An Overview of Regulation Topologies in Resonant Wireless Power Transfer Systems for Consumer Electronics or Bio-Implants

Abstract

Owing to its relatively high efficiency, extended transmission range, and less exposure to radio frequency radiation, near-field resonant wireless power transfer (R-WPT) has been widely used in consumer electronics and bio-implants. For most applications, a well-regulated output voltage is required against the coupling and loading variations, and thus a regulation scheme should be employed in an R-WPT system. To achieve an optimal receiver (RX) or overall efficiency, together with a reduced cost overhead, several regulation schemes have been proposed in recent years, where the regulation can be implemented at either the RX or transmitter (TX) side, or both. These regulation schemes have been reviewed and comprehensively discussed in this paper. Hence, the main contribution of this paper is to provide a guideline for designing the regulation scheme in R-WPT systems. Moreover, potential new topologies of regulation are investigated here.

1. Introduction

The wireless power transfer (WPT) technique is at the critical point of explosive growth. Many consumer electronics and bio-implant systems have integrated WPT circuits for their compactness, being water-proof, and their reduced maintenance cost. However, the WPT circuits’ transfer efficiency is inherently lower than that of their wired counterparts [1,2]. To balance this trade-off, high-efficiency WPT techniques, e.g., near-field transmission (such as inductive, resonant, capacitive, and ultrasonic power transfer), may be more favorable than far-field WPT (such as optical and microwave). In addition, the near-field technique advances far-field WPT in terms of less exposure to radio frequency (RF) radiation. Among the near-field WPT techniques, resonant WPT (R-WPT) has gradually drawn widespread attention. This is because the R-WPT technique can extend the power transfer range to several tens of centimeters, which is much wider than that of the inductive coupling technique. On one other hand, the resonant coupling technique does not require a precise coil alignment and tight coupling, and thus multiple receivers can be applied to receive power from a transmitter.

Some previous studies have reviewed the R-WPT techniques [3,4,5,6,7]. In [3,4], the historical background, challenges, and engineering applications of R-WPT were discussed. The authors in [5] presented the coil design challenges. A comparison between the inductive and capacitive power transfer in power level, gap distance, operating frequency, and efficiency were given in [6]. In addition, [7] discussed the design of resonant circuits and the compensation networks for near-field WPT systems.

Taking an R-WPT system with series-resonant inductor and capacitor (LC) tanks as an example, as illustrated in Figure 1, it consists of a transmitter (TX), a wireless link, and a receiver (RX). In general, the TX is composed of a direct current (DC)-DC converter for power supply, gate drivers, and a power amplifier (PA), where the VDD is the supply voltage; the wireless link consists of two series LC tanks (L_TX C_TX and L_RX C_RX) resonant in the same angular frequency ω_res, where k is the coupling coefficient between L_TX and L_RX; and the RX is composed of a rectifier. The alternating current (AC) power, generated from the PA, is transferred from the L_TX to the L_RX, where the AC voltage across the L_RX is V_R and the equivalent resistance seen from the RX is R_eq. Then, the rectifier converts the V_R into a DC voltage V_OUT for a given load R_L.

There are four important parameters for this WPT system: (1) the power delivered to the load (PDL) equaling to $V_{\mathrm{OUT}}^2$/R_L; (2) the power transmission efficiency (PTE) PDL/P_S, where P_S is the TX input power; (3) the power conversion efficiency (PCE) PDL/P_R, where P_R is the RX input power; and (4) the voltage conversion efficiency (VCE) V_OUT/V_R.

For most of the applications, the power supply should be well-regulated. For instance, the power supply should be regulated to >10 V for the neural stimulators in implantable medical devices (IMDs) [8] or flash memory circuits [9]. For battery charging, a constant current and voltage control is required [10]. Also, the regulation becomes especially important in an R-WPT system considering load and coupling distance variation and a coil misalignment [11]. Additionally, a poorly designed regulation scheme may degrade the PTE. Therefore, a comprehensive review of regulation in R-WPT is essential.

How can the regulation be implemented in an R-WPT system? It is straightforward to fulfill the regulation at the RX side, but it can also be fulfilled at the TX side. For clarification, a simplified circuit model of an R-WPT system is presented in Figure 2a without considering the coil resistance. The PA output can be modeled as a source V_PA with a source resistor R_S. As shown in Figure 2b, the effect of the RX’s resonant magnetic coupling with the TX is presented as a reflected resistance R_refl in series with the L_TX, which can be written by

$$R_{\mathrm{refl}}=k^2{\omega }_{\mathrm{res}}{L}_{\mathrm{TX}}{Q}_{\mathrm{load}}$$

(1)

where Q_load is the loaded Q-factor of the RX resonant tank, which is given by:

$$Q_{\mathrm{load}}=\{\begin{array}{l}\frac{\omega L_{\mathrm{R}\mathrm{X}}}{R_{\mathrm{e}\mathrm{q}}}\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{e}\mathrm{s}-\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{R}\mathrm{X}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{k}\\ \omega C_{\mathrm{R}\mathrm{X}}{R}_{\mathrm{e}\mathrm{q}}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{l}-\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{R}\mathrm{X}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{k}.\end{array}.$$

(2)

It should be noted that the power received by the RX is equivalent to that which dissipates on R_refl, which can be expressed as

$$P_{\mathrm{R}}=V_{\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{l}}\times I_{\mathrm{T}\mathrm{X}}$$

(3)

where V_refl is the voltage across R_refl. Based on Equation (3), once V_refl or I_TX is regulated at the TX side, the received power can be regulated as well as V_OUT. Therefore, regulation can be achieved at the TX side.

Therefore, the regulation schemes investigated in the previous works can also be categorized into two types: RX and TX regulation. As illustrated in Figure 3, RX regulation includes post-stage regulation (achieved by a cascading low dropout regulator (LDO [12,13,14,15] or a DC–DC converter [16,17,18,19,20]) and one-stage regulation, including active diode conduction time control [21,22,23], reconfigurable regulating rectification [24,25,26,27], and switching-based current-mode regulation [28,29,30,31]. On the other hand, TX regulation can be achieved by PA supply voltage control [32,33], resonant frequency control [34], PA power switch duty cycle control [35,36,37,38,39,40], and vector power summing control [41,42]. Additionally, switching frequency modulation [35,36], pulse density modulation [37,38], and phase-shifted modulation [39,40] can be classified as power switch duty cycle control.

This paper is organized as follows: Section 2 reviews the operation principles of the previous RX regulation topologies. Then, the operation principles of TX regulation are reviewed in Section 3. Possible combinations and potential new topologies are given in Section 4. Finally, a conclusion is drawn in Section 5.

2. RX Regulation

2.1. Post-Stage Regulation

At the RX side, post-stage regulation is straightforward and has been widely used [12,13,14,15,16,17,18,19,20]. This scheme adopts a rectifier cascaded by a regulating stage as shown in Figure 4. Both the LDO [12,13,14,15] and the DC–DC converter [16,17,18,19,20] can be implemented as the cascaded stage. These schemes are discussed as follows.

2.1.1. The Rectifier Cascaded by an LDO

An LDO cascading the rectifier can provide precise regulation while keeping a small voltage ripple compared to a DC–DC converter. For example, as in Figure 5, three LDOs are cascading the rectifier in [12], supplying the analog, digital, and reference circuits, respectively, in a system-on-a-chip (SoC). Additionally, due to the high isolation among LDOs, each regulation loop can be independently optimized. However, the PCE is inherently low due to the LDOs’ efficiency being directly determined by the ratio of the output and input voltages. Therefore, the maximum rectifier efficiency and PCE of [12] was 85% and 74.8%, respectively, which is limited by the efficiency of the post-regulation stage.

2.1.2. The Rectifier Cascaded by a DC–DC Converter

The PCE can be improved by using a high-efficiency post-regulator, e.g., a DC–DC converter. The authors in [16] showed a rectifier cascaded by a buck converter for battery charging as illustrated in Figure 6. Additionally, average current-mode control (ACMC) is applied for precise load current control in both continuous and discontinuous inductor current modes. With this topology, the measured rectifier efficiency and PCE were enhanced to 92.8% and 84.6%, respectively. However, additional bulky passive components, e.g., an off-chip inductor, are required in the DC–DC converter, resulting in a significant cost overhead and low integration. Moreover, the switching operation of the DC–DC converter increases the output ripple and ground noise.

2.1.3. The Rectifier Cascaded by an Inductorless Switching Converter

To eliminate the bulky inductor in [16], a resonant regulating rectifier (3R) was proposed in [17]. The working principle of this 3R scheme is illustrated in Figure 7a, where a switch S₁ is inserted between the rectifier and the load. When S₁ is turned on, the rectifier output current I_REC charges the load (On duty in Figure 7b), while in the Off duty, S₁ is turned off and the resonant current I_RX freewheels without charging. Then, V_OUT can be regulated by controlling the turn-on duty cycle of S₁ using the pulse width modulation (PWM). During the off duty, the I_REC reaches zero when S₁ is turned off due to a very large equivalent resistance R_eq. Hence, the rectifier is working in Discontinuous Conduction Mode (DCM) similar to a DC–DC converter. This feature is not desirable, since the root meam square (RMS) resonant current I_RX-RMS in this case will be much higher than that in Continuous Conduction Mode (CCM). This results in a higher coil power loss represented by I_RX-RMS²×R₂, where R₂ represents the L_RX resistance.

To reduce the RMS resonant current, a three-switch 3R scheme working in CCM was also presented in [17]. The working principle of this scheme is shown in Figure 8. When in on duty, both S₁ and S₃ are turned on and S₂ is turned off, making C_FL and C_L connect in parallel. On the contrary, when in off duty, S₁ and S₃ are turned off and S₂ is turned on, resulting in C_FL and C_L being connected in series. Under this configuration, a significantly smaller equivalent resistance R_eq can be achieved in off duty compared with DCM, allowing I_REC to charge the load continuously similar to CCM as shown in Figure 8c. Similarly, the output voltage can be regulated using PWM to switch between the on- and off-duty states. However, considering DCM is still useful, especially under a light load condition, the three-switch 3R can also be configured to DCM by turning S₁ and S₃ on and S₂ off in the on state and turning S₁, S₁, and S₃ off in the off state. Hence, the load range can be extended by configuring the rectifier to DCM in light load conditions and CCM in heavy load conditions. This three-switch 3R showed a measured maximum 86% PCE when the loading current ranged from 70 to 700 mA, and precise regulation was achieved with a 3.3% output voltage deviation.

Another issue for the 3R scheme is that a potentially high V_REC is expected at the beginning of off duty, which may damage the switches. To address this, a limiting capacitor C_LM is added between the rectifier inputs (V_AC1 and V_AC2), which limits the V_REC to V_OUT + 2V_D at on duty and V_LM –2V_D at off duty.

For the aforementioned post-stage regulations [12,13,14,15,16,17,18,19,20], they all suffer from loss from the cascaded stages. The PCE can be written as:

$$\mathrm{P}\mathrm{C}\mathrm{E}={\eta }_{\mathrm{r}\mathrm{e}\mathrm{c}}\times {\eta }_{\mathrm{r}\mathrm{e}\mathrm{g}}$$

(4)

where η_rec and η_reg are the efficiencies of the rectifier and post-stage regulators, respectively. As such, although η_reg can be reasonably high, the PCE is still limited. Consequently, multiple one-stage regulation schemes have been proposed as a solution.

2.2. One-Stage Regulation

2.2.1. Active Diode Conduction Time Control

To eliminate the post regulator for a higher PCE, it is straightforward to integrate the rectification and regulation into one stage. The authors in [21,22,23] presented a one-stage regulating rectifier. In these schemes, the diode is implemented by a gate-controlled power transistor. The diode conduction time can be controlled by modulating the pulse width or the frequency of the power transistor gate control signal. As a result, the amount of current delivered to the load is controlled, and thus we have output regulation. These schemes are discussed as follows.

The authors in [21] proposed a regulating rectifier, and the regulation is achieved by controlling the active diode conduction time as in Figure 9a. The n-channel metal-oxide-semiconductor field-effect transistor (NMOS) M₁ and M₂ are cross-connected as the down rectifying diodes. For the up rectifying p-channel metal-oxide-semiconductor field-effect transistor (PMOS) M₃ and M₄, they are controlled by a pulse generator. When V_AC1 > V_OUT, M₃ is turned off and M₄ is turned on and vice versa. By controlling the M₃ and M₄ conduction time, V_OUT regulation can be achieved. A PWM scheme will be straightforward, but the pulse width of the gate control signals V_GP1 and V_GP2 may be too narrow to turn on M₃ and M₄ under a light load condition for a high working frequency. To circumvent this, hybrid pulse modulation (HPM) is utilized as a combination of PWM and pulse frequency modulation (PFM) to provide regulation for a wide load range as given in Figure 9b. When the V_GP1 and V_GP2 pulse width controlled by PWM is decreased to a threshold value, PFM takes over the control loop by adjusting the V_GP1 and V_GP2 pulse frequency. The measurement result of [19] showed a maximum 60% PCE with a 10-mm coil distance. Obviously, the PCE is not optimized, which is mainly due to the relatively large rectifying diode drop (between V_AC1(2) and V_OUT) under certain loading conditions, especially when M₃ and M₄ may be turned on around the peak of V_AC1(2) as in Figure 10a. As such, an additional power loss will be found on M₃ and M₄ and thus a PCE degradation.

To address this issue, the authors of [22], whose idea is illustrated in Figure 10c proposed a turn-on phase control technique to turn the active diodes on with a minimized diode drop. The M₃ and M₄ gate control signals in this scheme are generated by the phase control comparator CMP₁ and CMP₂ rather than a conventional comparator. The waveforms of V_AC1(2) and V_OUT are illustrated in Figure 10b. When V_AC just exceeds V_OUT, the rectifying diodes M₃ and M₄ are turned on, similar to a conventional rectifier, but they are turned off when V_OUT exceeds a reference voltage V_REF. Moreover, M₃ and M₄ also adopt a dynamic body biasing circuit for further voltage drop reduction and PCE improvement. The measurement results showed that this scheme can provide a regulated V_OUT from 2.5 V to 4.6 V with an improved PCE from 72% to 87%.

The PCE can be even more improved by optimizing the conduction time of both the up and down rectifying diodes [23] as in Figure 11. The V_OUT regulation is achieved by adaptively adjusting the duty-cycle D and phase ϕ of the gate control signals V_GP1, V_GP2, V_GN1, and V_GN2 simultaneously with a rectification controller. The desired D and ϕ are adaptively synthesized based on an I_RX sensor using M₅ and M₆. The measurement result showed that this phase and duty-cycle control can regulate the output voltage from 3.5 V to 5 V, and the maximum PCE was 96% at a 4.64 V output voltage.

2.2.2. Reconfigurable Regulating Rectification

Another one-stage topology is based on the reconfigurable resonant regulating (R³) rectification technique [24,25]. In these schemes, the R³ rectifier can be reconfigured to multiple basic rectifier topologies, e.g., full-wave (1×) and half-wave rectifiers (½×) and a voltage doubler (2×), and the rectifier output voltages are 1×, ½×, and 2× V_OUT, respectively. As such, RX regulation can be achieved by switching among these topologies.

In [26,27], a 1×/2× reconfigurable rectifier was demonstrated as in Figure 12, where the switches S_1~5 are utilized to fulfill the reconfiguration. When S₃, S₄ is turned on while the others are turned off, the power transistors M₃ and M₄ are cross-connected as two upper diodes, and D₁ and D₂ act as active diodes. In this scenario, it works as a full-wave rectifier as shown in Figure 12a. On the other hand, when S₁ and S₂ are turned on while S₃ and S₄ are turned off, M₁ and M₃ are configured to active diodes and M₂ and M₄ are disabled. Meanwhile, S₅ is turned on to connect V_AC2 to the middle of the two load capacitors C_L1 and C_L2, making the rectifier a voltage doubler as depicted in Figure 12b. It should be noted that R_eq equals R_L/2 and R_L/8 in 1× and 2× mode, respectively.

This reconfigurable rectifier topology was applied in [24] for regulation with PWM control as illustrated in Figure 13a. Once V_AC1(2) has a fixed amplitude, the rectifier will output voltages V_1× and V_2× at 1× and 2× mode, respectively. As shown in Figure 13b, the PWM controller switches the reconfigurable rectifier periodically between the two modes so that V_OUT can be regulated at an intermediate voltage between V_1× and V_2×­. Thanks to the one-stage scheme, the maximum PCE of this R³ rectifier was 92.6% at a 60 mW output power in [24].

However, the R³ rectifier in [24] may fail to correctly regulate V_OUT under certain circumstances. Firstly, V_OUT cannot be regulated to lower than V_1× or higher than V_2×. Secondly, V_OUT cannot be correctly regulated if the term V_2× > V_1× is not true, which is discussed as follows.

From [43], V_2× andV_1× can be written as:

$$V_1{}_{\mathrm{X}}=k\sqrt{\frac{L_{\mathrm{R}\mathrm{X}}}{L_{\mathrm{T}\mathrm{X}}}}\frac{Q_1{Q}_2}{1+k^2{Q}_1{Q}_2+Q_2/Q_{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d},1}{}_{\times }}·A_{1\times }·V_{\mathrm{S}}$$

(5)

$$V_{2\mathrm{X}}=k\sqrt{\frac{L_{\mathrm{R}\mathrm{X}}}{L_{\mathrm{T}\mathrm{X}}}}\frac{Q_1{Q}_2}{1+k^2{Q}_1{Q}_2+Q_2/Q_{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d},2}{}_{\times }}·A_{2\times }·V_{\mathrm{S}}$$

(6)

where A is the voltage conversion ratio V_OUT/V_AC. From Equations (5) and (6), there exists a breakeven value where V_2× = V_1×, which can be given by:

$$R_{\mathrm{L}\mathrm{a}}=\frac{2Q_2}{{\omega }_{\mathrm{r}\mathrm{e}\mathrm{s}}{C}_2(1+k^2{Q}_1{Q}_2)}·\frac{A_{1\times }{A}_{2\times }}{A_{2\times }-A_{1\times }}$$

(7)

and the resulting V_1× and V_2× versus the load is presented in Figure 13c. As can be seen, V_2× > V_1× will possibly take place under some heavy loading condition (R_L < R_La), which undermines the regulation.

To overcome the limited load range and facilitate correct regulation, a three-mode R³ rectifier is presented in [25]. As illustrated in Figure 14, it can be configured into three modes: a full-bridge rectifier (1× mode), a half-bridge rectifier (½× mode), and freewheeling (0× mode). The ½× mode is added to fulfill an even distribution of power for a reduced output voltage ripples. The output regulation of this rectifier can be achieved by switching between two of the three modes. Specifically, it switches periodically between 1× and ½× mode under a heavy load, and between ½× and 0× mode under a light load. These two control schemes can be automatically changed based on the output current sensed. A first and Type II compensation are adopted in PWM to obtain a fast response and a stabilized system. A peak 92.2% PCE was measured with a 3.5 W output power, and a maximum 6 W output power was observed.

To sum up, the aforementioned regulating rectifiers [21,22,23,24,25,26,27] can achieve high PCE and self-regulation. However, the VCE is typically low in these schemes, which is not favorable especially when the coil distance is increased or the coils are misaligned.

2.2.3. Switching-Based Current-Mode Regulation

To achieve a high VCE, a switching-based current-mode (SCM) regulating technique was proposed in [28,29,30,31]. This technique differs from voltage-mode ones by firstly storing the received energy in the RX LC resonant tank (as the resonant phase) and then delivering it to the load (charging phase). With SCM regulation, the power delivered to the load (PDL) can be regulated by controlling the length of the resonant phase.

A SCM RX based on Q-modulation was proposed in [28] as in Figure 15a, where the regulation is realized by modulating Q_load. As in Figure 15b, the resonant phase (with T_Φ1 duration) is activated by turning on the single switch S₁. For maximum energy storing, S₁ is turned on at the zero-crossing point of the resonant current I_RX, as in Figure 16a, which should be twice every cycle. Additionally, when SW is turned off, it is in a charging phase (with T_Φ2 duration) as in Figure 15c.

Two advantages can be found in this SCM RX. For one thing, the equivalent resistance R_eq and thus the Q-factor are modulated by the duration ratio (m = T_Φ1/T_Φ2) as

$$R_{\mathrm{e}\mathrm{q}}=R_{\mathrm{L}}\left[1-D+\frac{1}{2\pi }\mathrm{s}\mathrm{i}\mathrm{n} (2\pi D)\right]$$

(8)

where D = m/(1 + m). Consequently, by adjusting m, the received and thus output power can be regulated. For the other thing, according to Equation (8), the equivalent resistance R_eq is decreased in Q-modulation, and thus the Q_load is increased. The V_R in this case can be expressed as:

$$V_{\mathrm{R}}=k\sqrt{\frac{L_{\mathrm{R}\mathrm{X}}}{L_{\mathrm{T}\mathrm{X}}}}\frac{Q_1{Q}_2}{1+k^2{Q}_1{Q}_2+Q_2/Q_{\mathrm{l}\mathrm{o}\mathrm{a}\mathrm{d}}}·V_{\mathrm{S}}$$

(9)

indicating that V_R can be boosted without using a bulky inductor as in a conventional boost DC–DC converter. The measured results showed that the V_R can be boosted to 5.5 V.

However, when maximum energy is stored in the L_RXC_RX tank, the SW turn-on timing should be restrictively synchronized to the I_RX zero-crossing point, which significantly increases the design difficulty. In addition, this synchronization makes it difficult for the system to work at a high resonant frequency, e.g., the 2 MHz resonant frequency in [28]. The measured result showed that the PTE was 40.5% at R_L = 200 Ω with an 8-cm coil distance, and greater than 20% PTE can be achieved when R_L ranges from 50 to 1000 Ω.

To allow for a higher resonant frequency, a multi-cycle Q-modulation (MCQ) technique was introduced in [30] that works at a 13.56 MHz resonant frequency. The principle of MCQ is similar to that of [28], but both the resonant and charging phase are extended to multiple carrier cycles as in Figure 16b. MCQ can work without synchronizing the SW turn-on instant to the I_RX zero-crossing points, which reduces the design difficulty. To overcome resonant frequency shifting due to the parasitic capacitance in the wireless link, an automatic resonance tuning scheme is also introduced in [30]. The measured result showed a 28.02% PTE at R_L = 100 Ω. Compared with a voltage-mode rectifier, the V_OUT has been increased significantly from an average of 2.61 to 4.15 V with the same input, coupling, and loading conditions.

In sum, the SCM technique can achieve a high V_R without a voltage doubler or boost converter. This is due to the fact that the high-Q resonant tank is established by reducing the load in the resonant phase such that the V_R can be much higher, resulting in a high output voltage delivered to the load. In addition, output regulation can be achieved by modulating R_eq. Unfortunately, in many cases PDL regulation and PTE optimization cannot be simultaneously achieved.

Table 1. The comparison of RX regulation topologies in state-of-the-art R-WPT systems.

References	[12]	[16]	[17]	[21]	[22]	[23]	[24]	[25]	[28]	[31]
Topology	Post-stage regulation			One-stage regulation
Max. PDL	40 mW	6 W	6 W	0.7 mW	12.8 mW	2.68 W	0.1 W	6 W	1.45 W	96 μW #
Max. Rectifier Eff.	85%	92.8%	92.5% #	Rectifier efficiency = PCE for one-stage regulation
Max. PCE	74.8%	84.6%	86%	60%	87%	96%	92.6%	92.2%	87.1%	N/A
Max. PTE	N/A	N/A	55%	N/A	N/A	47.2%	50%	N/A	~46% #	5.3%
Max. VCE	N/A	N/A	N/A	0.92	0.92	N/A	N/A	~0.9 #	0.82 #	3.1

^# Calculated from figures in the paper. PDL, power delivered to the load; PCE, power conversion efficiency; PTE, power transmission efficiency; VCE, voltage conversion efficiency.

presents a comparison of the RX regulation topologies used in state-of-the-art works. For the post-stage regulation, although they have a high rectifier efficiency, PCEs are limited due to the loss from the cascaded stage. By contrast, the one-stage schemes typically achieve a higher PCE, except [19] where a large rectifying diode drop takes place. In addition, to address the low VCE of the regulating rectifiers [21,22,23,24,25], the SCM technique is proposed in [28,31] to boost the V_R. The VCE of [28] is still smaller than 1 due to its application to R_L in the range of hundreds of ohms and below, while it is much higher in [31] when applied to a low output power system.

3. TX Regulation

Besides regulation at the RX side, the output can be regulated at the TX side as well. This scheme is defined as TX regulation, which can be achieved by controlling the PA supply voltage [24,32,33], the resonant frequency [34], or the power switch duty cycle [36,37,38,39,40]. The necessity for TX regulation and its implementations are discussed in the following sections.

3.1. Why TX Regulation is Necessary

TX regulation is pivotal in many cases. For one thing, TX regulation manages to widen the load range considering that the RX regulation range is typically limited. For the other thing, it is difficult to simultaneously optimize the PTE with RX regulation under a wide range of coil coupling distances, misalignments, or loading conditions. Hence, to optimize the PTE, TX regulation based on global feedback from the RX side is necessary.

The authors in [24] presented a scenario for how TX regulation is useful to extend the output range, where V_2× < V_1× and thus false regulation may take place under certain load conditions. To handle this, the TX output power was increased during the 2× mode to ensure that V_2× > V_1× was unconditionally correct. The load condition at the RX side can be fed back to the TX side to facilitate TX power control. As shown in Figure 17a, the feedback is achieved with a global control loop, and the load condition can be sensed by a backscattering technique. Then, the significant difference of R_eq between 1× and 2× mode is backscattered to the primary side, causing an I_TX difference, which is sensed by an additional coil L_sen coupling to the TX coil. This additional coil only takes up a small area so as to minimize its effect on the coupling coefficient and the cost overhead.

The authors in [32] demonstrated another TX regulation scheme to ensure V_2× > V_1×. Based on the analysis in [32], the V_R is approximately proportional to V_refl, which means that V_R can be indirectly regulated by regulating V_refl at the TX side instead. In this scheme, a fixed V_R can be achieved over a much wider workable coupling and loading range. Within this range, V_2× is approximately twice V_1×, leading to correct output voltage regulation.

To regulate V_refl, it must be sensed first. Unfortunately, R_refl is not a physical resistor, so V_refl cannot be sensed directly. Hence, as illustrated in Figure 17b, a current-based V_refl sensor is applied for V_refl detection. Then, by adjusting the supply voltage using a PWM-controlled DC–DC converter, the V_refl can be regulated to be equal to reference voltage V_REF under different modes in an R³ rectifier, keeping V_R constant. In addition, the mode switching information D₀ can feed back by backscattering and then convert into V_REF by DAC (digital to analog converter) and FPGA (field programmable gate array). Measurement results showed that with this TX regulation, the workable coupling and loading ranges were extended by 250% with 120 mW output power and by 300% with a 1.2-cm coil distance compared to [24]. In addition, a maximum 92.5% PCE and 62.4% PTE were achieved.

3.2. Power Amplifier Supply Voltage Control

The PA supply voltage control, which is typically achieved with a DC–DC converter [33], is the most straightforward approach to TX regulation. Let us take a TX based on a class D PA as an example. As shown in Figure 18a, by setting a proper V_G1 and V_G2 to drive the M₁ and M₂, the PA will output a square wave V_PA with a 50% duty cycle as in Figure 18b, and the Fourier series of V_PA can be expressed as:

$$V_{\mathrm{P}\mathrm{A}}(\mathrm{t})=\frac{VDD}{2}+\frac{2VDD}{\pi }\left(\mathrm{s}\mathrm{i}\mathrm{n} ({\omega }_{sw}t)+\frac{1}{3}\mathrm{s}\mathrm{i}\mathrm{n} (3{\omega }_{sw}t)+\frac{1}{5}\mathrm{s}\mathrm{i}\mathrm{n} (5{\omega }_{sw}t)+\cdot \cdot \cdot +\frac{1}{n}\mathrm{s}\mathrm{i}\mathrm{n} (n{\omega }_{sw}t)+\cdot \cdot \cdot \right)$$

(10)

where ω_sw = 2πf_sw and f_sw is the switching frequency. It is noteworthy that here n is an odd number. Then, the DC and high order harmonics components are filtered out by the L_TXC_TX tank. Consequently, the PA output voltage V_PA is proportional to the supply voltage from Equation (10), and thus V_PA can be regulated by controlling the supply voltage. Measurement results in [33] showed that a 40.2% PTE improvement had been achieved with a 7-mm coil distance and 250 mW output power.

3.3. Resonant Frequency Control

It should be noted that TX regulation can be achieved not only by adjusting the supply voltage, but also the resonant frequency f_res. The more f_res is tuned to be deviated from the resonant frequency of the L_TXC_TX tank, the less power will be transmitted.

The authors in [34] presented a resonant frequency control scheme as illustrated in Figure 19. The resonant frequency here was adjusted by controlling the value of the capacitor C_TX in the resonant TX tank. The C_TX implements a weighted-capacitor array, which is controlled dynamically by the load condition from the RX side through a wireless communication network. The measurement results showed that the PDL can be regulated effectively over a wide load range, and 80% PCE can be achieved when transferring 15 W over a 10-mm coil distance.

Nonetheless, the C_TX in [34] can only be tuned discretely, which prevents high-resolution regulation. Furthermore, for the commonly used megahertz Industrial Scientific Medical (ISM) band, the allowable bandwidth is pretty narrow, e.g., 15 KHz for 6.78 MHz and 7 KHz for 13.56 MHz [44]. Consequently, the tunable f_res and regulation range will be limited to accommodate the ISM specifications. Additionally, a low PTE is expected, since the resonant frequency of the TX LC tank is purposely adjusted to deviate from the RX tank’s resonant frequency for regulation [43].

3.4. PA Power Switch Duty-Cycle Control

TX regulation can also be implemented by a PA power switch duty-cycle control technique based on switching frequency modulation [35,36], pulse density modulation [37,38], and phase shifted modulation [39,40]. These schemes advance the resonant frequency control scheme by keeping a constant f_res. These schemes are discussed in the following sections.

3.4.1. Switching Frequency Modulation

It should be noted that f_sw can be also designed to not be equal to f_res. According to Equation (10), when f_sw = f_res/n, the nth subharmonic component can be used for the power transmission. Considering that the DC and other components are filtered out by the TX resonant tank, V_refl can be written as:

$$V_{\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{l}}\left(\mathrm{t}\right)=\frac{1}{n}\times \frac{2VDD}{\pi }\times \mathrm{s}\mathrm{i}\mathrm{n} (n{\omega }_{\mathrm{s}\mathrm{w}}t)|{}_{f_{\mathrm{s}\mathrm{w}}=\frac{1}{n}{f}_{\mathrm{r}\mathrm{e}\mathrm{s}}}=\frac{f_{\mathrm{s}\mathrm{w}}}{f_{\mathrm{r}\mathrm{e}\mathrm{s}}}\times \frac{2VDD}{\pi }.$$

(11)

According to Equation (11), V_refl is proportional to f_sw. Therefore, changing f_sw according to the global feedback manages to regulate V_refl and thus V_OUT.

The authors in [35] demonstrated a switching frequency modulation technique as illustrated in Figure 20. In this work, the PA switching frequency f_sw can be set to f_res or f_res/3 as shown in Figure 21a,b, respectively. Based on Equation (11), the V_refl under f_sw = f_res/3 is 1/3 of that when f_sw = f_res. Hence, V_refl can be regulated by switching f_sw between f_res and f_res/3 using a PWM scheme while the resonant frequency is kept constant. Additionally, the error amplifier (EA) output is fed back to TX through the wired data link, and a 2nd Δ-Σ modulator is applied to switch the PA between the f_res and f_res/3 modes to reduce spurious emission. However, the regulation range is limited from f_res/3 to f_res. The measured results showed that maximum power of 0.52 W can be transferred with a 50% PTE.

To extend the regulation range, [36] presented an enhanced subharmonic resonant switching scheme. Different from [35], the regulation can be achieved not only using odd-order harmonics, but also even-order harmonics. An even-order harmonic is implemented by averaging the adjacent two odd-order harmonics in the time domain, e.g., f_res/4 can be achieved by averaging out f_res/3 and f_res/5 as illustrated in Figure 22b. As such, any frequency within (0, f_res] can be chosen as f_sw, resulting in a wider V_OUT regulation range. The measurement results showed a 50% V_OUT regulation range extension with the proposed scheme compared to [35].

3.4.2. Pulse Density Modulation

The authors in [37] showed a pulse density modulation (PDM) technique based on On-Off Keying (OOK) modulation. This scheme regulates the transmitted power by switching the PA between the working and idle modes using OOK modulation. As illustrated in Figure 23, the differential PA consists of four power switches M_1~4, which are driven by the gate control voltages (V_G1~4) with the resonant frequency. The switching signal S₁, modulated with an OOK envelope S₂, are applied to generate the gate control signals V_G1~4. When S₂ is logic high, the PA operates normally and when V_LF is logic low, the PA operates in idle mode. The measured maximum PTE was 72.6% at a 10 Ω load resistance with a 0.2-m coil distance.

The authors in [35] proposed another PDM technique for both differential PA output voltage V_PA regulation and optimized efficiency as illustrated in Figure 24a. This scheme regulates V_PA by adjusting the pulse density d, which is defined as the total density of the positive (P) and negative (N) pulses of the voltage V_PA, e.g., Figure 24b shows a V_PA waveform when d = 1, while Figure 24c shows the d = 0.5 scenario, where some pulses are removed and denoted by “0”. Considering the root-mean-square (RMS) value of the V_PA fundamental component is:

$$V_{\mathrm{P}\mathrm{A}}=\frac{2\sqrt{2}}{\pi }VDD\times d$$

(12)

V_PA can be well-regulated with any specified d within the range of [0, 1]. The measured results showed that this scheme maintained a constant output power of 10 W and achieved a maximum efficiency from 93% to 73% when the coil distance varied from 0.1 to 0.4 m under a 100 Ω load resistance. In addition, the gate control voltages V_G1~4 are controlled by a specially designed ΔΣ-modulator to maintain the PA’s stability.

3.4.3. Phase-Shifted Modulation

The authors in [36] presented a scheme that regulates the output voltage V_PA by varying the phase-shifted angle α of the gate control signals V_G1~4 in differential PA. As shown in Figure 25, the duty-cycle of each switching signal V_G1~4 is 50%, but pulses of switch for M₄ and M₂ can lag M₁ and M₃ at a certain phase angle α ranging from 0° to 180°. Hence, by increasing α between V_G1(2) and V_G4(3), the simultaneous conduction time T₁₄₍₂₃₎ of the power transistors M₁₍₂₎ and M₄₍₃₎ will be reduced, and thus the V_PA will be decreased. The measured results demonstrated that the V_PA was regulated to 28 V (rms) when the supply voltage ranged from 35 to 75 V, and the PA efficiency was around 94.5%.

However, the PA switching loss increases as the phase-shifted angle α approaches 180°, which results in a low efficiency under a light load condition. To address this, [40] demonstrated a TX regulation with harmonic-based phase-shifted modulation (HPSM). This technique applies the nth harmonic component of the switching frequency to regulate the transmitted power, as shown in Figure 26b, taking the 3rd HPSM as an example as follows.

A half-switching period is subdivided into six stages. Stage 1 [t₀, t₁]: M₂ is turned on, the power is oscillating freely through M₂, L_TX, C_TX, and D₁, and V_PA is equal to 0. Stage 2 [t₁, t₂]: M₁ is turned on, the power is oscillating freely through M₁, C_TX, L_TX, and D₂, and V_PA is equal to 0. Stage 3 [t₂, t₃]: M₂ is turned off, the power is oscillating freely through M₁, C_TX, L_TX, and D₂, and V_PA is still equal to 0. Stage 4 [t₃, t₄]: M₄ is turned on, the power is transferred from the supply voltage to the ground through M₁, C_TX, L_TX, and M₄, and V_PA is equal to VDD. Stage 5 [t₄, t₅]: the I_TX changes its direction, the power is circulated from the ground to the supply voltage through D₄, L_TX, C_TX, and D₁, and V_PA is equal to VDD. This stage finishes when I_TX reaches zero. Stage 6 [t₅, t₆]: the I_TX changes its direction again, and the power is transferred from the supply voltage to the ground through M₁, C_TX, L_TX, and M₄. As a result, the current I_TX circulates three times during one switching period, which means lower switching loss compared with [39].

For higher-order harmonic control, there will be more current circulation per period and thus much lower switching loss, but smaller output power. The measurement results showed that HPSM with the 3rd harmonic component can improve PA efficiency by 10% compared to fundamental-based phase-shifted modulation.

3.5. Vector Power Summing Control

The aforementioned forms of TX regulation [32,33,34,35,36,37,38,39,40] are achieved only with a single TX, while it can also be implemented by summing the power from multiple TXs. The authors in [41,42] presented a vector power summing control technique to regulate the received power P_total as demonstrated in Figure 27. In this scheme, two power vectors, implemented by separate TXs, are then summed at a single RX. The two TXs are driven by two switching clocks (CLK₁ and CLK₂) with different phase θ under the same switching frequency (f_sw = 1/T_sw). As a result, two transmitted powers, P_o and P_oe^jθ, are achieved in the two physically overlapped TX coils L_TX1 and L_TX2, respectively. Additionally, the transmitted power combined can be written as:

$$P_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}=P_{\mathrm{o}}\times \left(1+\mathrm{c}\mathrm{o}\mathrm{s} \theta \right).$$

(13)

From Equation (13), the transmitted power can be regulated by controlling θ using a delay locked loop (DLL) and phase control circuit based on global feedback from the RX. In addition, wireless data communication can be simultaneously achieved using this vector summing technique [42].

Nevertheless, the vector summing technique will lead to a higher loss and system complexity due to the multiple TXs used. The measurement results showed that V_OUT can be regulated from 3.3 to 16.3 V with 1 W output power and 50% PTE. Also, boosting up to 20 V was achieved at a 0.6 W power transfer without a boost-type DC–DC converter or charge pump circuit. Additionally, a 35 μs response time was measured against a 1 ms load fluctuation interval.

Table 2. The comparison of TX regulation topologies in the state-of-the-art R-WPT systems.

References	[32]	[33]	[34]	[35]	[37]	[39]	[40]	[41]	[42]
Topology	Supply voltage control		fres control	PA power switch duty cycle control				Vector power summing control
Max. PDL	234 mW	250 mW	15 W	0.52 W	23.2 W	N/A	N/A	1 W	1 W
Max.PA Eff.	N/A	N/A	80%	N/A	N/A	94.5%	N/A	N/A	N/A
Max. PTE	62.4%	65.8%	N/A	50%	72.6%	N/A	63.94%	50%	61.8%
Num. of TX	1							2

gives a comparison of the TX regulation topologies among state-of-the-art works, where all achieve reasonably good PTE. For the supply voltage control scheme, it is the most straightforward approach to TX regulation. However, the switching loss can be further reduced by maintaining a low PA switching frequency, while using its subharmonic component as the resonant frequency, as in the PA duty-cycle control scheme. For the other two schemes, the narrow ISM bandwidth limits the performance of the f_res control scheme, while an additional TX requirement undermines the vector power summing control scheme.

4. Discussions and Development Trends

For the resonant coupling WPT systems, as reviewed in this paper at the circuit level, output regulation can be achieved by post-stage regulation and one-stage regulation at the RX side as well as PA supply voltage control, resonant frequency control, duty-cycle control, and vector power summing control at the TX side.

For RX regulation, due to the poor efficiency of post-stage regulation, one-stage regulation, such as active diode conduction time control and R³ rectifier schemes, has been proposed for high PCE. However, the shortcoming of one-stage regulation is that the VCE is always smaller than 1.

Another one-stage regulation based on the switching-based current-mode (SCM) technique adopts the switching control method to utilize power transfer within two phases: store energy in the RX LC tank and then deliver the energy to the load. As a result, the voltage across the resonant RX tank can be boosted and this technique allows a >1 VCE at the RX side, which is thus suitable for a high-voltage application. Although the output regulation can be achieved by modulating the R_eq, the PTE is still unoptimized.

There are two disadvantages for RX-only regulation schemes. For one thing, the RX output may fall outside of regulation considering a limited RX regulation range. For the other thing, the regulation may deviate the R_refl from the one for an optimal PTE considering that the loading and coupling conditions vary. Hence, TX regulation that optimizes the PTE based on global feedback from the RX side is also necessary.

For TX regulation, the PA supply voltage control scheme, typically implemented with a DC–DC converter, is straightforward but has relatively low efficiency and high cost. Another TX regulation scheme is resonant frequency control, based on a binary-weighted capacitor array, but its low resolution and high cost limit its further application. PA switching duty-cycle control is an effective way to achieve a continuously adjustable output, but zero voltage/current switching is required for high efficiency. In addition, a vector power summing scheme can also fulfill output regulation, but the regulation accuracy and efficiency are not favorable.

Moreover, for all of the TX regulation schemes, a global control loop is required to feed the RX output information back to the TX side through a data uplink channel. As such, the load transient response speed depends not only on the bandwidth of the global feedback loop, but also the data rate of the uplink channel. The data uplink telemetry can be implemented either in wired [17,35,41] or wireless ways. The wireless uplink schemes include Bluetooth, which has already be applied in A4WP [16,37], and backscattering based on load shift keying (LSK) [24,32,33].

To simplify the design of the binary-weighted capacitor array used in the resonant frequency control, a single phase switched fractional capacitor can be adopted for TX regulation by using the resonant frequency trimming technique as given in [45].

Another potential regulation topology is that the automatic maximum efficiency point tracking method [46] is implemented at the RX side and the regulation is achieved at the TX side. With this combined topology, the PTE can be optimized dynamically over a coupling and loading range with the help of TX regulation.

Last but not least, it is desirable to analyze the system stability and response speed because additional poles and zeros might be introduced with the regulation topologies.

5. Conclusions

In this work, the state-of-the-art regulation topologies in R-WPT systems for consumer electronics and bio-implants were comprehensively summarized and compared by mainly focusing on how to optimize the PTE, PCE, VCE, and PDL under loading or coupling variations. In addition, based on the advantages and drawbacks of these topologies, potential topologies are also proposed for researchers in this area. The regulation topologies design guidelines are not only suitable for R-WPT systems, but also for other near-field WPT systems.