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In this article, a subharmonics switching technique named bifrequency pulse train (BF-PT) control for wireless battery charging system with tapped transmitter (Tx) winding is proposed to regulate the output power against the variation of load and coupling coefficient. The tapped Tx winding is spilt into two subwindings: subwinding I is connected to the inverter while subwinding II is in open circuit. The charging current and charging voltage can be acquired by measuring the induced current of subwinding I and the induced voltage of subwinding II, respectively, without dual-side communication. BF-PT control, which contains high- and low-frequency pulse trains, can achieve zero voltage switching over a wide operating range. The high- and low-frequency pulse trains are uniformly distributed to suppress the winding current oscillation and to minimize the output voltage ripple. When the coupling becomes weaker and/or light-load conditions, the switches are operated at the subharmonics frequency to further reduce the average switching frequency of the system. To verify the validity of the proposed method, a wireless charging system with 72 V/3 A output is fabricated. The experimental results confirmed that the proposed method is able to maintain constant current and constant voltage output regardless of the load and coupling variations. [ABSTRACT FROM AUTHOR]

To ensure the effectiveness of the inductive power transfer (IPT) systems for high-power applications, multiple coils are being used. However, cross couplings among the same-side coils reduce the efficiency of the system. Thus, decoupling coils are commonly used to mitigate the same-side couplings in a multiple-transmitter and multiple-receiver system. The decoupling coils are either used outside of the main coils or concentric with the main coils. In both cases, these decoupling coils do not take part in the power transmission and have some adverse effects on the system performance. In this article, a new IPT system with dual transmitters and dual receivers with integrated decoupling coils is introduced. Besides mitigating the mutual inductances of the same-side coils, the proposed decoupling coils are also taking part in power transmission. In addition, the proposed coils also have good misalignment performance. A 3-D finite-element analysis tool ANSYS MAXWELL is used to investigate the proposed magnetic coupler. A scaled-down experimental setup is used to verify the feasibility of the proposed structure. The maximum dc–dc efficiency of this system is 93.14% while delivering 700 W to the load with a 200-mm air gap. Besides, zero-voltage switching is also achieved in the experiment, which suggests that the proposed system can be an effective solution for the current drawbacks of the multiple-transmitter and multiple-receiver system. [ABSTRACT FROM AUTHOR]

This article proposes a free-positioning omnidirectional wireless power transfer (WPT) system with a reticulated planar transmitter, which enables multiple receivers to be powered simultaneously in arbitrary positions and orientations. The reticulated planar transmitter is equipped with four interleaved and overlapped meander coils, thus, a three-dimensional (3-D) rotating magnetic field is generated with the designed excitation current. Therefore, only a planar single-coil (such as a loop-type coil) is required to realize free-positioning omnidirectional WPT. According to the theoretical modeling of the magnetic field, the excitation current that can generate a 3-D rotating magnetic field is given. To obtain a uniform and strong magnetic field distribution, the transmitter grid width is optimized. Furthermore, an excitation current modulation strategy based on phase-shift control is presented to regulate the amplitude of the excitation current. The experimental results show that the output power is greater than 13.1 W no matter how the center of the receiver moves or rotates freely within 400 × 400 mm. When five receivers are powered simultaneously in different positions and orientations, 82.5 W total output power and 55.6% efficiency can be achieved. The experimental results demonstrate that free-positioning omnidirectional WPT can be realized with only planar single-coil receivers by using the proposed reticulated planar transmitter and its excitation current modulation strategy. [ABSTRACT FROM AUTHOR]

In this article, an optimized non-uniformly distributed turn (NUDT) coil antenna is proposed to mitigate the lateral misalignment problem in wireless power transfer (WPT) systems. The proposed $ {Q}$ -assisted ${H}$ -field forming technique is analytically implemented using a minimum mean square error (mmse)-based algorithm. This results in an optimized transmitter (Tx) coil with clustered turns achieving a widespread uniformity of the ${H}$ -field in the receiver (Rx) working region. The proposed optimal design shows a consistent mutual inductance and power transfer efficiency (PTE) irrespective of the Rx misalignment which is realized using the circuit parameters. The analytical and simulated results of the proposed Tx coil designed using the $ {Q}$ -assisted mmse-based ${H}$ -field forming technique is experimentally verified. The misalignment tolerance of the proposed antenna is improved over the existing design by 224%. The proposed design proves its advantage to realize misalignment tolerant wireless charging platforms for WPT applications. [ABSTRACT FROM AUTHOR]

Because a transmitter-side controller of an inductive power transfer (IPT) system cannot directly measure its load conditions, i.e., receiver-side output voltages and currents, wireless communications are commonly used in many IPT systems. However, the wireless communication can cause a devastating failure of the IPT system because of its tens of milliseconds delays and frequent data losses. The mismatch between the transmitted and the received power can destroy the receiver-side power converters. In this article, receiver-side load voltage and current observers for a series–series tuned IPT system are proposed using the well-known disturbance observer theories. A load current observer that has a 10 kHz estimation bandwidth and a load voltage observer that has a 200 Hz bandwidth are proposed. The estimated load voltage and current have much faster dynamics than the wireless feedback signals without any data loss. Therefore, the proposed observers can bring significant advances in reliability and performance of the IPT system. Design guidelines for the observers that have low steady-state errors and fast dynamics are suggested. The theoretical performances of the proposed observers are evaluated by simulations and experiments. The simulated frequency- and time-domain responses of the proposed observers are consistent with the theoretical results. An experimental testbed was built to evaluate the proposed observers. The estimated current follows its actual value in 0.1 ms and the estimated voltage follows its measured value in 4 ms as expected from the simulations. [ABSTRACT FROM AUTHOR]

In this article, an optimized design for a dual-coupled inductor–capacitor–capacitor-series (LCC-S)-compensated wireless power transfer (WPT) system with zero-phase angle (ZPA) input condition and load-independent constant current (CC) output is presented. To this end, based on the misalignment characteristics of the reversed-series compensation coil structure, a novel design method for determination of the compensation parameters is proposed. By introducing a stability factor, any restriction on the variation correlation of the mutual inductances between the transmitter and receiver coils, and between the compensation and receiver coils within the range of misalignment tolerant design, is eliminated, thereby increasing the degree of freedom in the coil structure. According to a predetermined misalignment tolerant range, the proposed method can limit the fluctuation of the output current within a certain range and maintain the ZPA input condition. A 200-W/85.3-kHz prototype based on the proposed method is implemented and its performance is experimentally validated. The system can operate in ZPA input and load-independent CC output with a misalignment tolerance factor of 4, as the load varies from 5 to 20 $\Omega$. [ABSTRACT FROM AUTHOR]

This article proposes and implements an integrated wireless motor system using the laminated magnetic coupler (LMC) and commutative-resonant control (CRC). Prominently, a unique wireless power transfer system is developed to directly drive the switched reluctance motor (SRM) over an extendable distance with all controls centralizing in the transmitter. Differing from the multifrequency wireless motor system, the proposed system first employs the single resonant frequency to wirelessly drive a multiphase SRM through the single power transfer channel. Particularly, two orthogonal bipolar coils and one unipolar coil are skillfully integrated and naturally decoupled to form an LMC which acts as the transmitter, intermediate, and receiver coils, respectively. By utilizing the CRC to sequentially energize coils in the transmitter, the SRM phase windings can be properly excited by relevant coils in the receiver, which takes the distinct advantages of balanced phase currents, flexible transfer distance, high integration, and free maintenance. A prototype is constructed with the system efficiency of 89.14% and motor speed of 1500 rpm under the distance of 200 mm. Both theoretical and experimental results are provided to validate the feasibility of the proposed system. [ABSTRACT FROM AUTHOR]

This article proposes and implements a novel wireless power and drive transfer system using orthogonal bipolar couplers and separately excited modulation (SEM). Specifically, two bipolar coils are orthogonally integrated and naturally decoupled to form a compact magnetic coupler which will be utilized in the transmitter and receiver, respectively. The key is to employ the SEM to alternatively energize bipolar coils in the transmitter while self-driven circuits in the receiver can directly extract the drive information to control receiver-side switches. Consequently, the concurrent wireless power transfer and wireless drive transfer can be skillfully realized via the shared transfer channel at the single resonant frequency. Moreover, the proposed system can effortlessly achieve the wireless dc motor drive with the capability of bidirectional motion, or the wireless ac motor drive with the variable-voltage variable-frequency control. Besides driving the dc and ac motors, a 200-W prototype is constructed with the transmission efficiency of 89.5% over the transfer distance of 100 mm for a resistive load of 40 Ω. Both theoretical and experimental results are provided to validate the feasibility and flexibility of the proposed system. [ABSTRACT FROM AUTHOR]

In a dynamic wireless charging (DWC) system, the mutual inductance between the transmitter and receiver coils may vary with the position of the receiver, resulting in a fluctuation of the output voltage. Although a three-phase DWC system can reduce output fluctuation by traveling wave magnetic field, the existing three-phase systems still cannot achieve a uniform output voltage. In order to further improve the output stability, this article analyzes the cause of output voltage fluctuation. The magnetic field generated by the three-phase transmitter coils is decomposed into the fundamental and the harmonic traveling wave magnetic fields for analysis in this article. And a new calculation method of induced voltage is proposed from the perspective of dynamic electromotive force. Then, the voltages induced by the fundamental and the harmonic magnetic fields in the receiver coil are compared, revealing that the fifth and above harmonic magnetic fields are the ultimate cause of the output fluctuation. Subsequently, two fundamental methods to reduce the output fluctuation are proposed, and the effect of the output fluctuation on the efficiency is analyzed. Finally, a prototype was built to verify the correctness of the theoretical analysis and the feasibility of the proposed output fluctuation reduction methods. [ABSTRACT FROM AUTHOR]

In this article, a design of bipolar nonsalient pole (BNSP) transmitter, which originates from motor theory, for high-power EV dynamic wireless power transfer (DWPT) system is proposed. To analyze and evaluate BNSP transmitter in aspect of principle, characteristic, and performance, the existing I-type, S-type, and N-type transmitters in DWPT application are classified as bipolar salient pole (BSP) transmitter, which establishes a reference for comparing. The design parameters and other contrast conditions of BNSP and BSP transmitters are given. Coupling flux and leakage flux of BNSP transmitter are analyzed by comparing the magnetic models and the finite-element models of BNSP and BSP transmitters. Based on the modular design in practical application, the sensitivity of coupling performance to the module gap in BNSP and BSP transmitters is analyzed and compared in simulation. All theoretical results are verified by contrast experiments. The maximum effective mutual inductance of BNSP transmitter is about 31.0% larger than that of BSP transmitter, and the efficiency of the system with output power of 10 kW is 93.5% with BNSP transmitter, about 2.4% higher than that with BSP transmitter. Besides, BNSP transmitter needs 5.9% shorter Litz wire and 53.1% smaller volume of cores, which makes it smaller in size. [ABSTRACT FROM AUTHOR]

This article proposes a tripolar plane-type (TPT) transmitter enabling three-dimensional (3-D) omnidirectional wireless power transfer (WPT) for consumer electronics, such as mobile phones and tablet computers. The proposed TPT transmitter is a 2-D plan-type structure, but it shows a 3-D omnidirectional power transmitting capability. This structure consists of two crossed bipolar coils and a unipolar circular coil, and the three coils are mutually decoupled naturally. By calculating the magnetic field distribution generated by the TPT transmitter, a 3-D omnidirectional magnetic field can be obtained. Then, a detailed circuit topology based on the inductor-capacitor-capacitor-series compensation networks and full-bridge inverters with phase-shift control is modeled and analyzed. On this base, an excitation current vector modulation strategy based on a targeting magnetic field is designed, which can improve and stabilize the system output power and efficiency. Finally, an experimental prototype is set up to verify the 3-D omnidirectional power transmitting capability of the proposed TPT transmitter and the effectiveness of the designed current vector modulation strategy. Besides, the superiority of the proposed 3-D omnidirectional WPT system is verified by comparison with other methodologies. The experimental results show that the system output power and efficiency are maintained at 61.4–80.6W and 80.7%–85.2% under arbitrary angular misalignment of the receiver. [ABSTRACT FROM AUTHOR]

Compared to air surroundings, the marine environment is not stable due to the influence of ocean currents and other factors. Misalignments always occur inevitably when autonomous underwater vehicles are charging wirelessly in the docking station. Therefore, misalignment insensitive underwater wireless power transfer system need to be investigated. In this article, a novel hybrid transmitter composed of conical and planar spiral coils is proposed that greatly improves the misalignment tolerance and transfer performance. First, the coil tilt angle theory (CTAT) is presented and verified to determine the optimum tilt angle of conical coil. Then, based on the CTAT, a circular uniform magnetic field zone with a diameter of 30 cm in charging plane can be achieved by flexibly designing the hybrid transmitter. Moreover, a three-dimensional finite-element simulation software is employed to study the eddy current loss under different circumstances. Finally, experimental results show that the proposed transmitter has better performance in output power and power transfer efficiency (PTE) stability within the possible working region compared with conventional transmitters. It has demonstrated that the output power changes only within 5.7% and the PTEs maintain at approximately 86% in excessive misalignment area with transfer distance of 2 cm. [ABSTRACT FROM AUTHOR]

In this article, we propose an amplitude-shift keying (ASK) modulation technique for Class-E power transmitters used in the inductive power and data transfer links. The proposed modulation circuit consists of a capacitor and a transistor, which switch the load network of the Class-E transmitter between two states; in one state, the drain waveform of the Class-E transistor satisfies both zero-voltage switching (ZVS) and zero-voltage-derivative switching conditions, while in the other one, the waveform approximately satisfies the ZVS condition. Therefore, at both states, the dc-to-ac power conversion efficiency is high, but the transmitted power is different, which allows the implementation of ASK data modulation in the transmitter. We also present an analytical procedure to design the circuit for the desired output power and data modulation index (MI). We have verified the design procedure in both simulation and measurement. The implemented inductive link consists of a 2.4- $\mu$ H transmitter coil and a 1.1- $\mu$ H receiver coil, separated by a 10-mm air gap. With a carrier frequency of 10 MHz, the power transfer efficiency and the power delivered to load were measured to be 64.6% and 35 mW, respectively. With MI = 10%, the bit error rate for the data rates of 1 and 2 Mb/s was measured to be less than 10–8 and 10–6, respectively. [ABSTRACT FROM AUTHOR]

A space-vector (SV) based excitation method for wireless power transfer systems with a bipolar transmitter is introduced in this article. Unlike traditional bipolar excitation techniques that rely on fixed transmitter current distributions, this SV approach provides an elegant analytical method of redistributing a greater magnitude of current to the transmitter coil, which is closer to a misaligned receiver. This method is shown to require a smaller transmitter current vector magnitude for a required output power compared to all other bipolar coil excitation schemes over a broad range of receiver misalignments, thereby reducing conduction losses within the system. Additionally, the gradual redistribution of transmitter current as a function of receiver misalignment achieved by the SV method causes it to be less influenced by errors in receiver position sensing compared to conventional methods. Experimental results shows that the proposed method in conjunction with single coil operation at extreme misalignments was able to achieve a coil efficiency profile with minimal variation due to misalignment (93.2% at perfect alignment to 92.7% at a misalignment of 20 cm, for 2 kW power transfer into a 200 V battery load.) [ABSTRACT FROM AUTHOR]

A step-down wireless power transfer converter with center-tapped pickup windings is proposed in this article. The pickup winding is split into two sections and only one is connected to the load. This topology is more suitable for low-voltage level applications, such as consumer electronic products. Like the conventional series–parallel compensation technique, the circuit does not induce high circulation current at the transmitter coil under light load operation. The loosely coupled coils are analyzed with mutual inductance model; in addition, the input impedance and voltage gain are derived. The input impedance is proportional to the load impedance, and the voltage gain is less sensitive to the load variation. The proposed topology performs better than the conventional one at higher load conditions, especially when the coupling is poor. The efficiency of a laboratory circuit reaches 88.8% at best condition and it is higher than 63% ranging from 10- to 100-W load at 10- or 60-mm coil separation. [ABSTRACT FROM AUTHOR]

This article introduces an adaptive self-tuned controller IC for resonant wireless power transfer (RWPT) transmitters. The controller IC comprises an on-the-fly very-high-frequency tracking hardware with high resolution and an independent high-resolution digital pulsewidth modulator (PWM)-based (HR-DPWM) current programmed control. These facilitate precise frequency generation as well as adaptive tuning of the reactive components in the matching network, which translate into tight current/power regulation capabilities while retaining optimized power transfer conditions on the transmitting side. The controller IC enables to effectively disengage the power-delivery capabilities from the variations of the resonators, electrical circuits, and wireless medium. The controller core is based on a fully synthesizable digital architecture that has been realized through HDL tools, and several key building blocks have been developed and described in detail: a delay-line-based phase detector, high-resolution digital frequency synthesizer, and HR-DPWM. To fully exploit the benefits of digital electronics, reduce power consumption, and save area, the digital core of the controller has been designed completely through asynchronous architecture, eliminating the need of high-speed clock and its related hardware. The mixed-signal controller IC has been designed, implemented, and fabricated in 0.18-μm 5-V CMOS process, resulting in effective silicon area of 0.6 mm2. To demonstrate the mixed-signal controller IC in closed-loop operation of a wireless power system, an experimental 20-W resonant capacitive-based WTP system has been designed and validated. The effectiveness of the controller is well demonstrated and evaluated at the MHz range up to 200 mm misalignment, meeting the strict requirements of resonant-based WPT systems. [ABSTRACT FROM AUTHOR]

In this article, a special magnetic coupler for three-coil wireless power transfer (WPT) is proposed to eliminate the mutual inductance between the source coil and the receiver coil, which can significantly improve the design freedom. Specifically, unipolar Q coil, mixed QDD coil, and bipolar DD coil are designed for the source coil, the transmitter coil ($\text{T}_{\mathrm {X}}$), and the receiver coil ($\text{R}_{\mathrm {X}}$), respectively. By making use of unipolar coils and bipolar coils, this structure magnetically decouples the receiver coil from the source coil. Meanwhile, under different lateral misalignment conditions, this new coupler facilitates maintaining high efficiency. A laboratory prototype has been constructed to validate the proposed structure, demonstrating that the proposed structure can realize inherent characteristics, enhance misalignment tolerance, and energy transfer. The potential applications are EV systems, but this design can be generalizable to other three-coil systems. [ABSTRACT FROM AUTHOR]

In this article, a wireless shaded-pole induction motor (SPIM) is proposed and implemented, which artfully integrates wireless power transfer into a single-phase SPIM to achieve the first wireless ac motor. Prominently, there is no controller at the SPIM side, as the controlling process is fully conducted at the transmitter side. Meanwhile, there is no need to specially design the motor, as all existing SPIMs can readily be used. The key is to propose a self-driving circuit in the receiver, which can provide variable-voltage variable-frequency control of the SPIM. As a result, the proposed wireless SPIM takes the definite advantages of electrocution-free and totally sealable. A 110 W prototype has been built for experimental verification. It can offer wireless speed control from 486 to 1330 r/min with the transfer distance of 30 mm and the transmission efficiency of 86.2%. [ABSTRACT FROM AUTHOR]

For the EV dynamic wireless charging system, the conventional single-phase magnetic couplers with alternately arranged magnetic poles, such as I-type, S-type, and N-type, have both the advantage of narrow power supply rail and the disadvantage of large output power fluctuation. Although the conventional three-phase meander-type magnetic coupler uses the traveling wave magnetic field to ensure uniform output, a wide transmitter is required in order to provide a large air gap. This article proposes a narrow-rail three-phase magnetic coupler, which realizes the advantages of the above two kinds of couplers by integrating the narrow rail with uniform output power in one coupler. The magnetic field distribution and the working principle of the proposed coupler are illustrated and the receiver structure and the transmitter coil's winding method are optimized. Moreover, the effect of the interphase mutual inductance between different phases in transmitter coils on the system is analyzed. Finally, an experimental prototype was built for the verification. The experimental results showed that the fluctuation of output voltage was within ±2.5% during the dynamic charging process. [ABSTRACT FROM AUTHOR]

Recently, an omnidirectional wireless power transfer (WPT) has attracted attention as a solution to the limitations of free-positioning and mobility of conventional WPT. However, the efficiency of the omnidirectional WPT is reduced due to the low mutual inductance relative to the transmitter size. Therefore, this article proposed an optimal magnetic structure to improve efficiency without increasing the size of the transmitter. Four magnetic structure candidates (spherical, cubical, crossed bar, three-orthogonal plane core) are presented and their performances are compared using finite element analysis software. A Pareto optimal set is selected using a multiobjective optimization design, and the optimal magnetic structure is determined considering the weight of the objective variable and the Tchebycheff distance. The optimal magnetic structure and omnidirectional WPT prototype are built for performance verification. The experimental results are consistent with the simulation results and demonstrate that the optimal magnetic structure improves the efficiency in the three-dimensional space. When the power transmission distance is 150 mm, the system efficiency is improved up to 18.6%. [ABSTRACT FROM AUTHOR]

Multiple-receiver resonant inductive coupling wireless power transfer (RIC-WPT) technique is emerging as a promising charging method for multiple household appliances, mobile devices, and wearable devices. However, this technique often suffers from output power fluctuation owing to the cross-interference among receivers as well as the manufacturing and aging tolerance of the resonant frequency (i.e., resonant frequency tolerance). This article proposes an autonomous RIC-WPT system concept to solve this difficulty. The proposed concept addresses the cross-interference and resonant frequency tolerance by incorporating the following two functions. First, the amplitude of the transmitter current is controlled to have a constant amplitude. Second, the phase of each receiver current is controlled to be orthogonal to that of the transmitter current by using an active reactance compensator installed in each receiver. The experiment of a two-receiver RIC-WPT system successfully verified that the two functions of the proposed system concept can stabilize the output voltage against the cross-interference and resonant frequency tolerance. [ABSTRACT FROM AUTHOR]

We describe efficient four-coil inductive power transfer (IPT) systems that operate at 100 MHz. The magnetically coupled transmitter and receiver were made from electrically small and high- ${Q}$ loop-gap resonators (LGRs). In contrast to the commonly used helical and spiral resonators, the LGR design has the distinct advantage that electric fields are strongly confined to the capacitive gap of the resonator. With negligible fringing electric fields in the surrounding space, the IPT system is immune to interference from nearby dielectric objects, even when they are in close proximity to the transmitter and/or receiver. We experimented with both cylindrical and split-toroidal LGR (TLGR) geometries. Although both systems performed well under laboratory conditions, the toroidal geometry has the additional advantage that the magnetic flux is weak everywhere except within the bore of the LGR and in the space directly between the transmitter and the receiver. Furthermore, we show that the TLGR system can be operated efficiently at a fixed frequency for a wide range of transmitter–receiver distances. The experimental results are complimented by 3-D finite-element simulations that were used to investigate the electromagnetic field profiles and surface current density distributions. Finally, we demonstrate the use of our IPT system at powers up to 32 W and discuss possible applications. [ABSTRACT FROM AUTHOR]

This article presents a closed-loop transmitter for wireless power transfer with automatic resonance frequency tracking to maintain high power transfer efficiency in the over-coupled region. The transmitter consists of a source oscillator, power amplifier (PA), PA driver, matching network, and feedback circuitry. By injecting the resonant output of coupled antenna coils into a source oscillator to form a positive feedback loop, the source oscillator is injection-locked and the closed-loop transmitter functions as a power oscillator with the oscillation frequency determined by the resonance of the coupled coils. The proposed resonant frequency tracking minimizes the change in the input impedance presented to the PA, and hence mitigates mismatch that causes a sharp drop in the PA efficiency of conventional transmitters. Implemented in 0.13 μm Bipolar–CMOS–DMOS (BCD) technology, the prototype maintains PA efficiency above 60% even at highly over-coupled spacings (10 mm), which is significantly below the critical coupling spacing (40 mm). Compared to a transmitter without feedback (i.e., running in open loop), the transfer efficiency at a coupling distance of 10 mm is improved by 6.6 times and the charging range with power transfer efficiency over 50% is also doubled. [ABSTRACT FROM AUTHOR]

The wireless power transfer system (WPT) is becoming increasingly important for smart home automation, in which an array of wireless sensors is used to monitor and manage smart devices and furniture. Charging the sensors, which may require different frequencies, at any position in the home is a challenge. In this article, a dual-band omnidirectional 3-D WPT system is introduced for the sensors in a smart home. The power transmitted by the transmitter can be received by any receivers operating at 13.56 and 27.12 MHz located at any position. The dual-band 3-D square and circular transmitters are designed and demonstrated. In particular, an equivalent circuit model of the proposed system is derived and numerically analyzed. In addition, the efficiency of the dual-band 3-D WPT system is evaluated based on the receiving angle through simulation and measurement. At a 16 cm distance, the system can achieve efficiencies of 61.6% and 65.4% (57.15% and 61.2%) for rotating 360° at 13.56 and 27.12 MHz without a null value in the square (circular) system. Furthermore, the effect of the angular misalignment of the receiver on efficiency is also analyzed. Finally, the performance of the WPT system in a concrete structure is validated for practical scenarios. [ABSTRACT FROM AUTHOR]

Dynamic wireless charging (DWC) is an attractive technology which can significantly extend the mileage of electric vehicles. However, experimental evaluation on a DWC system is often implemented at high costs due to the requirement on a movable platform. To address this problem, this article proposes a receiver-side-oriented DWC simulator characterized with wide speed range, compact size, flexible configurations, and controllable testing conditions. First, the emulated I-type multiphase receiver system and its basic operating characteristics are introduced. Then, the fundamental principle employing receiver-induced voltage equivalence and an implementation for a DQ-phase receiver DWC system are demonstrated. Further, movable platform experiments and circuit simulations are conducted to verify the accuracy of the simulator at full-range driving speeds. Finally, application demonstrations for operating the simulator are presented to show the feasibility and flexibility. [ABSTRACT FROM AUTHOR]

The closed-loop control of wireless power transfer (WPT) systems requires a communication link between the power transmitter and the power receiver for dual-side cooperation. Near-field communication techniques that utilize the power link are preferred for this purpose due to high reliability and security. In this letter, we propose a frequency-modulated phase shift keying (FMPSK) communication technique for the closed-loop maximum efficiency point tracking (MEPT) control of WPT. The technique uses very shallow phase modulation depth to minimize the disturbance on power flow and reduce the efficiency drop caused by the PSK. Meanwhile, it ensures the signal accuracy and precision by multiple methods and precise frequency modulation and demodulation. In experiment, we obtained 82%–85% system efficiency with a 25–125 W load over a distance equal to the coil diameter, and 93% efficiency over a distance equal to the coil radius. The efficiency drop caused by FMPSK was less than 1%. The dynamic processes of voltage regulation and MEPT took only about 1 ms and 10 ms, respectively. [ABSTRACT FROM AUTHOR]

Recently, omnidirectional wireless power transfer (WPT) systems have been studied intensely, due to their improved flexibility as compared to their planar counterparts. The LCCL-LC resonant converter topology is selected due to its current source characteristics in this article. The system frequency is pushed to megahertz (MHz) to increase the spatial charging freedom. In a megahertz WPT system, the reactance of the full bridge rectifier can no longer be neglected; therefore, an analytical model of the full bridge rectifier input impedance is built. Furthermore, zero-voltage switching (ZVS) of the switching devices is essential in reducing the switching loss and noise in a megahertz system. A design methodology of the LCCL-LC circuit is proposed to achieve the ZVS operation in the case of one transmitter and one receiver. Then, the ZVS analysis is extended to the scenario of multiple transmitter coils and one receiver coil. Finally, a 6.78-MHz wireless charging system is built according to the proposed design methodology. Experimental results validate the accuracy of the ZVS analysis, and the ZVS operation is well achieved under different coupling and load conditions. The peak system efficiency of 82% at 5-W output power is achieved. [ABSTRACT FROM AUTHOR]

The voltage stress of compensation capacitors in the wireless charging system could be up to several kilovolts. Things get worse for the dynamic operating condition because the resonant current gets fluctuating with the rigid variations of the coupling condition. In this article, a constant resistance (CR) control scheme on a boost converter is proposed to mitigate receiver current stress, i.e., the peak currents in the resonant tank and the boost chopper inductor. The receiver-side dynamic wireless charging (DWC) system with a postregulated boost converter is introduced by the static operating waveforms. To investigate how speed affects current stress, a receiver-side current analytical model is established based on the closed-loop input admittance of boost and the dc circuit model of resonant tanks. The modeling results illustrate that the overstress problem is prone to occur at high-speed condition under constant current charging control. CR control, which shapes boost input current and voltage in phase, is adopted to address this problem. Comparative studies for full-range speeds and nonideal coupling conditions, conducted by the DWC simulator, show that uniform low-stress performance is obtained under CR control with the same amount of energy transferred. Maximum stress improvement on the receiver resonant current is 29% for ideal condition and 44% for a nonsinusoidal condition when driving at 80 km/h. [ABSTRACT FROM AUTHOR]

This article proposes and implements a selective wireless power transfer (WPT) system based on magnetic field editing technology. Compared with the traditional WPT without control of power regions, the proposed system can deliver the energy with higher safety, flexibility, selectivity, and can be applied to multiple receivers. The algorithms for current calculation and synchronized control strategies are given to construct the desired magnetic field effectively. The optimization process based on the receiver configuration and voltage threshold is also demonstrated. Both simulation and experimental results validate that the magnetic field distribution can be arbitrarily edited through the proposed current control strategy, and realize the selectivity of the powering area. A prototype of the proposed system with five transmitters is constructed and tested, which can successfully deliver wireless power of 14 W over the distance of three times larger than the radius of the receiver coil with the transmission efficiency over 79%. [ABSTRACT FROM AUTHOR]

While detection of foreign or unintended metallic objects is an important topic for wireless power transfer (WPT), operation of WPT systems with intended metallic objects is largely an unchartered territory. This article presents a methodology for analyzing the effects of intended metallic object on a WPT system through the study of the magnetic field distribution and the use of a reduced-order equivalent model of the systems for comparing the WPT system with and without the metallic object. The methodology is applied to a metallic corona ring of low resistance used with a WPT system. The analysis quantifies how an intended metallic object could change the magnetic coupling between the transmitter and receiver coils, and alter the equivalent resonant tank parameters of the WPT system. Recompensation of the resonant tank can only enhance the power transfer capability but not the energy efficiency. The theory and practical verification of a new performance-enhancement method based on a combination of recompensating the resonant tanks and maximizing the equivalent mutual inductance of the Tx and Rx coils is presented. Such methodology provides a general approach to analyze WPT systems with or without relay resonators in the presence of intended metallic objects. [ABSTRACT FROM AUTHOR]

This article presents a maximum efficiency point tracking (MEPT) scheme for a multiple receivers and loosely coupled wireless power charging (WPC) system with a mutual inductance tracking method. In general, the WPC system should satisfy the requirements of constant output voltage and the highest possible efficiency according to sensitive variation of charging environments. To this end, a state-of-the-art MEPT scheme has been studied in this work. Additionally, one of the advantages of the loosely coupled WPC system is the ability to charge multiple devices simultaneously. However, most studies have focused on a single-input and single-output (SISO) system. In this article, we propose a MEPT scheme for a multiple receiver WPC system and a mutual inductance tracking method. The proposed control scheme determines the current of the transmitter based on the mutual inductance between the transmitter and receivers. For validation, the proposed single-input multiple-output (SIMO) WPC system was implemented at 1 MHz using loosely coupled series-series resonant coils and the proposed mutual inductance tracking method. The results verified the performance of the proposed MEPT scheme in a SIMO system regardless of changing charging environments. [ABSTRACT FROM AUTHOR]

Compensation capacitors are important components of any resonant wireless power transfer (RWPT) systems and significantly affect the output power, operating frequency, and efficiency. Depending on the compensation network, these capacitors can be placed in series or parallel with the coils. The physical capacitor reduces reliability and increases the size and cost of RWPT systems. Self-resonant RWPT systems have been proposed to remove the physical capacitor, but have to work with high frequency, several megahertz, as reported in existing literatures. In this article, a new planar coil that utilizes parallel-connected multilayer Printed Circuit Boards (PCB) to generate large parasitic capacitance is proposed for RWPT. Both transmitter and receiver coils are made using PCB coils and a spiral winding layout is used to achieve the required inductance and capacitance. Benefit from large parasitic capacitance, the resonant frequency of the proposed RWPT system is reduced to below 200 kHz. Meanwhile, because of the elimination of physical capacitance, the proposed RWPT system has a compact structure, improved reliability, and reduced size, weight, and cost. A coil prototype is designed, constructed, and tested. Simulation and experimental investigations validate the effectiveness of the proposed design. [ABSTRACT FROM AUTHOR]

The elimination of integrated batteries in biomedical implants holds great promise for improving health outcomes in patients with implantable devices. However, despite extensive research in wireless power transfer, achieving efficient power transfer and effective operational range have remained a hindering challenge within anatomical constraints. Objective: We hereby demonstrate an intravascular wireless and batteryless microscale stimulator, designed for (1) low power dissipation via intermittent transmission and (2) reduced fixation mechanical burden via deployment to the anterior cardiac vein (ACV, ∼3.8 mm in diameter). Methods: We introduced a unique coil design circumferentially confined to a 3 mm diameter hollow-cylinder that was driven by a novel transmitter-based control architecture with improved power efficiency. Results: We examined wireless capacity using heterogenous bovine tissue, demonstrating >5 V stimulation threshold with up to 20 mm transmitter-receiver displacement and 20° of misalignment. Feasibility for human use was validated using Finite Element Method (FEM) simulation of the cardiac cycle, guided by pacer phantom-integrated Magnetic Resonance Images (MRI). Conclusion: This system design thus enabled sufficient wireless power transfer in the face of extensive stimulator miniaturization. Significance: Our successful feasibility studies demonstrated the capacity for minimally invasive deployment and low-risk fixation. [ABSTRACT FROM AUTHOR]

A control-oriented circuit model of an inductive power transfer system is needed to design a high-performance controller. In this article, a dq synchronous reference frame model of a series–series tuned resonant inductive power transfer system is proposed. A single-phase dq modeling technique for a resonant converter is used to derive the model. The proposed control-oriented model clearly demonstrates the cross- and mutual-coupling between the state variables of the wireless power transfer system. It is interesting to note that the proposed model is similar to a dq synchronous reference frame model of a three-phase induction motor. The well-known controller design methods, such as proportional-integral controller design, manipulated input decoupling, disturbance input decoupling, state observers, and disturbance observers, etc. can be extended to the inductive power systems with the proposed model. The large- and small-signal responses of the transmitter current versus its input voltage are identified. Considering the frequency response, a new transmitter current controller that has a control bandwidth of 500 Hz is designed to show the validity of the proposed model. The proposed model and the controller are evaluated using simulated and experimental results. The simulated open- and closed-loop frequency responses of the model agree well with the theoretical bode plots of them. Also, the experimental results show that the proportional-integral with feedforward input controller regulates the transmitter current within 1 ms for three conditions: a step change of the reference, a step change of the load, and a step change of the mutual-coupling. [ABSTRACT FROM AUTHOR]

This article develops a new method of data-driven modeling for a class of multiple-transmitter single-receiver wireless power transfer (WPT) systems. A continuous-time multiple-input single-output (MISO) model with pure time delays is used to characterize the input–output behavior of the system, where the transfer functions associated with each input channel are not constrained to have the same denominator. Moreover, the time delays are allowed to be a fraction of the sampling interval in order to account for the delay effects that stem from circuit components and wireless communication, which are, by nature, often a fraction of the sampling interval. An optimal refined instrumental variable method is proposed to estimate the parameters and time delays of the MISO model based on sampled input–output data. In contrast to the conventional circuit-theory-based modeling methods that rely on circuit parameters and result in models which are often complex, the proposed data-based method yields parsimonious models, whose parameters are directly estimated from input–output data. Due to the easy availability of sampled data in control engineering applications, the proposed method is clearly more user-friendly, having a broad prospect for efficient operation of WPT systems, such as prediction, optimization, and control. Numerical and experimental results are presented to validate the effectiveness and merit of the proposed method. [ABSTRACT FROM AUTHOR]

We propose a maximum efficiency tracking for a multiple-transmitter system that optimizes both the current ratios of transmitter (Tx) coils and the effective Rx load. It is found that unlike the single-Tx case, the optimal load impedance of multiple-Tx system depends on the current ratios among Tx coils. Meanwhile, the Tx current ratios should be controlled to be the same with magnetic coupling ratios between each Tx and Rx. Hence, we propose a two-step tracking method that first optimizes the Tx current ratios and then optimizes the Rx load impedance. To match the Tx current ratio with the magnetic coupling ratio, it is analyzed that the reflected resistances at every Tx become identical to each other when the Tx coil current ratios are equal to the magnetic coupling ratios. It is also revealed that the reflected resistance at specific Tx is reduced (increased) when its Tx current is increased (reduced) relative to other Tx currents. The proposed feedback equalizes all reflected resistances based on this property. The second step of the proposed tracking is to optimize the Rx load while fixing the Tx current ratios by globally scaling up or down the strengths of whole Tx currents. Maximum of 478 W is delivered at 79% efficiency. The algorithm does not have a limit on the number of Txs except the small standby power consumption. The proposed theoretic analysis and control method enable the first-ever maximum efficiency tracking for multiple-Tx system, where the first step optimizes the relative Tx current ratios and the second step optimizes the load impedance. [ABSTRACT FROM AUTHOR]

With the rapid development and extensive application requirements of wireless power transfer (WPT) technology, the common symmetrical WPT system is growing more mature, but it may still struggle to meet the vast demands. When the WPT system has a long transmission distance and the dimensions of transmitter and receiver coil are asymmetric, the current in the transmitter coil of traditional two-coil symmetrical structure may be excessive. The addition of a relay coil between the transmitter and the receiver coil can effectively reduce the current of transmitter coil, thereby improving system efficiency and reducing electromagnetic field (EMF) leakage. In this article, the parameters of relay coil are optimized by theoretical calculation and multiobjective genetic algorithm. The results show that the optimized three-coil system can reduce the current of transmitter coil by 73.1%, improve the efficiency by 10.7%, and suppress the EMF leakage by 12 dB simultaneously. Finally, the effectiveness of the proposed system is verified by experiments. [ABSTRACT FROM AUTHOR]

Expandable and flexible wireless power transfer (WPT) systems have been in demand in numerous industry applications, especially for dynamic chargers in electric vehicles. Those systems, however, bring about certain technical issues such as modulation technique and topology of the transmitter side, and transferred power profile of the transmitters. In this article, a new converter topology to drive closely spaced segmented dynamic wireless power transfer (DWPT) systems is proposed. The proposed converter can be expanded to cater for different number of transmitters, and it can provide a uniform transferred power profile throughout the path of transmitter coils, known as track. Furthermore, this article focuses on analyzing the operation of the converter and the effect of closely spaced transmitters over its operation. To show the effectiveness of the proposed topology and its modulation technique, the converter is simulated and experimentally tested using a laboratory prototype. The results are compared and analyzed, and their close agreement shows the validity of the proposed technique. [ABSTRACT FROM AUTHOR]

In high-power electric vehicle wireless charging systems, the charging distance is short, and the coupling is strong in order to increase the power density and reduce the coil size and the system cost. With a strong coupling, the receiver-side compensation can be eliminated, and a high efficiency can still be obtained. The inductor-capacitor-inductor-none (LCL-N) topology is formed with the LCL compensation on the primary side. The phase difference between the transmitter and receiver currents is larger than 90°, leading to the magnetic flux cancelation in the ferrites. Thus, the required ferrite thickness of the LCL-N topology is smaller than the fully-compensated topologies. Therefore, a compact, lightweight, and low-cost receiver structure is achieved with the omitted compensation and thinner ferrite. Moreover, the LCL-N topology can achieve zero voltage switching for all loading conditions, withstand open-circuit and short-circuit faults, and is suitable for constant-current and constant-voltage charging due to the fact that it has neither a CC nor a CV output characteristic. A 100-kW system is designed and simulated. A downscaled 1-kW system is implemented. The simulations and experimental results verify the effectiveness of the analysis. [ABSTRACT FROM AUTHOR]

In this paper, a gallium nitride (GaN)-based single-inductor multiple-output (SIMO) dc–ac inverter, which generates multiple frequencies at the ac outputs, is introduced. The proposed time-multiplexed switching sequences enable the SIMO inverter to simultaneously generate sinusoidal-like outputs with different frequencies. In the absence of a parasitic body diode in the GaN transistor and with correct bias voltage, the proposed inverter requires no additional blocking diodes and/or cascaded power switches while still ensuring unidirectional flow of the inductor current for proper circuit operation. Compared with its silicon counterpart, this GaN-based inverter achieves a simplified circuit structure, reduced component count, small form factor, increased power density, and high efficiency. A practical application of this inverter is to act as a single wireless power transmitter which concurrently drives multiple transmitter coils at different frequencies for multi-standard wireless power transfer. A hardware prototype of a single-inductor three-output inverter producing three distinct resonant frequencies, namely, 100, 200, and 300 kHz, is constructed. The effectiveness of the proposed switching sequences and control method for this inverter is experimentally verified. No cross regulation is observed across the three individual ac outputs. [ABSTRACT FROM AUTHOR]

In this paper, a metamaterial-coupled, highly efficient, miniaturized, and long-range wireless power transfer (WPT) system based on a cubic high-dielectric resonator (CHDR) is explored. The proposed WPT system consists of two CHDR metamaterials separated by a distance and excited by two rectangular coils. Initially, this WPT system is analyzed by considering the cube dielectric permittivity, $\varepsilon _{r}$ = 1000, and loss tangent, tan $\delta$ = 0.00001. From the Ansoft HFSS simulation, it is observed that the system operates in the hybrid resonance mode resonating as a horizontal magnetic dipole providing more than 90% power transfer efficiency at a distance of 0.1 $\lambda$. In addition, parametric studies regarding the transmitter and receiver sizes, loss tangent, receiver misorientation, cube periodicity, etc., are carried out. One of the significant findings of this parametric study reveals that the suggested WPT system is less sensitive to the displacement of the receiver coil, and the WPT efficiency due to misorientation of the receiver can be increased by changing the CHDR cube rotation. Due to inaccessibility of the very high $\varepsilon _{r}$ = 1000, 18 microwave ceramic samples of EXXELIA TEMEX E5080 (Oxide composition: Ba Sm Ti), which has a permittivity, $\varepsilon _{r}$ = 78, permeability, $\mu _{r}$ = 1, and a loss tangent, tan $\delta$ = 0.0004, was made for experimental verification. These cubes are surrounded by Teflon to make the CHDR resonators. From simulations and measurements, it is found that the proposed system outperforms the most recent high-dielectric or copper-based WPT systems in terms of efficiency, range, size, and specific absorption rate. [ABSTRACT FROM AUTHOR]

A single-stage 6.78 MHz transmitter is proposed, which directly converts a utility ac input to a regulated, high-frequency (6.78 MHz) ac output for wireless power transmission. The topology integrates a totem-pole rectifier operating in a discontinuous conduction mode and an asymmetrical voltage cancellation controlled full-bridge inverter. Compared with the traditional cascaded multistage transmitters, this single-stage approach achieves high power efficiency over the full load range, utilizes fewer fast-switching devices, and shrinks the size of the converter. Constant current behavior at the output of the transmitter enables a fast response to a sudden load change. The operation and theoretical analysis of the single-stage transmitter is verified using a 100 W, GaN-based prototype. Experimental results demonstrate the capability of the converter to provide high power factor, low total harmonic distortion of the input current, and high conversion efficiency over the whole power range. The resulting prototype is suitable for implementation in wireless power systems where multiple consumer electronics loads are charged from a single transmitter. [ABSTRACT FROM AUTHOR]

This paper proposes and implements a novel multi-frequency multi-power wireless power transfer (MFMP-WPT) system based on one single transmitter for simultaneously and compatibly energizing multi-standard receivers. Generally, implementing a multi-frequency WPT often requires a compromise in system complexity, control difficulty, switching frequency, or transmission efficiency. By using only a single transmitter with an artful inverter topology, the proposed MFMP-WPT system can effectively achieve multi-frequency multi-magnitude superposition and switching frequency reduction while maintaining the control fitness and convenience of square-wave generation with 50% duty cycle. Moreover, by switching at the fundamental frequency in a range of 80–130 kHz, the single transmitter becomes competent for one-to-many MFMP-WPT operation for diverse wireless power on-demands. Consequently, the fundamental and high-order harmonic wireless energies with multiple power levels can be, respectively, picked up by the multi-standard receivers, depending on their energy requirements. The experimental transmission and system efficiencies can reach 81.57% and 64.74% under MFMP-WPT, respectively. Theoretical analysis, computer simulation, and experimental results are provided to verify the feasibility of the proposed MFMP-WPT system. [ABSTRACT FROM AUTHOR]

This paper studies simultaneous wireless information and power transfer (SWIPT) techniques for point-to-point multiple-input multiple-output channels, where a multi-antenna transmitter conveys information and energy at the same time to a multi-antenna receiver equipped with time switching (TS) circuits for an energy harvesting (EH) mode and an information decoding (ID) mode. Unlike conventional uniform TS (UTS) structure where all the receive antennas at the receiver employ a single TS circuit, in this paper, we propose a general dynamic TS (DTS) receiver architecture which has an individual TS circuit for each antenna. In the proposed DTS, the operation modes of the antennas can be dynamically changed to improve SWIPT performance. We aim to identify the achievable rate–energy (R–E) tradeoff of the DTS protocol for both linear and non-linear EH models by maximizing the information rate subject to the EH constraint. This results in joint optimization of the transmit covariance matrices and the time durations for the EH and the ID modes of the receive antennas, which is jointly non-convex in general. To tackle the non-convexity of the original problem, the successive convex approximation technique is adopted by addressing a series of approximated convex problems. As a result, efficient optimization algorithms are proposed for determining the boundary points of the achievable R–E region. We also provide a low-complexity algorithm which achieves near-optimal performance with much reduced complexity. Numerical results demonstrate that the proposed DTS presents significant performance gains over conventional UTS approaches. [ABSTRACT FROM AUTHOR]

Wireless power transfer systems in seawater inevitably suffer some energy loss as a consequence of eddy current loss. Here, we present a coil structure utilizing two transmitter coils placed symmetrically adjacent to each side of the receiver coil. This coil arrangement, termed a 1 × 1 × 1 structure, yields improved power transfer efficiency. The eddy current loss caused by the transmitter coils in a 1 × 1 × 1 system can be reduced to roughly half of that in a 1 × 1 system, with one transmitter coil and one receiver coil. The experimental results show that the power transfer efficiency from the transmitter to the receiver is improved by nearly 10%. After the introduction of equivalent eddy current loss impedance into the circuit, two arrangements of the 1 × 1 × 1 circuit topology are investigated. They consist of a shared or separately compensated capacitance topology. It is found that the shared-compensated capacitance topology is more robust to the change of mutual inductance than the separately compensated capacitance topology. This kind of structure is very useful in underwater vehicle applications. [ABSTRACT FROM AUTHOR]

The paper proposes optimal driving conditions of two transmitters (TXs) in magnetic wireless power transfer, where the couplings from each TX to an RX are not identical. First, for the case of identical TX coil currents, a criterion for deactivating a specific TX element is proposed. Specifically, one TX element among the two TXs often has weaker coupling coefficient than the other TX element. It is found that the TX element with weaker coupling should be deactivated if its coupling coefficient is less than 0.414 times of the stronger coupling. Second, for the case of adjustable TX coil currents, the optimal current ratio between the two TX coils is proposed. It is found that the TX coil current ratio should be equal to the coupling coefficient ratio, e.g., the TX coil with twice coupling with an RX should carry twice current. The results are widely applicable regardless of absolute coupling strength and load condition because it turns out that the results only depend on the ratio of couplings. Finally, it is discussed that the required component values of an LCC inverter should be adjusted based on the current ratios and coupling between adjacent TXs. [ABSTRACT FROM AUTHOR]

In recent years, wireless power technology has been promoted for recharging systems for portable devices that are used in everyday life. The conventional technology used for this purpose, which is based on magnetically coupled resonators, has provided promising results but is limited in range and direction at the receiving terminal. In this paper, we propose an omnidirectional wireless power transfer (WPT) system with a novel cubic transmitter to achieve relatively high efficiency. Specifically, a single power source is utilized to drive the current of the transmitter without phase and current control methodology. Energy delivery is transmitted to the receiver through magnetic resonant coupling in the medium-range WPT mode. In addition, an equivalent circuit model of a coupling two-coil system is derived and mathematically analyzed. The efficiency of the proposed omnidirectional WPT system depending on the various distances between the transmitter and the receiver, as well as the transmitter structure, is evaluated via analysis and implementation. Finally, practical experimental results from the resonant coupling system confirm the theoretical analysis of the cubic transmitter and the omnidirectional power transfer capability, which demonstrate approximately 60% power transfer efficiency. [ABSTRACT FROM PUBLISHER]

A new wireless power transfer (WPT) system based on ball-joint structure is presented in this paper. A ball-joint WPT system consists of a ball structure with a mechanical rod attached to the ball and a ball socket that accommodates the ball structure. This ball-joint structure comprises at least one winding in the ball structure and at least one winding in the ball socket structure. The ball structure can be flexibly rotated over a wide range of angle inside the ball socket, while wireless power can still be transferred from the transmitter winding to the receiver winding through magnetic resonance. The magnetic coupling coefficient between the transmitter and receiver coil over a wide rotating angular range has been analyzed and experimentally checked. Experimental results confirm that an energy efficiency of up to 81% can be achieved. [ABSTRACT FROM PUBLISHER]

This paper presents a rigorous optimization technique for wireless power transfer (WPT) systems enhanced by passive elements, ranging from simple reflectors and intermediate relays all the way to general electromagnetic guiding and focusing structures, such as metasurfaces and metamaterials. At its core is a convex semidefinite relaxation formulation of the otherwise nonconvex optimization problem, of which tightness and optimality can be confirmed by a simple test of its solutions. The resulting method is rigorous, versatile, and general—it does not rely on any assumptions. As shown in various examples, it is able to efficiently and reliably optimize such WPT systems in order to find their physical limitations on performance, optimal operating parameters, and inspect their working principles, even for a large number of active transmitters and passive elements. [ABSTRACT FROM PUBLISHER]