Dual-Domain Maximum Power Tracking for Multi-Input RF Energy Harvesting with a Reconﬁgurable Rectiﬁer Array

: This work proposes a dual-domain maximum power tracking (MPPT) technique for multiple-input RF energy harvesting systems. A differential rectiﬁer array is used to implement 4-channel reconﬁgurable RF to DC power conversion, and an adjustable 4-bit capacitor array is designed to improve the impedance matching between the antennas and the rectiﬁers. Using the perturbation and observation (P&O) method, both arrays are adaptively conﬁgured in the background with the variations of the input energy and output loading. Experimental results show that the proposed circuit successfully tracks the maximum power points while harvesting RF energy, with the peak conversion efﬁciency of 49.06% when the input energy is − 6 dBm. With the proposed dual-domain MPPT, the high efﬁciency range of the energy harvesting system is greatly extended to 21 dB ( − 21–0 dBm).


Introduction
With the continuously advancing wireless communication technologies, internet of things (IoTs) is becoming popular in many new applications nowadays. Devices with various sensing techniques, such as temperature, illumination, pressure, and humidity sensing, are commonly used in buildings, industrial controls, health monitoring, and smart home appliances [1][2][3][4][5]. Figure 1 shows the smart home system with IoTs, which usually consists of dozens to hundreds of wireless sensor nodes. Due to the large number of sensor nodes, the maintenance cost will significantly increase to replace the batteries on a regular basis. Moreover, the batteries typically occupy a considerable portion of the system volume and weight. Solar energy is proposed to replace the batteries in [6,7]. However, solar energy is dramatically affected by the weather or the indoor light sources, and it also requires a photovoltaic panel. Energy harvesting is mainly used in IoTs to reduce network maintenance costs and replace the use of batteries [8][9][10][11][12][13]. Variations in the environment will cause disturbance to the input energy, and may possibly lead to a system shutdown. Therefore, smooth energy transfer is a significant challenge for the power management system. Wireless power transfer offers another solution to deliver energy to the IoT devices. Batteries and complex power lines could be avoided [14]. However, the power conversion efficiency of the wireless power transfer systems is affected by the linkage between power sources. To improve the power conversion efficiency, impedance matching between the antenna and the rectifier is crucial [15]. Particularly, when IoT systems have multiple antennas and the input energy may change intensely, it becomes very challenging to maintain high conversion efficiency for a wide input energy range and output loading. LoRa, Wi-Fi, and fifth-generation mobile communications (5G) are popular protocols using on the IoTs. Because of the limitation of safety regulations, the output power of the transmitter is strictly limited, the energy received by the sensing node is about −25 dBm to 0 dBm. Hence, RF energy harvesting systems often face the following challenges.
(1) Peak power conversion efficiency (PCE) of the RF-DC rectifier, which is defined as Pout,DC/Pin,RF, where Pin,RF is the received energy at the input of the rectifier and Pout,DC is the output power. (2) High conversion efficiency range, which means the range of input power while PCE is above a certain level (20% in [16] and 30% in [17]). (3) High sensitivity, which is defined as the minimum input power to keep Vout = 1 V with a 1 MΩ loading.
The charge pump has become popular in integrated circuits for energy harvesting in wireless sensor nodes to acquire high output voltages [18][19][20]. For IoT applications, the main constraints are the cost and the power conversion efficiency. The Dickson rectifier is a typical RF rectifier architecture. Since it is used in high-frequency circuits, its capacitor does not need to be too large, so it is also suitable for applications in integrated RF energy harvesting systems. However, the efficiency and output voltages of the Dickson rectifiers are greatly affected by the threshold voltage of the diodes, Vth. The gate biasing technology adds an extra voltage to the gate terminal of the transistor, which is equivalent to lowering Vth. An additional bias circuit is required. The unstable bias voltage will reduce the conversion efficiency and increase the cost. Other solutions such as Schottky diodes increase manufacturing costs, and zero Vth transistors lead to problems of leakage currents.
In a typical wireless power transfer system, the rectifier is responsible for converting the high-frequency AC energy into DC voltages, then power regulation circuits are required to further reduce the voltage ripples at the output. The efficiency of the AC to DC conversion often becomes the bottleneck of the overall system and will directly limit the performance of the energy harvesting systems. To improve the conversion efficiency of the rectifier, a differential architecture is used to reduce the threshold voltages, Vth, and the turn-on voltage [21][22][23][24]. Self-bias techniques are used to prevent the reverse current LoRa, Wi-Fi, and fifth-generation mobile communications (5G) are popular protocols using on the IoTs. Because of the limitation of safety regulations, the output power of the transmitter is strictly limited, the energy received by the sensing node is about −25 dBm to 0 dBm. Hence, RF energy harvesting systems often face the following challenges.
(1) Peak power conversion efficiency (PCE) of the RF-DC rectifier, which is defined as P out,DC /P in,RF , where P in,RF is the received energy at the input of the rectifier and P out,DC is the output power. (2) High conversion efficiency range, which means the range of input power while PCE is above a certain level (20% in [16] and 30% in [17]). (3) High sensitivity, which is defined as the minimum input power to keep V out = 1 V with a 1 MΩ loading.
The charge pump has become popular in integrated circuits for energy harvesting in wireless sensor nodes to acquire high output voltages [18][19][20]. For IoT applications, the main constraints are the cost and the power conversion efficiency. The Dickson rectifier is a typical RF rectifier architecture. Since it is used in high-frequency circuits, its capacitor does not need to be too large, so it is also suitable for applications in integrated RF energy harvesting systems. However, the efficiency and output voltages of the Dickson rectifiers are greatly affected by the threshold voltage of the diodes, V th . The gate biasing technology adds an extra voltage to the gate terminal of the transistor, which is equivalent to lowering V th . An additional bias circuit is required. The unstable bias voltage will reduce the conversion efficiency and increase the cost. Other solutions such as Schottky diodes increase manufacturing costs, and zero V th transistors lead to problems of leakage currents.
In a typical wireless power transfer system, the rectifier is responsible for converting the high-frequency AC energy into DC voltages, then power regulation circuits are required to further reduce the voltage ripples at the output. The efficiency of the AC to DC conversion often becomes the bottleneck of the overall system and will directly limit the performance of the energy harvesting systems. To improve the conversion efficiency of the rectifier, a differential architecture is used to reduce the threshold voltages, V th , and the turn-on voltage [21][22][23][24]. Self-bias techniques are used to prevent the reverse current flowing in the negative half cycle [25,26]. A reconfigurable rectifier array is also proposed to adapt the regulation system to the various received power due to the variations of the distance and the influence of the environment in [27]. Furthermore, to make the harvesting system work with low input energy, multi-stage rectifiers could be used in series to increase the output voltage. However, with a fixed number of rectifiers in series, the range of high conversion efficiency is often relatively small.
In this work, reconfigurable rectifiers are designed to adjust the output impedance of the RF-DC rectifiers by connecting the rectifiers in various topologies to match different output loading conditions, thereby improving the range of high conversion efficiency. Since the input impedance of the RF rectifier varies with the input energy, fixed matching network will cause serious impedance mismatches when the input energy is extremely high or low. That will not only decrease the conversion efficiency, but also lower the range of high conversion efficiency. By configuring both the rectifier array and impedance matching array according to different input energy levels and output loading, a higher dynamic range is achieved. With the proposed dual-domain maximum power point tracking (MPPT) configurations, the high efficiency range of the overall harvesting system is also greatly extended.

System Architecture
As shown in Figure 2, the proposed system consists of 4 groups of reconfigurable rectifier arrays with various stages in each group, the adaptive impedance matching capacitor arrays, the dual-domain maximum power tracking circuits, and a buck-boost converter.
Energies 2022, 15, x FOR PEER REVIEW In this work, reconfigurable rectifiers are designed to adjust the output imp of the RF-DC rectifiers by connecting the rectifiers in various topologies to match d output loading conditions, thereby improving the range of high conversion eff Since the input impedance of the RF rectifier varies with the input energy, fixed m network will cause serious impedance mismatches when the input energy is ex high or low. That will not only decrease the conversion efficiency, but also lower th of high conversion efficiency. By configuring both the rectifier array and imp matching array according to different input energy levels and output loading, a dynamic range is achieved. With the proposed dual-domain maximum power poin ing (MPPT) configurations, the high efficiency range of the overall harvesting sy also greatly extended.

System Architecture
As shown in Figure 2, the proposed system consists of 4 groups of reconfi rectifier arrays with various stages in each group, the adaptive impedance match pacitor arrays, the dual-domain maximum power tracking circuits, and a buck-bo verter. The proposed reconfigurable rectifier array and adaptive impedance matchin array are controlled by the stage control and the AIM control, respectively. The pr dual-domain MPPT continuously detects the output voltage of the rectifier array. T turbation observation method is utilized to find the optimal array configuratio compensation capacitance will be configured to provide the optimal impedance m for the current input energy. The cycle time of the proposed maximum power tra The proposed reconfigurable rectifier array and adaptive impedance matching (AIM) array are controlled by the stage control and the AIM control, respectively. The proposed dual-domain MPPT continuously detects the output voltage of the rectifier array. The perturbation observation method is utilized to find the optimal array configurations. The compensation capacitance will be configured to provide the optimal impedance matching for the current input energy. The cycle time of the proposed maximum power tracking is 22 µs. The output voltage is further regulated to 1 V through a buck-boost converter. In this work, the input RF energy range is from −25 to 5 dBm, and the output loading varies from 20 kΩ to 1 MΩ.

Multi-Input Reconfigurable Rectifier Array
Although the active rectifiers can provide high power efficiency, it requires a minimum energy supply for the controller, limiting the dynamic range of energy harvesting. As shown in Figure 3a, a differential rectifier composed of 4 diode-connected low-V th NMOS is used to improve the conversion efficiency and the dynamic range. The performance of conventional Dickson rectifiers is often limited by the high threshold voltages. In this work, low-V th NMOS transistors are utilized to improve the efficiency. The number of maximum stages in these 4 groups of rectifiers are designed to be 6, 8, 10, and 12, respectively. The DC path of the rectifier array is connected in parallel by the method of DC power combining [25]. In this way, the phase difference between different antennas will not affect the conversion efficiency of the entire system. The differential rectifier cell is composed of 4 diode-connected low-V th NMOS transistors, as shown in Figure 3b. The possible configurations and the equivalent output impedance of each group are summarized in Table 1. For example, the group of 12 rectifiers could all be connected in series, providing the output impedance of 12 × R stg , where R stg is the output impedance of a single-stage rectifier. Additionally, 6 rectifiers could be connected in series to form a sub-group, and then the two sub-groups are connected in parallel, providing the output impedance of 3 × R stg . To guarantee better matching between two sub-groups, the number of cascaded stages in each sub-group are designed to be equivalent in this work. Therefore, there are only 3 configurations for the groups of 6, 8, and 10 rectifiers, while there are 5 configurations for the group of 12 rectifiers. Each group of arrays can provide various output impedance through these configurations. By paralleling 4 groups of different numbers of arrays, the entire system has more combinations of output impedance to approach the optimal value for maximum power tracking. In addition, to reduce the conduction loss, transmission gates are used as the switches. Taking into account the maximum current of the overall system, the chip area, and the power consumption of the driver, the conduction resistance of the switches is designed to be 30 Ω in this work.

Adaptive Impedance Matching (AIM) Network
The input impedance of the rectifier changes with the received input energy and complicates the design of the impedance matching network. When the impedance of the antenna and the rectifier do not match to each other, the reflection coefficient becomes large, so the energy collected from the environment fails to completely flow into the rectifier. It causes the input voltage of the rectifier to drop, and the output voltage and the conversion efficiency also decrease. Adding an impedance matching network between the antenna and the rectifier reduces the reflection coefficient. As mentioned above, the reflection coefficient is approximately inverse proportional to the received input energy of the rectifier. We also apply the maximum power tracking in the AC energy domain in this work. The matching network is conventionally designed with a time-consuming recursive process [14]. A simple and efficient process is adopted from [17]. The required parameters of the impedance matching network are designed according to the input energy with a fixed loading. Compared to the recursive method, this process saves much time. Here, the AIM network makes the input impedance of the rectifier match to 50 Ω as much as possible with the feedback of the proposed dual-domain MPPT sensing the input energy, as shown in Figure 4. Figure 5 illustrates the AIM network, composed of a 4-bit binary weighted capacitor array, where C total is 1 pF. To accommodate various ranges of input energy at the rectifier, the capacitor array is made up of two 2 pF capacitors in series. When Q cn = 1, M 1 , M 2 , and M 3 are on, the drain and source of M 2 are connected to ground to reduce its on-resistance, which improves the conversion efficiency. shown in Figure 4. Figure 5 illustrates the AIM network, composed of a 4-bi weighted capacitor array, where Ctotal is 1 pF. To accommodate various ranges energy at the rectifier, the capacitor array is made up of two 2 pF capacitors i When Qcn = 1, M1, M2, and M3 are on, the drain and source of M2 are connected to to reduce its on-resistance, which improves the conversion efficiency.

Dual Domain MPPT
Under the same loading condition and input energy, the configuration tha the highest output voltage means that maximum power points have been reac maximum power is obtained at the output loading. Figure 6 shows the maximum tracking circuit including a dual-phase sample-and-hold circuit, a comparator, mum power tracking logic, a configuration controller, and an AIM controller. Th uration controller signal is designed according to the configuration of the 4 group tifier arrays with a 9-bit control signal. There are 5 configurations for the 12-cell ar control signal is from 000 to 101. For the 10, 8, and 6-level arrays, there are 3 co tions, and the control signal is 00, 01, and 10. The capacitor array is controlled b thermometer code, 0000 to 1111.
The proposed dual-domain MPPT firstly configures the rectifier (DC-domai

Dual Domain MPPT
Under the same loading condition and input energy, the configuration that obtains the highest output voltage means that maximum power points have been reached and maximum power is obtained at the output loading. Figure 6 shows the maximum power tracking circuit including a dual-phase sample-and-hold circuit, a comparator, a maximum power tracking logic, a configuration controller, and an AIM controller. The configuration controller signal is designed according to the configuration of the 4 groups of rectifier arrays with a 9-bit control signal. There are 5 configurations for the 12-cell array. The control signal is from 000 to 101. For the 10, 8, and 6-level arrays, there are 3 configurations, and the control signal is 00, 01, and 10. The capacitor array is controlled by a 4-bit thermometer code, 0000 to 1111. the sampled voltage will be compared to the held value from the previous sample. At the beginning of MPPT, the 4 rectifier arrays will be initialized to the 2-stage state to avoid possible circuit damages caused by excessively high output voltages. The maximum power tracking in the RF domain starts at the 15th cycle. When performing RF domain MPPT, the control signal of the capacitor array will be reset to 1000 to reduce the time it takes to track the maximum power points. Measurement results show that the proposed dual-domain MPPT takes 22 μs to complete each detection cycle.  Figure 6. The MPPT controller. Figure 6. The MPPT controller.
The proposed dual-domain MPPT firstly configures the rectifier (DC-domain MPPT) and then adjusts the impedance matching array (RF-domain MPPT). The algorithm of the maximum power tracking is shown in Figure 7. The perturbation and observation (P&O) method is used to detect V out of the rectifier to find the maximum power point. If the output voltage with the current configuration is greater than that in the previous configuration, more stages will be connected in series. On the other hand, fewer serial stages will be connected if the output voltage drops. Using the two-phase sample and hold circuit, the sampled voltage will be compared to the held value from the previous sample. At the beginning of MPPT, the 4 rectifier arrays will be initialized to the 2-stage state to avoid possible circuit damages caused by excessively high output voltages. The maximum power tracking in the RF domain starts at the 15th cycle. When performing RF domain MPPT, the control signal of the capacitor array will be reset to 1000 to reduce the time it takes to track the maximum power points. Measurement results show that the proposed dual-domain MPPT takes 22 µs to complete each detection cycle.

Measurement Results
The proposed reconfigurable rectifier array is designed and fabricated in a TSMC 0.18-μm 1P6M process. Figure 8 shows the chip micrograph. The total active area is 1.2 mm × 1.2 mm and KEYSIGHT 81160A is used to emulate the RF signal. Off-chip power dividers and baluns are employed to provide the 4-channel differential inputs.

Measurement Results
The proposed reconfigurable rectifier array is designed and fabricated in a TSMC 0.18-µm 1P6M process. Figure 8 shows the chip micrograph. The total active area is

Measurement Results
The proposed reconfigurable rectifier array is designed and fabricated in a TSMC 0.18-μm 1P6M process. Figure 8 shows the chip micrograph. The total active area is 1.2 mm × 1.2 mm and KEYSIGHT 81160A is used to emulate the RF signal. Off-chip power dividers and baluns are employed to provide the 4-channel differential inputs.   Figure 9 shows the measurement results of the maximum power tracking process. The input energy is −21 dBm, the output loading is 600 kΩ, and the voltage at the best power point is 0.28 V. The steady-state voltage is 0.28 V. At the beginning of the maximum power tracking, all rectifiers will be reset to a two-stage series connection state. In other words, the control signals for the 4 groups are 000, 00, 00, and 00, respectively. The output voltage drops to 0.17 V when the maximum power tracking starts. The perturbation observation method is used to determine the maximum power points, and it will be maintained until the initialization of the next maximum power tracking cycle. After the configuration of the 6-cell rectifiers is locked, the voltage will fluctuate slightly because the AIM circuit will adjust the compensation capacitance so that the lowest AC energy is reflected at the input of the rectifier.

mm
Energies 2022, 15, x FOR PEER REVIEW 8 of 12 Figure 9 shows the measurement results of the maximum power tracking process. The input energy is −21 dBm, the output loading is 600 kΩ, and the voltage at the best power point is 0.28 V. The steady-state voltage is 0.28 V. At the beginning of the maximum power tracking, all rectifiers will be reset to a two-stage series connection state. In other words, the control signals for the 4 groups are 000, 00, 00, and 00, respectively. The output voltage drops to 0.17 V when the maximum power tracking starts. The perturbation observation method is used to determine the maximum power points, and it will be maintained until the initialization of the next maximum power tracking cycle. After the configuration of the 6-cell rectifiers is locked, the voltage will fluctuate slightly because the AIM circuit will adjust the compensation capacitance so that the lowest AC energy is reflected at the input of the rectifier.  Figure 10 shows the measured results of Vout in the process of MPPT when the input power is −19 dBm. When the output loading is varied from 1 MΩ to 50 kΩ, Vout varies from 0.46 V to 0.32 V, correspondingly. The control signals, QR12, QR10, QR8, and QR6, in the 12, 10, 8, and 6 stage are 010, 01, 00, and 00, which will configure the number of cascaded rectifiers in the sub-group as 4, 5, 2, and 2, respectively.  from 0.46 V to 0.32 V, correspondingly. The control signals, Q R12 , Q R10 , Q R8 , and Q R6 , in the 12, 10, 8, and 6 stage are 010, 01, 00, and 00, which will configure the number of cascaded rectifiers in the sub-group as 4, 5, 2, and 2, respectively.  Figure 10 shows the measured results of Vout in the process of MPPT when the input power is −19 dBm. When the output loading is varied from 1 MΩ to 50 kΩ, Vout varies from 0.46 V to 0.32 V, correspondingly. The control signals, QR12, QR10, QR8, and QR6, in the 12, 10, 8, and 6 stage are 010, 01, 00, and 00, which will configure the number of cascaded rectifiers in the sub-group as 4, 5, 2, and 2, respectively.   Figure 11 illustrates the measured diagram of the input energy versus the output voltage under various loading conditions. The loading resistance ranges from 20 kΩ to 1 MΩ. The larger the loading resistance, the steeper the slope of the output voltage rises with the input energy. The output voltage saturates at about 2.3 V when the input energy is about 0 dBm. When the output loading resistance of 1 MΩ is used, the output voltage of the rectifier reaches 1 V with the input energy of −13.6 dBm. Due to the reconfigurable rectifier array, the output voltage will be adjusted to an appropriate configuration along with the loading conditions to maintain the maximum transmission efficiency. Therefore, the sensitivity of this work is −13.6 dBm.
Energies 2022, 15, x FOR PEER REVIEW 9 of 12 Figure 11 illustrates the measured diagram of the input energy versus the output voltage under various loading conditions. The loading resistance ranges from 20 kΩ to 1 MΩ. The larger the loading resistance, the steeper the slope of the output voltage rises with the input energy. The output voltage saturates at about 2.3 V when the input energy is about 0 dBm. When the output loading resistance of 1 MΩ is used, the output voltage of the rectifier reaches 1 V with the input energy of −13.6 dBm. Due to the reconfigurable rectifier array, the output voltage will be adjusted to an appropriate configuration along with the loading conditions to maintain the maximum transmission efficiency. Therefore, the sensitivity of this work is −13.6 dBm.  Figure 12 demonstrates a three-dimensional graph of the input energy versus the measured efficiency with different loading conditions. When the loading resistance is above 500 kΩ, the efficiency is only 5% or less, and the conversion efficiency becomes higher with loading resistance lower than 300 kΩ. The efficiency peaks appear in the input energy ranges of −6 dBm to −9 dBm. Figure 13 shows measurement results of the input energy vs. efficiency with an output loading resistance of 20 kΩ. The maximum conversion efficiency is 49.06% at Pin of −6 dBm. The dynamic range where the conversion efficiency is higher than 20% is 21 dB, from −21 dBm to 0 dBm.  Figure 12 demonstrates a three-dimensional graph of the input energy versus the measured efficiency with different loading conditions. When the loading resistance is above 500 kΩ, the efficiency is only 5% or less, and the conversion efficiency becomes higher with loading resistance lower than 300 kΩ. The efficiency peaks appear in the input energy ranges of −6 dBm to −9 dBm. Figure 13 shows measurement results of the input energy vs. efficiency with an output loading resistance of 20 kΩ. The maximum conversion efficiency is 49.06% at P in of −6 dBm. The dynamic range where the conversion efficiency is higher than 20% is 21 dB, from −21 dBm to 0 dBm. measured efficiency with different loading conditions. When the loading resistance is above 500 kΩ, the efficiency is only 5% or less, and the conversion efficiency becomes higher with loading resistance lower than 300 kΩ. The efficiency peaks appear in the input energy ranges of −6 dBm to −9 dBm. Figure 13 shows measurement results of the input energy vs. efficiency with an output loading resistance of 20 kΩ. The maximum conversion efficiency is 49.06% at Pin of −6 dBm. The dynamic range where the conversion efficiency is higher than 20% is 21 dB, from −21 dBm to 0 dBm.   Table 2 summarizes the comparison of our proposed system with the previous works. Comparing with previous works, a 4-channel rectifier array in parallel with asymmetric configuration is employed in this work. It extends the high PCE range to 21 dB, with a peak efficiency of 49.06% at Pin of −6 dBm.

Conclusions
The paper proposes a multi-antenna reconfigurable-input rectifier array with dualdomain maximum power tracking. A matching capacitor array and rectifier array are both implemented to be reconfigurable to reach the RF-DC maximum output power. The reflections and RF-DC conversion are both optimized at the same time to improve the over-  Table 2 summarizes the comparison of our proposed system with the previous works. Comparing with previous works, a 4-channel rectifier array in parallel with asymmetric configuration is employed in this work. It extends the high PCE range to 21 dB, with a peak efficiency of 49.06% at P in of −6 dBm.

Conclusions
The paper proposes a multi-antenna reconfigurable-input rectifier array with dualdomain maximum power tracking. A matching capacitor array and rectifier array are both implemented to be reconfigurable to reach the RF-DC maximum output power. The reflections and RF-DC conversion are both optimized at the same time to improve the overall sensitivity and efficiency. As a result, the range of high conversion efficiency is greatly extended. Measurement results show that maximum PCE is 49.06% and the high PCE range is 21 dB with an input energy of −6 dBm.