Frequency Splitting Phenomena Research Articles

Analysis of /t̪a:/ and /t̪ʊn/ bols of the tabla from a musical standpoint

Tabla, the Indian harmonic musical drum, produces several distinct sounds or bols, which are rhythmically arranged into different taals (beat-cycles) to work as a syllabic musical poem. Prior research on tabla has primarily focused on the tabla membrane’s vibrational attributes and how such attributes get influenced by the tabla’s structure. Thus, there is a need to study the tabla from a musical standpoint and understand the linkages between its vibrations and the acoustical attributes of its musical bols. We fill this gap by analyzing the two most important bols; /t̪a:/ and /t̪ʊn/. Towards this, we studied bols produced by ten experienced tabla players using four different tablas tuned to different notes spanning an octave. To extract the tabla’s vibro-acoustical features, we employed two stereoscopically arranged high-speed cameras and an audio data acquisition system in tandem. Our work brings out several salient features of these bols including correspondences between the method of producing a bol and its acoustical attributes, the presence of nearly degenerate modes, the phenomenon of frequency splitting due to asymmetric loading of tabla membrane and the consequential beats, the musical importance of some inharmonicities, and psychoacoustic implications of certain frequencies missing in a bol’s spectrum. Such understanding will not only help us understand the musical acoustics of the tabla better, but also guide us towards an improved tabla design.

Maximum Wireless Power Transmission Using Real-Time Single Iteration Adaptive Impedance Matching

Wireless power transfer (WPT) systems’ efficiency is significantly impacted by non-monotonic variations in the coupling coefficient. For very short distances or strong-coupling cases, the WPT efficiency is minimal at the natural resonant frequency, with two peaks around this frequency, known as the frequency splitting phenomenon. On the other hand, WPT capability decreases for long distances or weak coupling cases. Therefore, adaptive matching is required for WPT systems with varying distances, like wireless charging systems for electric vehicles (EVs). This paper first presents a detailed analysis of the frequency splitting phenomenon by studying the root locations of the WPT system’s transfer function. Then, a real-time fixed-frequency adaptive impedance matching (IM) method is proposed, in which the amplitude and phase of the input impedance is estimated using the average active power, the average reactive power, and the amplitude of input voltage. Unlike traditional search-and-find techniques, the proposed method calculates the optimal IM network parameters only in a single iteration, which improves the convergent speed. A scaled-down 20-Watt prototype controlled by the TMSF2812 is fabricated and used to validate the effectiveness of the proposed method over a wide range of coil-to-coil distances.

Nonlinear Modeling and Transmission Efficiency Optimization of MCR-WPT System Based on Monte Carlo-Interior Point Method

With the optimization goal of improving the transmission efficiency of the magnetically coupled resonant wireless power transmission (MCR-WPT) system, the influencing factors and suppression methods of frequency splitting phenomenon (FSP) are analyzed from the perspective of input impedance based on the mutual inductance model. Then we propose the Monte Carlo-Interior Point method (MC-IPM) for nonlinear modeling to determine the optimal system parameters while ensuring that the system does not suffer from FSP. Finally, the simulation results show that the proposed method can obtain the optimal parameters faster and achieve higher transmission efficiency. The optimized system can meet the practical requirements and provides a reference value for improving the transmission performance of MCR-WPT.

Frequency splitting suppression in wireless power transfer using hemispherical spiral coils

In wireless power transfer (WPT) systems, frequency splitting phenomena always occur when the transfer distance is too small to obtain the maximum output efficiency in the working frequency. In this paper, a hemispherical spiral coil structure is proposed to suppress frequency splitting phenomena by containing the coupling the system without changing the original system size and transfer distance. Meanwhile, compared with the planar system, the hemispherical system can maintain high power and transfer efficiency and has better angular misalignment tolerance. A WPT system consisting of a hemispherical spiral coil and a planar spiral coil resonating at 110 kHz called the single hemispherical spiral coil WPT (SHWPT) system and another with two hemispherical spiral coils called the double hemispheric spiral coils WPT (DHWPT) system are suggested. Analytic models of these two structures are established to analyze the influence of the coil height on the frequency splitting. The critical coil height is closely related to the critical coupling that provides a reference for the design of the coil. Finally, the experimental results show that the hemispherical coil structure can suppress the frequency splitting to ensure the transmission stability of the WPT system. In the SHWPT system with a 1 cm inner diameter and a 13 cm outer diameter, the critical height of the coil is 5.2 cm, which can suppress frequency splitting when the transmission distance is 0 cm. In the DHWPT system, the critical height of the coil is 4.3 cm.

Genetic-Algorithm-Based Optimization of a 3D Transmitting Coil Design with a Homogeneous Magnetic Field Distribution in a WPT System

In magnetically coupled resonant wireless power transfer (MCR-WPT) systems, the nonhomogeneous magnetic field of the transmitting coil can lead to frequency splitting phenomena and lower efficiency. In this paper, a 3D transmitting coil (TX) with a homogeneous magnetic field distribution is proposed. The proposed coil structure consists of two layers with different numbers of turns per layer, i.e., with different current distributions. To achieve a homogeneous magnetic field distribution with a high magnetic field value and a low profile of the 3D coil structure, the optimal layer placement and current distribution were optimized using a genetic algorithm (GA). The prototype of the optimized coil was fabricated, and its magnetic field distribution was measured. The measurement results agreed more than 95% with the simulation results. The measured homogeneous area was at least 12.5% larger than reported in the literature. By using a different current distribution, the profile of the 3D coil structure was successfully reduced by 29% and the average magnetic field value was increased by 25% compared to our previous work.

Design of magnetic coupling mechanism for wireless power transmission system based on magnetic flux analysis

Aiming at the wireless charging system that can dynamically change arbitrarily in a three-dimensional space such as a smart robot, this paper proposes a new type of magnetic coupling mechanism that combines a disc coil and a spiral coil. It can not only avoid frequency splitting in the short-distance range, but also effectively enhance the coupling strength in the long-distance range. In addition, it can also effectively improve the position robustness and anti-offset ability of the robot’s wireless charging system. In this paper, the geometric framework of the new magnetic coupling mechanism is first given. Based on the analysis of magnetic flux, it is theoretically confirmed that the magnetic coupling mechanism can reduce the coupling strength in the near range, avoid the frequency splitting phenomenon, and improve the coupling strength of the system and the energy efficiency of the system in the long range. Finally, based on the finite element simulation software COMSOL, it is proved that the proposed magnetic coupling mechanism can achieve high energy efficiency output in a large range, and has strong position robustness and anti-deviation.

Performance Analysis and Design of Frequency Controlled Series-Series Compensated Inductive Power Transfer System for Electric Vehicle Battery Charging

This article presents a new method to design the coils of a series-series inductive power transfer system taking into consideration the compensation network, the battery charging profile and the efficiency of the system. Harmonic balance technique is used to derive the transient and steady-state model of the coil. Equations defining the possible frequency trajectories for the entire charging profile are derived. A design algorithm for the coil and selection of the compensation network capacitance is presented. To prevent the frequency splitting phenomenon a reduction of the secondary (receiver coil) inductance value is required. To this end the condition under which frequency splitting occurs is derived, without any simplifying assumptions, and used to guide the selection of the new secondary inductor value. An analysis for the redesigned system with the reduced secondary inductance is presented. It is observed that operating the system close to the transmitter coil resonant frequency results in both zero voltage switching and optimum efficiency. For the redesigned system, the upper frequency trajectory of the system operates close to the resonant frequency of the transmitter coil and hence ensuring high efficiency and zero voltage switching.

Magnetically coupled planar microwave resonators for real-time saltwater ice detection

Buildup of saltwater ice can cause serious issues in many industries if not identified. This work presents a comparison between electrically and magnetically coupled planar microwave resonators for saltwater ice detection applications. Due to the highly coupled nature of both sensors, the frequency splitting phenomenon occurs resulting in each sensor having two resonant frequencies. The proposed electrically coupled resonator has operational frequencies of 4.726 GHz and 4.942 GHz whereas the magnetically coupled resonator has operational frequencies of 4.647 GHz and 4.960 GHz. The quality factor of the low and high frequency for the electrically coupled resonator were 260 ± 2 and 175 ± 2 respectively and were 195 ± 2 and 260 ± 2 respectively for the magnetically coupled resonator. The sensitivity of each sensor was investigated through simulation. Experiments were conducted using reverse osmosis (RO) water and saltwater with 5% and 10% salt concentrations. These experiments demonstrated the magnetically coupled sensor to be sensitive to the formation of both RO ice and saltwater ice, whereas the electrically coupled sensor could only detect the presence of RO ice due to the increased conductivity of saltwater. This magnetically coupled sensor is a proof of concept for saltwater ice sensing and is well suited for the application due to its high sensitivity, low-cost, and real-time sensing capabilities.

Optimization of a Two-Layer 3D Coil Structure with Uniform Magnetic Field

Conventional magnetically coupled resonant wireless power transfer systems are faced with resonant frequency splitting phenomena and impedance mismatch when a receiving coil is placed at misaligned position. These problems can be avoided by using uniform magnetic field distribution at receiving plane. In this paper, a novel 3D transmitting coil structure with improved uniform magnetic field distribution is proposed based on a developed optimization method. The goal is to maximize the average magnetic field strength and uniform magnetic field section of the receiving plane. Hence, figures of merit (FoM1 and FoM2) are introduced and defined as product of average magnetic field strength and length or surface along which uniform magnetic field is generated, respectively. The validity of the optimization method is verified through laboratory measurements performed on the fabricated coils driven by signal generator at operating frequency of 150 kHz. Depending on the allowed ripple value and predefined coil proportions, the proposed transmitting coil structure gives the uniform magnetic field distribution across 50% to 90% of the receiving plane.

Half-space response to trains moving along curved paths by 2.5D finite/infinite element approach

For a train moving along a curved path, centrifugal forces are induced in addition to gravitational loads. In this paper, the 2.5D approach for loads moving along a straight path is extended to treating both the vertical and horizontal loads moving along a curved path. Firstly, closed-form solutions for the problem are derived for the cases of vertical and horizontal loads. Then, the 2.5D approach with finite/infinite elements in the Cartesian coordinates are summarized. By approximating a curved path by a number of small chordwise segments and by using the 2.5D approach to simulate each segment, the displacements in the global polar coordinates are obtained by summing up those of each segment in the local Cartesian coordinates, considering the time lags and direction changes. For linear systems, the responses due to vertical and radial loads can be computed separately. In the numerical simulation, the theory presented will be verified by two typical cases. The frequency-splitting phenomenon is found to exist for the horizontal loads, as well as for the vertical loads, moving over a curved path. The radial response induced by the centrifugal force cannot be ignored, and the displacement outside the railway track is larger than that inside. Such an effect should be considered in the design of curved paths for highspeed railways. The method presented herein can be adopted to solve problems with varying radius of curvature.

Analysis and Utilization of the Frequency Splitting Phenomenon in Wireless Power Transfer Systems

The frequency splitting phenomenon (FSP) is a critical issue in wireless power transfer (WPT) systems. When the FSP exists, the load power will sharply increase and can be dozens of times of the power obtained at the resonant frequency if the driving frequency varies from the resonant frequency, which seriously affects the system safety. This article studies the impacts caused by the FSP in detail and then proposes a system control method by utilizing the advantages of the FSP to realize constant power output and zero voltage switching (ZVS) of the dc-ac inverter simultaneously. The splitting frequencies are tracked and the driving frequency is precisely adjusted together with the dc-link voltage. The specific implementation method is given in this article to minimize the impacts on the power transfer performance. An 85 kHz, 3.3 kW WPT system is built up to validate the proposed method. The experimental results show that when the FSP occurs at 150 mm coil-to-coil distance and 5 Ω load resistance, the load power can be hold at 3.3 kW with the dc-link voltage reduced from 327 to 160 V. Meanwhile, ZVS of the inverter is realized and the inverter efficiency is improved from 95% to 97%.

Selection of high transfer stability and optimal power-efficiency tradeoff with respect to distance region for underground wireless power transfer systems

Magnetic resonant wireless power transfer (MR-WPT) has become a significant method for powering the measurement units in landslide monitoring boreholes. This paper focuses on the effects of quality factor, coupling distance and load on the power transfer stability, sensitivity and performance of an MR-WPT system. Firstly, through a numerical model of an MR-WPT, the effect of quality factor and coupling distance on the output power, transfer efficiency and frequency splitting phenomenon of MR-WPT systems have been comparatively analyzed. The relationship between the load and the coupling distance region corresponding to optimal transfer performance has been studied. Results show that improving the quality factor of the coils is beneficial for the transfer performance and stability of WPT system. Furthermore, through the selection of the load, a coupling distance region with high transfer stability and an optimal tradeoff between power and efficiency can be obtained. Finally, the above theoretical simulation results have been verified by experimental results.

Research on mechanism and evolution features of frequency split phenomenon of tire acoustic cavity resonance

The acoustic cavity resonance inside the tire–wheel assembly is known to contribute to audible noise in the passenger compartment of vehicles. To obtain control methods of tire acoustic cavity resonance, its characteristics and producing mechanism need to be clarified first. In this article, the finite element model of a tire coupled with acoustic medium in the tire cavity is constructed. The Euler method is introduced to study the modal characteristics of tire cavity under the influence of tire inflation pressure, load, and tire rotation velocity. Frequency splitting phenomena under four separate conditions (stationary tire without load, stationary tire with load, rotating tire without load, and rotating tire with load) are simulated and analyzed. The slope change of the resonance frequency as a function of rotation speed is found to be close to the reciprocal of tire radius which can be explained by a model of wave propagation in a ring-shaped channel with moving media inside the ring. The obtained function of the slope change can help determine the frequency variation range under different vehicle velocity, structure load, and tire inflation pressure, which can then help to control the cavity resonance energy and provide a more comfortable driving experience.

Frequency Splitting and Transmission Characteristics of MCR-WPT System Considering Non-Linearities of Compensation Capacitors

The frequency splitting phenomenon and transmission characteristics have been research hotspots in the field of magnetically coupled resonance wireless power transfer (MCR-WPT). In this paper, non-linear dynamics theory was innovatively introduced into the research, and non-linear coupled transmission dynamics modelling of the MCR-WPT system was established considering the non-linearities of the compensation capacitor. The mechanism of the frequency splitting phenomenon of the MCR-WPT system was revealed through systematic mathematical analyses based on the modelling. The analysis results showed that the system usually has dual natural frequencies which are low resonance frequency and high resonance frequency. Based on non-linear dynamics theory, the transmission characteristics of the system with different non-linear parameters were discussed comprehensively in relation to the modelling. The results of the numerical simulations and theoretical analyses showed that non-linear parameters can cause the jumping phenomena with the output responses, and the output responses in the vicinities of the lower resonance frequencies were extremely sensitive to changes in the coupling coefficient. According to analyses of the linear and non-linear systems, the energy transmissions performed in the vicinity of the high resonance frequency had a wider working frequency band and a better transmission stability under non-linear conditions.

Capacitance Tuning Method for Maximum Output Power in Multiple-Transmitter Wireless Power Transfer System

It is common knowledge that wireless power transfer (WPT) systems with multiple transmitters (Txs) and a single receiver (Rx) have robust efficiency against lateral misalignment. However, the unnecessary coupling among Txs in actual multi-Tx WPT systems causes transmission efficiency degradation, and then additional tuning work is required to adjust some system parameters, such as the phase or frequency of Tx sources. Moreover, the frequency-splitting phenomenon caused by over-coupling between the Txs and Rx still occurs in multi-Tx systems. Thus, output power degradation is inevitable in the over-coupled state. In this article, we propose an optimal capacitance tuning method that is applicable to multi-Tx WPT systems. A multi-Tx WPT system tuned with the optimal capacitances, which are obtained from the critical coupling condition between Txs and Rx, not only compensates the inner coupling among Txs but also achieves the maximum output power in the over-coupled state. To verify the validity of the proposed method, we implemented two-and three-Tx and single Rx WPT systems and measured the output power of load with respect to the Rx position along the $x$ - and $y$ -axes. As a result, with the proposed method without any changes in the operating frequency or phase, the systems could deliver higher output power than the conventional phase-controlled system. In particular, with the proposed method, the systems maintained the constant maximum transmission efficiency of 80% in the over-coupled state.

Secondary-Side Voltage Control via Primary-Side Controller for Wireless EV Chargers

In inductive power transfer (IPT) system, the magnetic coupling has significant effects on power and system efficiency. The voltage and current on the secondary side are coupling dependent. Load measurements are not possible through sensors on the primary side. This article proposes the secondary-side voltage controller based on the primary-side control by means of bifurcation approach. The main advantage of operation under bifurcation is that the coupling and load on the secondary have no effect on the voltage gain. This enables the secondary voltage control through the primary voltage. With the proposed sensing coil on the primary side, the bifurcation detection is possible. The proposed control can utilize the frequency split phenomenon and track the bifurcation frequency to ensure maximum efficiency in various coupling conditions. In addition, the design guidelines of the parallel-parallel compensation configuration are introduced for a desired load profile and transfer distance. The constant voltage gain with respect to conditions of magnetic coupling variation is verified by using finite element analysis and experimental study. A 1-kW IPT prototype is constructed to validate the proposed bifurcation detection and voltage control. Experimental results show that the proposed IPT can achieve up to 90% of maximum efficiency while maintaining constant secondary voltage.

Efficiency analysis of coupled resonant radio energy transmissions

In order to improve the transmission efficiency of magnetic coupling resonance for wireless transmission technology, the dual coil wireless transmission system was designed and simulated based on ANSYS. Influencing factors of transmission efficiency include coil turns, material properties, frequency characteristics, and maximum transmission distance. A relevant experimental circuit is designed to verify the correctness of the theoretical analysis and provide an effective reference to improve the efficiency of radio energy transmission. Through the analysis of past improvement schemes, the performance of wireless transmission equipment is optimised based on electromagnetic field simulation and the frequency-splitting phenomenon is verified.

Shear Alfvén wave continuum spectrum with bifurcated helical core equilibria

The radial structure of the continuum spectrum of shear Alfvén and Alfvén-acoustic waves in the beta-induced Alfvén eigenmode (BAE) frequency range is modeled for tokamak plasmas in the presence of 3D effects obtained from the bifurcated MHD equilibrium reconstruction. Plasma compressibility and geodesic curvature effects responsible for the low-frequency continuum spectrum calculations are invoked. In the equilibrium calculations we find that the helically distorted MHD equilibria may exist even for the axisymmetric devices if q = 1 rational surfaces are present. The continuum calculations with the bifurcated equilibria lead to a frequency splitting between the highest frequency branch and the lowest frequency branch continua at the frequency accumulation point. Radially localised shifting of modes happens via coupling of the adjacent n − 1 continuum around an accumulation point. Our modelling (including 3D effects) correctly reproduces the phenomenon of continuum frequency splitting and provides a possible solution for the differences of few kHz in frequency splitting, which remained unexplained with the 2D kinetic calculations (Curran et al 2012 Plasma Phys. Control. Fusion 54 055001). The pressure scaling confirms the increase of helical excursion of the magnetic axis in equilibrium reconstruction and hence the range of continuum frequency splitting. In our calculations, the existence of low-frequency continua is in agreement with the experimentally observed low-frequency modes.

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.