Frequency Splitting Phenomena Research Articles

Resonant Near-Field Power Transfer: Revisiting the frequency-splitting phenomenon using the spherical mode theory antenna model

In this article, the resonant coupling phenomenon is revisited using the antenna theory. The methods for extracting the maximum power by the load (i.e., the frequency tracking, conjugate matching, and critical coupling adjustment) are addressed. To obtain the best performances in terms of the highest power and the greatest transmission range, the system's tuning needs to be very sharp regardless of the method applied. Conjugate matching is shown to be the best method for reaching the highest possible antenna separations and the maximum efficiency, but the critical coupling adjustment turns out to be more practical in the sense of the bandwidth when the antenna separations are not too large.

Investigation on power optimization principles for series-configured resonant coupled wireless power transfer systems

This paper is a thorough theoretical analysis of a two-coil wireless power transfer system (WPTS) configured in series with a focus on power optimization rather than maximizing transmission (link) efficiency. Different definitions of the system efficiency in the pertaining literature are distinguished and clarified. The frequency splitting phenomenon is precisely explained, and furthermore, the analytical solutions are derived based on analysis of the input impedance. The effects of this behavior on the power transfer to a load resistance are discussed. Various aspects of the power optimization problem are explored. In particular, for the case when the system is driven at the resonance frequency, (i) the explicit expression of the optimal coupling factor between the two coils for a given load, and (ii) the optimum power with respect to the load are provided. The impedance matching methods using different circuit topologies are analytically or numerically investigated, revealing that the drive frequency can be arbitrarily chosen and not necessarily equal to the resonance frequency. This provides more options for exciting the system apart from the resonance condition, without compromising the delivered power. A comparison between optimization techniques is given in terms of the coupling factor k, showing that the bi-conjugate matching with Π-networks results in the maximum generated power and the transducer power gain (i.e., defined by the ratio between the received power and the power available from the source), which reaches 80% at k=84.4×10-3, for example.

Investigation of magnetic resonance coupling circuit topologies for wireless power transmission

AbstractMagnetic resonance coupling circuits have four general topologies; however, there is a lack of comprehensive theoretical analysis with experimental verification for each of these topologies regarding their attractiveness for wireless power transfer (WPT). This article provides this for each of the four topologies to fully understand their differences and allow the selection of the most appropriate type based on system requirements. In addition, a problem associated with the resonance coupling method is the phenomenon of frequency splitting, which can lead to a high‐power transfer efficiency but low‐load power at the resonant frequency. Reasons for frequency splitting and methods of circumventing the problem will be illustrated in this article. Of the four topologies, the series‐parallel (SP) (input‐output) circuit configuration is the most efficient for the realization of a WPT system with a large load impedance, in terms of achieving both a high power transfer efficiency and high‐load power.

Control method of magnetic resonant WPT maintaining stable transmission power with wide misalignment tolerance

Many applications of wireless power transmission (WPT) require high misalignment tolerance. However, the transmission power of WPT is highly susceptible to the misalignment. To solve this problem, the magnetic resonant WPT control method with high misalignment tolerance is proposed here. First, based on the general mutual model, the complex ratio transformer model is established. This model gives an intuitive physical picture in power transmission process and frequency splitting phenomenon. Second, approximately constant voltage gain at frequency splitting point in a wide range of misalignment is analysed. Considering this frequency splitting characteristics of Magnetic resonant WPT, the maximum peak point tracking control methods for wide misalignment, maintaining constant output power is proposed. Finally, the corresponding simulation and experimental validation is given, demonstrating the feasibility of the control method. When the misalignment reached 40%, the fluctuation of the output voltage will be <4%, the DC–DC transmission efficiency will be enhanced to 80%.

Circuit Analysis of Achievable Transmission Efficiency in an Overcoupled Region for Wireless Power Transfer Systems

On nonradiative wireless power transfer (WPT) using a pair of magnetically coupled resonators, we investigate the achievable transmission efficiency for a different set of resonators. Using a simplified equivalent circuit model, we analyze the phenomenon of frequency splitting mathematically in the overcoupled region ( $k > k_{\rm {ref}}$ ). Even though the transmission efficiency tends to gradually decrease as the distance between the two resonators gets closer and closer in the overcoupled region, the transmission efficiency can be improved by tracking one of two separated frequency modes. Based on this observation, we prove mathematically that the achievable transmission efficiency at $k_{\rm {ref}}$ is maintained almost constantly even when $k > k_{\rm {ref}}$ if the identical resonators are used. In order to validate the accuracy of the analysis, we design and fabricate two types of magnetically coupled resonators: one is the set of identical resonators and the other is the set of nonidentical resonators. Through experiments in various environments, we show that the analytical results are in good agreement with the measured ones. Our work can provide an insight into design resonators for short-range WPT systems, in order to ensure better and stable performance.

High efficiency wireless charging system design for mobile robots

In order to solve the problems of difficult and unintelligent charging of the mobile robot after the exhaustion of battery power, this paper applies wireless power transfer (WPT) technology to the charging of robot, and designs a wireless charging system that meets the characteristics of the robot. In this paper, the basic theory of wireless charging system is analysed. The expressions of output power and efficiency are derived, and the expressions above are input as code into MATLAB. By the MATLAB code, the effects of parameters such as coil inductance and coupling coefficient on the output power and efficiency of the system are studied, and the relevant parameters of the system are determined. Through MATLAB Simulink simulation, it is found that the voltage of the battery pack of the robot is too low and frequency split occurs. This paper proposes a frequency control strategy to deal with the frequency split phenomenon. The overall scheme of the robot wireless charging system design is given, and the design and hardware implementation of the transmitter controller, the energy coupler, and the receiver controller are given respectively. Finally, through the installation experiment, the correctness and practicability of the robot wireless charging system designed in this paper are verified.

Frequency Splitting-Based Wireless Power Transfer and Simultaneous Propulsion Generation to Multiple Micro-Robots

Multiple microrobots are needed in biomedical applications to perform time-bound complex clinical practices. Simultaneous wireless power transfer (WPT) and propulsion generation helps the designer to miniaturize the size and capable of executing multitasking operation. However, the selective power and force transfer to multiple devices is challenging and requires multiple frequency magnetic fields at the transmitter (Tx). This paper proposes a new approach of simultaneous independent wireless power and force generation using frequency splitting phenomena present in magnetic resonance. In the proposed approach, three coils at the Tx side is operated under over coupled (OC) mode, which produces three different split frequencies. The split frequency at the Tx side is utilized for the simultaneous independent power and force transfer to three different micro-robots and the number of micro-robots can be increased by operating the Tx side coil at different OC region. In addition, the split frequency of three coil WPT circuit comprises of the original resonant frequency irrespective of variation in coupling between the coils. This feature can be applied for the design of leader–follower control approach to the multiple micro-robots environments. The mathematical, simulations, and experimental analysis of power transfer and force generation at frequency splitting are performed for the proposed system with five load coils (considered as micro-robots).

Dynamic impedance compensation for wireless power transfer using conjugate power

Wireless power transfer (WPT) via coupled magnetic resonances has been in development for over a decade. However, the frequency splitting phenomenon occurs in the over-coupled region. Thus, the output power of the two-coil system achieves the maximum output power at the two splitting angular frequencies, and not at the natural resonant angular frequency. According to the maximum power transfer theorem, the impedance compensation method was adopted in many WPT projects. However, it remains a challenge to achieve the maximum output power and transmission efficiency in a fixed-frequency mode. In this study, dynamic impedance compensation for WPT was presented by utilizing the compensator within a virtual three-coil WPT system. First, the circuit model was established and transfer characteristics of a system were studied by utilizing circuit theories. Second, the power superposition of the WPT system was carefully researched. When a pair of compensating coils was inserted into the transmitter loop, the conjugate power of the compensator loop was created via magnetic coupling of the two compensating coils that insert into the transmitter loop. The mechanism for dynamic impedance compensation for wireless power transfer was then provided by investigating a virtual three-coil WPT system. Finally, the experimental circuit of a virtual three-coil WPT system was designed, and experimental results are consistent with the theoretical analysis, which achieves the maximum output power and transmission efficiency.

Frequency Splitting Elimination and Cross-Coupling Rejection of Wireless Power Transfer to Multiple Dynamic Receivers

Simultaneous power transfer to multiple receiver (Rx) system is one of the key advantages of wireless power transfer (WPT) system using magnetic resonance. However, determining the optimal condition to uniformly transfer the power to a selected Rx at high efficiency is the challenging task under the dynamic environment. The cross-coupling and frequency splitting are the dominant issues present in the multiple Rx dynamic WPT system. The existing analysis is performed by considering any one issue present in the system; on the other hand, the cross coupling and frequency splitting issues are interrelated in dynamic Rx’s, which requires a comprehensive design strategy by considering both the problems. This paper proposes an optimal design of multiple Rx WPT system, which can eliminate cross coupling, frequency splitting issues and increase the power transfer efficiency (PTE) of selected Rx. The cross-coupling rejection, uniform power transfer is performed by adding an additional relay coil and independent resonance frequency tuning with capacitive compensation to each Rx unit. The frequency splitting phenomena are eliminated using non-identical transmitter (Tx) and Rx coil structure which can maintain the coupling between the coil under the critical coupling limit. The mathematical analysis of the compensation capacitance calculation and optimal Tx coil size identification is performed for the four Rx WPT system. Finite element analysis and experimental investigation are carried out for the proposed design in static and dynamic conditions.

Improved ant colony algorithm for adaptive frequency‐tracking control in WPT system

When the distance between resonators is low enough for the coupling condition to be greater than the critical coupling, the single resonant peak at the load splits to form double peaks. This frequency-splitting phenomenon results in a reduction in the power transferred. In this study, an adaptive frequency-tracking control (AFTC) approach based on a closed-loop control scheme is implemented to overcome this problem. An improved ant colony algorithm (IACA) was proposed in AFTC to track the maximum power point in real time. Then, simulations were performed to test the real-time characteristics of IACA. Finally, a wireless power transfer system with AFTC is demonstrated experimentally to validate the IACA results and the tracking of the optimal frequency.

Study on frequency characteristics of wireless power transmission system based on magnetic coupling resonance

In order to study the frequency characteristics of the wireless energy transmission system based on the magnetic coupling resonance, a circuit model based on the magnetic coupling resonant wireless energy transmission system is established. The influence of the load on the frequency characteristics of the wireless power transmission system is analysed. The circuit coupling theory is used to derive the minimum load required to suppress frequency splitting. Simulation and experimental results verify that when the load size is lower than a certain value, the system will appear frequency splitting, increasing the load size can effectively suppress the frequency splitting phenomenon. The power regulation scheme of the wireless charging system based on magnetic coupling resonance is given. This study provides a theoretical basis for load selection and power regulation of wireless power transmission systems.

Analysis and experimental results of frequency splitting of underwater wireless power transfer

Underwater wireless power transfer (UWPT) is an important technique to power underwater devices while its frequency splitting phenomena are not fully elucidated. In this study, frequency splitting phenomena of a symmetrical planar two-coil wireless power transfer (WPT) system resonated at 90 kHz are investigated in seawater and freshwater. A concise frequency splitting analysis of this WPT system in air based on circuit model is given first and then experimental data are reported to show there is little difference between power transfer in air, freshwater and seawater in the range of 40–140 kHz of this WPT system. Consequently, the frequency splitting analysis and observations in air are also applicable in freshwater and seawater. It is found a V-type frequency splitting pattern exists in this WPT system under seawater and freshwater. Frequency shift is observed in this UWPT system in overcoupled region, and no frequency shift is observed in undercoupled region. In undercoupled region, in the low frequency zone of 40–90 kHz the load voltage characteristics in three media are identical; in the high-frequency zone of 90–140 kHz, the load voltage in air is slightly larger than those in freshwater and seawater.

Analysis and Optimization of Three-Resonator Wireless Power Transfer System for Predetermined-Goals Wireless Power Transmission

Three-resonator wireless power transfer (WPT) systems have been proposed to improve the power transfer efficiency (PTE) and power delivered to the load (PDL) in recent years. However, analysis formulas of a three-resonator WPT system are complicated, and the parameters for clarifying the transfer characteristics of this system are difficult to extract. In this paper, concise formulas for analyzing PTE and PDL of the three-resonator system are derived by introducing three factors. Diagram discriminance based on the derived formulas is proposed to obtain the frequency splitting criterions of PTE and PDL in this system. Further, at the transfer distances, where the PTE and PDL are low at original frequency due to frequency splitting phenomenon, the two predetermined-goals of maximizing PTE and PDL are achieved by optimizing coupling strength between the three resonators. The third predetermined-goal of obtaining a constant amount of PDL transfer at maximum PTE is also implemented based on basic algorithms in numerical software. Finally, Simulation and measurement results verify the correctness of analyzing the transfer characteristics of three-resonator WPT system using the presented concise formulas and discriminance. Moreover, effectiveness of realizing the three predetermined-goals via the proposed optimization method is confirmed with experiments.

Circuit model based design and analysis for a four-structure-switchable wireless power transfer system

The four-coil wireless power transfer (WPT) technology can effectively improve the transfer efficiency. The high efficiency, however, cannot be obtained along the whole transfer distance due to the phenomenon of frequency splitting in the over coupled region. Aiming at this limitation, this paper presents a switchable WPT system to improve the overall efficiency by changing the number of working coils. The switching conditions for the designed system are determined based on the analysis of the transfer efficiencies of four structures, which is deduced through modeling the equivalent circuits. The simulation results well comply with the experimental results and both of them indicate that the switchable system can greatly improve the overall transfer efficiency along the whole transfer distance. The overall efficiency of the experimental system can reach above 70% at 9.97 MHz without additional complexity, which is higher than any single structure system.

Frequency Splitting Phenomena of Magnetic Resonant Coupling Wireless Power Transfer

In magnetic resonant coupling wireless power transfer (WPT) system, the frequency splitting phenomena have a vital influence on the output power. This paper mainly focuses on the frequency splitting of two-coil and three-coil WPT. First, the frequency characteristics of transfer power and system efficiency of the two-coil WPT are analyzed by circuit theory. In addition, the magnetic field distribution of the two splitting frequencies is simulated to analyze which frequency is better for the operating frequency. Second, considering the reference resistance of RF power, the frequency splitting of two-coil and three-coil WPT is analyzed. Finally, the critical coupling, which determines the over coupled region, of two-coil and three-coil WPT is derived. Meanwhile, we propose a tuned frequency method according to the numerical results. In addition, the transfer power can be kept at a relatively constant level in the over coupled region.

A Critical Review of Wireless Power Transfer via Strongly Coupled Magnetic Resonances

Strongly coupled magnetic resonance (SCMR), proposed by researchers at MIT in 2007, attracted the world’s attention by virtue of its mid-range, non-radiative and high-efficiency power transfer. In this paper, current developments and research progress in the SCMR area are presented. Advantages of SCMR are analyzed by comparing it with the other wireless power transfer (WPT) technologies, and different analytic principles of SCMR are elaborated in depth and further compared. The hot research spots, including system architectures, frequency splitting phenomena, impedance matching and optimization designs are classified and elaborated. Finally, current research directions and development trends of SCMR are discussed.

Frequency-Splitting Analysis of Four-Coil Resonant Wireless Power Transfer

Based on four-coil magnetically coupled resonant wireless power transfer, this paper demonstrates, explains, and analyzes the frequency-splitting phenomenon by using the circuit theory. First, the complete and simplified models are built to describe the whole system. The numerical formulas of the system efficiency both at and away from the resonant frequency are presented. Then the frequency-splitting phenomenon is displayed and further explained mathematically and physically. An important factor for frequency splitting is introduced. The boundary condition for frequency splitting and its splitting frequency points are deduced. The amplitude-frequency and phase-frequency characteristics of the input impedance are measured and described to verify the explanation. Three related factors are studied, and the sensitivity analysis is conducted. A solution is proposed that helps improve the efficiency when frequency splitting occurs. The theoretical calculations and experimental results provide a sound basis.

Efficient performance optimisation of wireless power transmission using genetic algorithm

Wireless power transfer (WPT) systems using a coupled magnetic resonance have to overcome the frequency splitting phenomenon for a certain distance in order to achieve the best efficiency. In this reported work, a simple and effective method is demonstrated to overcome the frequency splitting for an optimal efficiency, regardless of the distance variation while maintaining the single desired operating frequency. Then, the systems do not need complicated frequency adjustment systems to track the split frequency. For the proposed method, the equivalent circuit parameters of the WPT system are extracted to overcome the frequency splitting by using the genetic algorithm (GA). Then, two adjustable capacitors are added at the source and the load with the optimal values calculated by the GA, again, at the desired operating frequency for the optimal efficiency.

A Planar Magnetically Coupled Resonant Wireless Power Transfer System Using Printed Spiral Coils

A fully planar wireless power transfer (WPT) system via strongly coupled magnetic resonances is presented. In it, both the transmitter and the receiver are planarized with the use of coplanar printed spiral coils (PSCs) and a printed loop. An equivalent circuit model of the proposed planar WPT system is derived to facilitate the design, and a flowchart is provided for the optimization of the system with given size constraints. To realize high peak power transfer efficiency, the quality factor of individual loop or resonator, the mutual coupling between resonators, and the frequency splitting phenomenon of the system are analyzed in addition to the effect of the input impedance of the system on the transmission efficiency. Furthermore, parallel current paths are created by applying auxiliary strips to the backside of the substrates and connecting to the prime resonators using vias to decrease the resistance and to increase the quality factor of the PSC resonators, and this in turn further improves the transfer efficiency of the proposed planar WPT system. The measured results show that the proposed WPT system is able to provide a stable wireless power transfer with up to 81.68% efficiency at a distance of 10 cm. The planar structure and the high transfer efficiency make the proposed design a suitable candidate for wireless power transfer of small portable electronic devices.

Frequency Splitting Analysis of Wireless Power Transfer System Based on T-type Transformer Model

Frequency splitting is a key characteristic of wireless power transfer system. With the increases of coupling coefficient, the power transferred to load drops sharply. The resonant frequency splits from one into two within splitting region. Previous reports about frequency splitting mainly focused on the analysis of coupled mode theory or the solutions of ridge equations. In this work, we presented the analytical results based on a simply T-type circuit model. With impedance analysis, the even and odd splitting frequencies were derived. In addition, the frequency splitting phenomena were analysed with output voltage curves at different coupling by the aid of simulation. Furthermore, the frequency splitting and the frequency bifurcation discussed frequently in inductively coupled wireless power transfer system were analysed comparatively based on the circuit model. Then, a half-bridge inverter based wireless power system was constructed to demonstrate the experimental results. Finally, the simulation and experimental results validated the theoretical analysis. DOI: http://dx.doi.org/10.5755/j01.eee.19.10.5455