Development of High-Power Charge Pump Rectifier for Microwave Wireless Power Transmission

This study theoretically and experimentally indicates that a charge pump rectifier for low-power rectifiers such as RF-ID can be applied to high-power rectifiers and can attain the same level of RF-dc conversion efficiency and twice as high power rectification as the single-shunt rectifiers. A high-power rectifier is primarily a single-shunt rectifier, and a charge pump rectifier that applies twice the output voltage is used in low-power applications such as RF-ID. We aim to enhance the power of charge pump rectifiers by focusing on their characteristics. A fabricated 5.8 GHz charge pump rectifier achieved an RF-dc conversion efficiency of 70.8% at an input power of 8.0 W and a load resistance of $150\,\Omega$. This result is also the highest efficiency for 39 dBm rectifiers in the 5.8 GHz band. Compared to a single-shunt rectifier with the same diode, the charge pump rectifier generated twice the input power and efficiency difference of 2.9% at the maximum input power. These results indicate that the charge pump rectifier has an advantage over the single-shunt rectifier in high-power rectifiers.


I. INTRODUCTION
Wireless power transmission (WPT) is an innovative technology that is becoming more commercialized. N. Tesla proposed WPT at the beginning of the 20th century, and it has been studied for over 100 years [1]. In recent years, WPT has been put to practical use in charging electric vehicles and smartphones [2], [3]. The microwave wireless power transmission (MWPT) has been the subject of several experiments since W.C. Brown's experiment in 1964 [4], [5]. MWPT technology is expected to be used in space solar power satellites, drones, and supplying power to buildings that are inaccessible because of disasters [6], [7], [8]. The system consists of signal generators, amplifiers, transmitting and receiving antennas, rectifiers, and output loads, and the total efficiency of these components is the final transmission efficiency. The efficiency of the rectifiers, which converts received radio waves into dc power, is an important factor in improving the MWPT system's efficiency. The diodes must have low parasitic resistance, junction capacitance, threshold voltage, and high breakdown voltage for RF-dc conversion efficiency [9]. In addition, the higher the input power, the greater the chance of diode damage from the heat generated by the diode current. There is a limit to the diode's breakdown voltage; hence, the input power is also limited. In MWPT with high frequency, the diodes must operate at high speed. Therefore, it is difficult to develop diodes that can generate both high power and efficiency. For example, rectifiers using GaAs Schottky barrier diodes have achieved a high efficiency of 91% at 5 W input power, but the basic frequency is 2.45 GHz [10]. At 5.8 GHz, the rectifier with a Si Schottky Barrier Diode (SBD) has an efficiency of 82% with 50 mW input power, whereas the one with a GaAs SBD (MA4E1317) has an efficiency of 82.7% with 49.09 mW [11], [12]. Furthermore, the development of Schottky barrier diodes with GaN, a power semiconductor, have progressed in recent years, and a rectifier with a GaN diode has achieved an efficiency of 71% at 2.5 W input power and 50% at 6.4 W input power in 5.8 GHz [13]. These circuits are single-shunt rectifiers with a single diode. This circuit type is fundamental at high frequencies and commonly used in rectifiers for high-power applications.
The purpose of this study is to design a 10 W class high-power and high-efficiency rectifier for high power applications like EVs and drones. To design a high-power and high-efficiency rectifier, we focused on a charge pump rectifier, which is used in low-power. The charge pump rectifier has the characteristic of doubling the output voltage compared to the single-shunt rectifier. WPT for low-power applications, including energy harvesting and RF-ID, requires a high output voltage. The WPT is often taken advantage of this characteristics of charge pump rectifiers. This characteristic is synonymous with halving the output current. This characteristic indicates that the diode current in the charge pump rectifier can be reduced. In a previous publication, a 5.8 GHz class-F charge pump rectifier for a satellite's internal wireless system was designed and achieved an RF-dc conversion efficiency of 71% [14]. However, since this rectifier's input power is 30 mW, it cannot be used in high-power systems such as EVs and drones. Thus, in this study, a high-power charge pump rectifier is proposed, and its advantage over a single-shunt rectifier is investigated in terms of efficiency and power.

II. THEORETICAL ANALYSIS FOR CHARGE PUMP RECTIFIER
In this section, the theoretical operation of an ideal charge pump rectifier is explained. It is also compared with a single-shunt rectifier. The single-shunt rectifier's theoretical operation has already been investigated [15]. The operation of a charge pump rectifier is analyzed in the same method. Fig. 1 shows a schematic of an ideal charge pump rectifier. This charge pump rectifier is solved using a distributed constant circuit. The diodes, D 1 and D 2 , in the charge pump rectifier are considered to have ideal I − V characteristics, as shown in Fig. 2.   First, we consider the point (P) between D 1 and D 2 . Fig. 3 shows the circuit around point P. Considering incident, reflection, and transmission waves in Fig. 3, the boundary conditions at point P are given by (1)-(4) from Kirchhoff's and Ohm's law. The capacitor (C 2 ) on the output side should be large enough to act as an RF short.

A. OPERATION OF AN IDEAL CHARGE PUMP RECTIFIER
Equation ( Next, we consider the dc voltages of the diodes. We consider each case of the two paths as shown in Fig. 4 with the dc voltages. First, we consider the path as shown on Case 1 of Fig. 4. With the dc voltage (V ddc ) of C 1 , (1) becomes (7).
Second, we consider the path shown on Case 2 of Fig. 4. Equations (11) and (12) can be obtained by considering the dc voltage (V dc ) of C 2 and V ddc .
By symmetry, the dc voltage of D 2 is the same as that of D 1 . Changing When the incident wave is negative, the incident and reflected waves are as shown in the upper part of Fig. 5. However, when the incident wave is positive, the incident and reflected waves are shown in the lower part of Fig. 5.
The diode voltages and currents in the steady state can be represented in Fig. 6 using these results. V in indicates the amplitude of v i . Fig. 7 shows the diode voltage and current in the ideal single-shunt rectifier. These figures show that the diode voltage has the same waveform and the diode current has exactly half the waveform compared to the single-shunt   rectifier because V dc of the single-shunt rectifier is half that of the charge pump rectifier. These results indicate that the charge pump rectifier is effective at high power because the power in the single diode is halved compared to the singleshunt rectifier.
The next step is to calculate the ideal maximum RF-dc conversion efficiency of the charge pump rectifier. The average current of the diodes in a steady state can be expressed using the following equation: V dc is equal to output voltage V out from Fig. 4. The input power P in and the output power P out are indicated as (20)-(21) with V in , V out , Z 0 and R L .
WhenV =V /2 andÎ = 2Î are substituted, (26) equals (27). This result shows that the charge pump rectifier doubles the output voltage and halves the output current when compared to the single-shunt rectifier. Furthermore, Fig. 8, which is the numerical results of (26) and (27), shows that the RF-dc conversion efficiency, η dc , in both rectifiers is 92.26%, and the optimal load resistance curve of the charge pump rectifier is shifted four times to the right compared to that of the single-shunt rectifier. When the input power is increased to n times, the diode voltage and current are increased √ n times. Thus, the diode voltage of the charge pump rectifier exceeds that of the singleshunt rectifier, and this circuit cannot achieve high power by charge pump rectifiers. In the next section, we increased the rectification power of a charge pump rectifier by adding a matching circuit.

B. SIMULATIONS OF IDEAL CHARGE PUMP AND SINGLE-SHUNT RECTIFIERS WITH MATCHING CIRCUITS FOR HIGH-POWER
Next, we analyze the charge pump rectifier and the singleshunt rectifier with the matching circuit and compare the efficiencies of the two rectifiers. The matching circuit lowers the rectifier's impedance, resulting in higher rectifier power.

1) THEORY OF AN IDEAL CHARGE PUMP RECTIFIER WITH AN IDEAL MATCHING CIRCUIT
A single-shunt rectifier can get a reflection power of 0% and an RF-dc conversion efficiency of 100% if its matching circuit processes all the diode's harmonics [16]. Fig. 9 shows the diode's theoretical voltage and current waveforms at that time. The shape of the diode waveforms is the current waveform to half-sine wave and the voltage waveform to a square wave, which are represented by (28) and (29).
In the ideal rectifier with a matching circuit, the output voltage V out , current I out , load resistance R L , and input power P in are expressed with a period T (= 2π/ω) by (30)-(33) since the RF-dc conversion efficiency is 100%.
Next, we assume the same conditions for the charge pump rectifier. From Section II-A, when diode D 1 is in ON mode, D 2 is in OFF mode. Assuming the same diode operation, as in the single-shunt rectifier, V d is applied to the capacitor C 1 as shown in Fig. 10. By contrast, when D 1 is in ON mode, D 2 is in OFF mode. Equations (34)-(37) can be derived from the V d of C 1 and the voltage and current of D 2 as in Fig. 10.
These equations indicate that the input power and load resistance of the charge pump rectifier are both twice as high as those of the single-shunt rectifier.

2) SIMULATIONS OF THE IDEAL CHARGE PUMP RECTIFIER WITH THE MATCHING CIRCUIT
Next, we verify the theory using a circuit analysis simulation.
In this analysis, we use Keysight's Advanced Design System (ADS) to analyze the circuits shown in Figs. 11 and 12. The rectifier's diodes should operate ideally, but the circuit in the ideal diode cannot be analyzed using the harmonic balance method in ADS. Therefore, we use the diode with the parameters in Table 1, which allows for an ideal operation as much as possible. The single-shunt rectifier's input power is 10 W, which is large enough to reduce the effect of the diode's threshold voltage. The load resistance is 100 for no particular reason. The input power and load resistance of the charge pump rectifier are 20 W and 200 , respectively, which is double those of the single-shunt rectifier. The basic frequency and characteristic impedance of the two rectifiers   are 1 GHz and 50 , respectively. The matching circuits of the two rectifiers consist of one lossless transmission line and six stubs for sufficient harmonic processing, and they are randomly optimized for 100% of RF-dc conversion efficiency. Both of the rectifiers have 99.9% RF-dc conversion efficiency, which is approximately 100%. Fig. 13 shows the  output voltage with sweeping input power. The charge pump rectifier's V − P curve is identical to the single-shunt rectifier's V − P curve when enlarged twice. By doubling the input power and load resistance, the diodes of the charge pump and single-shunt rectifiers perform an equivalent operation. Furthermore, the two efficiencies at this time are essentially equal. This result shows that the charge pump rectifier has an equivalent rectifying capability and can increase power by two times when compared to the single-shunt rectifier. This means that the charge pump rectifier is superior to the single-shunt rectifier in high power. Moreover, in the design of the charge pump rectifier, the diodes operate similarly to those in the single-shunt rectifier by making the load resistance twice as large as that of the single-shunt rectifier. In the next section, we design and fabricate the charge pump rectifier. Then, by comparing the charge pump rectifier to the single-shunt rectifier, we verify the former's advantage.

III. DESIGN OF A HIGH-POWER CHARGE PUMP RECTIFIER
In this section, we will design single-shunt and charge pump rectifiers. The design was done using Keysight's ADS. The diode to be used is a GaAs Schottky barrier diode with the SPICE parameters listed in Table 2. The package of this diode is SOD-523, and the equivalent circuit model for the package is the one shown in Fig. 14.

A. DESIGN OF A SINGLE-SHUNT RECTIFIER
In this section, we design and compare a single-shunt rectifier. Fig. 15 shows the designed rectifier. The output filter is a class-F filter that processes even-order and second-order harmonics. To achieve the maximum RF-dc conversion efficiency, the rectifier is designed for a continuous wave at 5.8 GHz with an input power of 5 W. The rectifier's substrate has The dielectric constant of 2.16, a dissipation factor of 0.0004, and a nominal thickness of 0.4 mm. Microstrip lines were selected as transmission lines, and the width of the lines   was set to 1.15 mm to achieve a characteristic impedance of 50 . Fig. 15 shows the designed single-shunt rectifier, and Fig. 16 shows the fabricated rectifier. Fig. 17 shows the η − P in characteristics of the fabricated rectifier. The maximum RF-dc conversion efficiency in this circuit was 74.8% at an input power of 3.5 W and a load resistance of 70 . When the circuit was supplied an input power of over 4 W, the temperature of the diodes instantly increased, and the rectifier failed. The diode's thermal runaway caused this phenomenon. In addition, the maximum input power in this circuit was 4.0 W with an RF-dc conversion efficiency of 73.7% and a load resistance of 70 . The circuit's size is 2.5 mm × 2.9 mm, and the dc power per unit area is 406.7 mW/mm 2 .

B. DESIGN OF A CHARGE PUMP RECTIFIER
Next, we design a charge pump rectifier. Based on the design results of the single-shunt rectifier in Section III-A and the analysis results in Section II-B, we estimated that the maximum input power of the charge pump rectifier using the diode with the SPICE parameters of Table 2 is 8.0 W. Based on the optimal load resistance obtained in the single-shunt rectifier, we designed the charge pump rectifier where the diode should perform the same operation under the conditions of twice the load resistance.

1) DESIGN OF AN OUTPUT FILTER
A charge pump rectifier with a class-F load was proposed by [14] for the rectifier's design at 5.8 GHz. This study proposes an output filter with open stubs of 90 • and 45 • behind diode D 2 . The smoothing capacitor of the charge pump rectifier makes the impedance of the output filter of zero at the harmonics generated by the diode. The λ n /4 open stubs inserted instead of the smoothing capacitor can process these harmonics. Therefore, in this study, we designed the output filter with only λ 1 /4 and λ 2 /4 open stubs. This filter can process the fundamentals and harmonics up to the third order.

2) DESIGN OF AN INPUT AND MATCHING FILTERS
In designing high-power charge pump rectifiers, it is necessary to operate diodes 1 and 2 (D 1 and D 2 , respectively) just below their breakdown voltage and allowable current. This enhances the power capacity of the charge pump rectifier. In the charge pump rectifier, the transmission lines L d1 to L d4 shown in Fig. 18 are used for matching. In this case, considering the path of the input wave to D 1 and D 2 , the positive input wave passes through the red dashed line, and the negative input wave passes through the black dashed line in Fig. 18. This means that the input impedance, voltage, and current at the ON mode of D 1 and D 2 are equal using the relationship shown in (38).
We designed the input filter and matching circuit under the conditions of (38).

3) DESIGN OF THE WHOLE CHARGE PUMP RECTIFIER
The charge pump rectifier was designed based on Sections III-B III-B1) and III-B2). Fig. 19 shows the designed circuit. The front stage input filter, the matching circuit before and after the diodes, and the backstage output filter make up the circuit. The basic wave is a continuous wave at 5.8 GHz, with the same substrate and line width as in Section III-A. The circuit  was matched to achieve the maximum RF-dc conversion efficiency at the input power of 8.0 W. Fig. 20 shows the fabricated charge pump rectifier. Fig. 21 shows the measured η − P in characteristics of the fabricated single-shunt and charge pump rectifiers. The maximum RF-dc conversion efficiency of 71.1% in the charge pump rectifier is practically the same level as that in the single-shunt rectifier. At the same time, the input power is 7.69 W, and the load resistance is 150 . The maximum input power of the charge pump rectifier is 8.0 W with an RF-dc conversion efficiency of 70.8%. This rectifier has the highest efficiency for 39 dBm rectifiers in the 5.8 GHz band, as shown in Table 3 [11], [12], [13], [17], [18]. When the maximum input power of the charge pump rectifier and the single-shunt rectifier were compared, the charge pump rectifier was twice as powerful. In addition, its optimal load resistance is 150 , which is about 2.1 times that of   the single-shunt rectifier. Fig. 22 shows the V out − P in characteristics of the two rectifiers. The charge pump rectifier's V − P curve was almost identical to the single-shunt rectifier's V − P curve when enlarged twice. Furthermore, we measured the temperature of the diodes in order to visualize the power delivered to the diodes. The result is shown in Fig. 23, and the temperatures of these two diodes are almost the same. The result indicates that similar power is delivered to these diodes, which results in heat due to similar diode losses. These results are alomost proven to be practically the same as the simulation results in Section II-B. Furthermore, the circuit size of the charge pump rectifier was 2.9 mm × 3.9 mm, which was 1.56 times larger than that of the single-shunt rectifier. Thus, the rectification power per unit area was 501 mW/mm 2 , which is 1.23 times larger than that of the single-shunt rectifier. These results indicate that a charge pump rectifier is preferable to a single-shunt rectifier for high-power rectifiers.

V. CONCLUSION
In this study, the advantage of charge pump rectifiers in high-power rectifiers was theoretically and experimentally investigated. At an input power of 7.69 W and a load resistance of 150 , the fabricated charge pump rectifier achieved a maximum RF-dc conversion efficiency of 71.1%. This result is also the highest efficiency for 39 dBm rectifiers in the 5.8 GHz band. The fabricated charge pump rectifier achieved an RF-dc conversion efficiency of 70.8% at an input power of 8.0 W and a load resistance of 150 , which is practically the same efficiency as that of the single-shunt rectifier using the same diode. Furthermore, the maximum input power of the charge pump rectifier was twice that of the single shunt rectifier. These results show that the charge pump rectifier has an advantage over the single-shunt rectifier for high-power rectifiers.