transformation network circuit.

Conclusions
The D-mode GaN HEMT fabricated at the authors' university, the National Chiao Tung University, was successfully implemented into the class-E amplifier circuit. The design of the D-mode GaN HEMT gate drive for the wireless power transfer is sensitive to parameters including the gate-drain parasitic capacitance Crss (=CGD) and the gate input parasitic capacitance Ciss (=CGD + CGS). These parasitic capacitances of the GaN HEMT are essential for higher frequency switching with low switching loss. In the circuit design aimed at achieving the maximum power transfer, the corresponding impedance matching control was obtained in this research via adjustment of the resonant frequency ωo,. Nevertheless, by controlling the duty ratio δ, a minimum power input control that trades off the power delivered to load for the switching loss of the GaN HEMT was obtained and found to yield good power transfer efficiency. The resulting resonant WPT was capable of transferring 1 W over the 140 cm distance between the PTU and PRU. Our minimum power input control is an empirical method that generates a look-up table to optimize efficiency in WPT applications. In the future, the proposed design will be implemented for multiple-input and multiple-output (MIMO) applications-i.e., multiple PTUs serving multiple PRUs, which need to obtain the proper optimization method from

Conclusions
The D-mode GaN HEMT fabricated at the authors' university, the National Chiao Tung University, was successfully implemented into the class-E amplifier circuit. The design of the D-mode GaN HEMT gate drive for the wireless power transfer is sensitive to parameters including the gate-drain parasitic capacitance Crss (=C GD ) and the gate input parasitic capacitance Ciss (=C GD + C GS ). These parasitic capacitances of the GaN HEMT are essential for higher frequency switching with low switching loss. In the circuit design aimed at achieving the maximum power transfer, the corresponding impedance matching control was obtained in this research via adjustment of the resonant frequency ω o ,. Nevertheless, by controlling the duty ratio δ, a minimum power input control that trades off the power delivered to load for the switching loss of the GaN HEMT was obtained and found to yield good power transfer efficiency. The resulting resonant WPT was capable of transferring 1 W over the 140 cm distance between the PTU and PRU. Our minimum power input control is an empirical method that generates a look-up table to optimize efficiency in WPT applications. In the future, the proposed design will be implemented for multiple-input and multiple-output (MIMO) applications-i.e., multiple PTUs serving multiple PRUs, which need to obtain the proper optimization method from among their individual look-up tables-via a 2.4 GHz communication network (recommended by the Airfuel Alliance) in order to improve the efficiency of power transfer.