Spatial Harmonics Research Articles

2D-smoothing of laser beam fluctuations in optical compressor

We propose a modification of the four diffraction gratings Treacy compressor (TC)—a double-smoothing grating compressor (DSGC)—which enables smoothing of spatial fluctuations of a laser beam in two directions. Smoothing along the groves is due to oblique incidence on the gratings or tilted grooves. Smoothing in the direction normal to the grooves is achieved due to the use of nonidentical pairs of gratings. It is shown that the far-field fluence and the focal beam intensity after the DSGC are like those after the TC. Smoothing is a consequence of spatial harmonics lagging behind or overtaking the main pulse in proportion to the transverse wave vector. Analytical expressions are obtained for the spectrum of fluence fluctuations and fluence rms at the DSGC output. The efficiency of suppressing small-scale self-focusing in transmissive optical elements after the DSGC, for example, in the case of post-pulse compression is assessed.

A method of timbral equalization for Ambisonics reproduction with irregular loudspeaker configuration

Ambisonics is a spatial sound reproduction technique based on spatial harmonics decomposition and each order approximation of target sound field. Given a spatial region, Ambisonics is able to reconstruct target sound field accurately up to a frequency limit imposed by Shannon–Nyquist spatial sampling theorem. Above that limit, spatial aliasing in reconstructed sound field occurs, and therefore, timbre equalization in loudspeaker signals is needed to reduce perceived timbre coloration in reproduction. Power equalization is a common and effective method in which the overall power of loudspeaker signals are equalized to be independent of target source direction. The power equalization can be easily implemented in the Ambisonics reproduction with regular rather than loudspeaker configuration. In this study, a method of power equalization for Ambisonics reproduction with irregular loudspeaker configuration is proposed. The fluctuation of overall power of loudspeaker signals with target source direction is controlled within 3 dB by appropriate choice of the decoding coefficients of higher-order spatial harmonics in Ambisonics reproduction. This method is applicable to Ambisonics signals obtained by simulation or microphone array recording. Psychoacoustic experiments indicate that the current method reduces the timbral coloration to some extent while keeps the localization performance in reproduction.

An Optimized PLL With Time Delay and Harmonic Suppression for Improved Position Estimation Accuracy of PMSM Based on Levenberg–Marquardt

This paper proposes an optimized phase-locked loop (OPLL) based on Levenberg-Marquardt (LM) to improve the estimation accuracy of the sliding mode observer (SMO) based position estimator. The position estimation suffers from dc bias caused by digital control delay, and harmonic caused by inverter nonlinearity and flux spatial harmonics. The OPLL is constructed with two parts to overcome the above negative effects. The delay phase is preliminarily calculated based on linear prediction, so as to compensate for the lag phase in the estimated back electromotive force (back-EMF); secondly, the objective function is built based on the reference and feedback position error, the former contains an unknown harmonic. The objective function can be minimized by the LM to solve for the harmonic amplitude, then the obtained harmonic is used to offset the harmonic components in the estimated position. Wherein, the required partial derivatives of the LM method can be deduced based on the transfer function of PLL and the delay-compensated back-EMF to achieve a stable update of harmonic amplitude. Finally, the corresponding comparative experiments in steady-state and dynamic conditions proved the superiority of the proposed method applied to permanent magnet synchronous motors.

Core Loss Equivalent Resistance Modeling of Small- and Medium-Sized Converter-Fed Induction Motors Considering Supply and Spatial Harmonics

In order to estimate the core loss resistance of converter-fed induction motor accurately and efficiently, an analytical piecewise variable-coefficient core loss model is proposed. By introducing two voltage harmonics related coefficients, the influence of converter harmonics on core loss is simply and effectively considered. In addition, the surface and pulse loss caused by slot harmonics and the additional harmonic core loss caused by harmonic magnetic potential of stator winding under load condition are also considered. Based on the proposed model, an advanced core loss equivalent resistance model of converter-fed induction motor considering supply and spatial harmonics is proposed. The effectiveness of the proposed model is validated by comparisons with the measured core losses of 5.5 kW induction motor under no-load condition. In addition, compared with the finite element method under load condition, the proposed analytical model reduces the computational time significantly while maintaining high accuracy.

A Leaky Wave Antenna With Capability of Fixed-Frequency Beamforming Scanning

A novel electrically controlled leaky-wave antenna (LWA) with capability of fixed frequency beamforming scanning is proposed in this communication. The antenna is designed on substrate-integrated waveguide (SIW), and the slot period of the antenna can be changed electronically by switching between “ON” and “OFF” states of PIN diodes connected to two edges of slots. Based on the reconfigurable property of slot period, the phase constant of the -1th spatial harmonic can be modified, thus the beam direction of antenna can be changed and continuous beam scanning can be realized. For specific applications in linear confined space, scanning beam with almost the same field strengths along a straight path is commonly required. Therefore, a hybrid coding method is proposed in this paper and applied to a 2×1 antenna array to realize bilateral beamforming scanning. Simulation and measurement results show that a wide beam scanning range of 99° at 5.98 GHz can be obtained in both cases of continuous beam scanning and beamforming scanning. The proposed LWA array is suitable for the future application of smart mobile communication.

The coupling between the spatial and temporal scales of neural processes revealed by a joint time-vertex connectome spectral analysis

Brain oscillations are produced by the coordinated activity of large groups of neurons and different rhythms are thought to reflect different modes of information processing. These modes, in turn, are known to occur at different spatial scales. Nevertheless, how these rhythms support different spatial modes of information processing at the brain scale is not yet fully understood. Here we use "Joint Time-Vertex Spectral Analysis" to characterize the joint spectral content of brain activity both in time (temporal frequencies) and in space over the connectivity graph (spatial connectome harmonics). This method allows us to characterize the relationship between spatially localized or distributed neural processes on one side and their respective temporal frequency bands in source-reconstructed M/EEG signals. We explore this approach on two different datasets, an auditory steady-state response (ASSR) and a visual grating task. Our results suggest that different information processing mechanisms are carried out at different frequency bands: while spatially distributed activity (which may also be interpreted as integration) specifically occurs at low temporal frequencies (alpha and theta) and low graph spatial frequencies, localized electrical activity (i.e., segregation) is observed at high temporal frequencies (high and low gamma) over restricted high spatial graph frequencies. Crucially, the estimated contribution of the distributed and localized neural activity predicts performance in a behavioral task, demonstrating the neurophysiological relevance of the joint time-vertex spectral representation.

Instantaneous Loss Integration Method to Estimate AC Losses in Superconductors With Spatial and Time Harmonics

Estimating AC loss is an essential step in designing fully superconducting (SC) machines, which typically involves using analytical and Finite Element Analysis (FEA) models. Established analytical models are available for stationary sinusoidal and uniform rotating fields. But, the fully SC armature winding experiences a non-uniform rotating magnetic field that can result in varying losses. In this paper, we propose extended analytical methods to estimate AC losses in non-uniform rotating magnetic fields. Our proposed methods can refine the AC loss estimation process and improve the subsequent cryogenic load design. The significant advantage of our proposed method is the ability to capture the impact of AC losses due to varying field magnitude within a single cycle. We estimate losses for various scenarios and compare them to FEA analysis results to verify the accuracy of our model. We then experimentally validate the FEA models used in the analysis for uniformly rotating fields, which establishes the feasibility of our proposed models.

Improved Position Observer Using Adaptive Training Control-Based Filter for Interior Permanent Magnet Synchronous Motor Drives

Rotor position is the key information to achieve superior performance for sensorless control of interior permanent magnet synchronous motor (IPMSM). Nevertheless, the back electromotive force (EMF) model-based position estimation suffers from severe contamination from the fifth and seventh harmonics resulting from inverter nonlinearity and flux spatial harmonics. Therefore, an adaptive training control-based adaptive filter combined with a sliding-mode observer (SMO) is presented for harmonics rejection in the estimated back-EMF, and thus improving the rotor position estimation performance. This method, based on the steepest descent algorithm, is capable of self-adjusting harmonic coefficients to obtain the fundamental component online under various frequency conditions adaptively. Additionally, the proposed method has simpler structure and less calculation burden since its reference signal is self-generated without external injection compared to the conventional method. The effectiveness is verified by experiments at a 1.5-kW IPMSM drive platform.

Application of stochastic filter to three-phase nonuniform transmission lines

ABSTRACT This paper implements the stochastic filters for state and parameter estimation of nonuniform transmission lines (NTL). In general, transmission line (TL) problem is a continuous time and space problem. By taking the line loading noise into account, the TL equations become a stochastic partial differential equation (PDE) rather than a simple set of coupled finite stochastic differential equations (SDE). By transforming the spatial variables into the Fourier domain, the stochastic PDE can be transformed into an infinite sequence of SDE. After truncation to a finite set of Fourier series coefficients, it becomes a finite set of coupled linear SDE, which is the required domain in which extended Kalman filter (EKF) and unscented Kalman filter (UKF) can be applied. For state space equation of EKF and UKF, the voltage and current of periodic NTL are expanded into an infinite set of spatial harmonics. In this way, the voltage and current measurement of NTL become an eigenvalue problem. The NTL is considered as cascade of small infinite NTL and the four distributed primary parameters of the periodic NTL are expressed using Fourier series expansion. Finally, the Kalman filter (KF)-based state estimation and the EKF- and UKF-based parameter estimation have been compared with recursive least squares (RLS) method. The simulation results present the superiority of the method.

Mapping and identification of potential groundwater development zones of an alluvial aquifer in parts of Ghaggar and Upper Yamuna basins in India.

Using an integrated analytical hierarchy process, remote sensing and geographic information system techniques, the current study aims to map and identify the potential groundwater zones of Kurukshetra District of Haryana, which is located in the Ghaggar and Upper Yamuna Basins in India. This is done in the context of a significant change in the use of groundwater pattern, with respect to its continuously increasing demand due to the growing population, expansion of area under irrigation and related economic factors. The amount and quality of groundwater are anticipated to be impacted by anthropogenic activities as well as natural factors such as geomorphology, soil type, lithology and rainfall variance owing to a changing climatic scenario. The potential index of groundwater for this study was calculated by using nine important factors, including geomorphology, rainfall, soil type, depth to groundwater level, lithology, land use land cover, normalized difference vegetation index, cumulative sand thickness and elevation. The integration of multiple thematic layers was accomplished using the overlay weighted method to generate a potential groundwater zonation map and the accuracy of the resulting map was validated against a groundwater resource potential map. Statistical measures demonstrate an 82% agreement between the two maps, indicating a high level of concurrence. Accordingly, three groundwater zones of good, average and bad potential have been identified in the study area. In the current study, a process that combines weighted ranking with spatial data transformation and harmonization has been developed to obtain information for accurate decision-making. The results accruing from this research have significant ramifications for creating regional sustainable groundwater management plans.

AC Distributed Winding with Low Higher Spatial Harmonics Content in Mmf Distribution

This paper presents a new winding with a low higher spatial harmonics content. This winding enables the elimination of the fifth harmonic, as the most significant, in three-phase winding and the third harmonic in two-phase symmetrical winding. The suppression of higher spatial harmonics is particularly evident with the number of slots per pole per phase qs = 2. The winding factors for the higher spatial harmonics of the order ν = 6 k ± 1 in the case of three-phase winding, and ν = 4 k ± 1 in the case of two-phase winding, for k = 1, 3, 5, …, will be equal to zero. A two-phase measurement winding, with the number of slots per pole per phase qs = 1, was used to evaluate the higher spatial harmonics content in the magnetic field in the air gap of the machine. Experimental verification of the designed winding was carried out.

A Stable and Computationally Efficient Spatial Harmonic Model for Predicting the DC Winding Induced Voltage in WFSF Machine

In order to predict the DC winding induced voltage under pulse width modulation excitation in the wound field switched flux (WFSF) machine with consideration of the impact of magnetic coupling among <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis and the DC winding, lamination magnetic saturation and current harmonics in both AC and DC windings, the field-circuit coupling method based on the high-fidelity spatial harmonic (SH) model is applied in this paper, including the inductance-based SH model and flux-linkage-based SH model. However, it is found that the inductance-based SH model of the WFSF machine suffers from numerical instability in dynamic operation due to the high condition number of the inductance matrix caused by the magnetic coupling among <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis and the DC winding, resulting in prediction errors of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis flux-linkages, and that of the DC winding. To solve this problem, a flux-linkage-based SH model is proposed for the WFSF machine in this paper, and it shows that the proposed flux-linkage-based SH model is numerically stable during the dynamic operation. In addition, the calculation speed of the flux-linkage-based SH model is 147 times faster than the inductance-based one, due to the exemption of the calculation of the partial derivation equations. Finally, the analyzed 24-stator-slot/10-rotor-pole WFSF machine is built and tested to validate the flux-linkage-based SH model, and the experimental results agree well with those of the SH model.

Formulation and mixing conditions of magnetic composite materials used for magnetic wedges in an interior permanent magnet synchronous motor

AbstractAn interior permanent magnet synchronous motor (IPMSM) is characterized by its high efficiency. However, torque ripple and loss occur because of the spatial harmonics generated by air‐gap permeance fluctuations. This study clarified that slot harmonic components can be suppressed by inserting magnetic wedges made of magnetic composite material in the slot opening of an IPMSM. First, the authors examined the torque and loss characteristics by varying relative permeability and saturation magnetic flux density of magnetic wedges using finite element analysis (FEA). Results indicated that the torque ripple and loss could be suppressed when the relative permeability of the magnetic wedge was μr = 10 to 22 and the saturation magnetic flux density was Bs = 0.5 to 0.75 T. Furthermore, the authors produced magnetic composite materials made of various soft magnetic material powders and examined their magnetic properties and viscosities. Results showed that a magnetic composite material with optimal magnetic properties and injectable viscosity could be manufactured using Fe‐Si‐Al with a low volume fraction.

Circular Polarization Annular Leaky-Wave Antenna with Conical and Broadside Beams

In order to properly cover different scenarios, radiation patterns of antennas should be accordingly designed. However, most antennas are unable to provide either broadside beams or designable conical beams, which are the typically used radiation patterns for radio coverage, based on one single-structure format through adjusting parameters before fabrication. In this paper, a planar circular polarized (CP) annular leaky-wave antenna (LWA) is proposed, which is realized on an annular substrate-integrated waveguide (SIW). A broadside beam or a conical beam could be easily obtained through fabricating the LWA with different structural parameters. The operating frequency is 5.75 GHz. The LWA allows only the −1st spatial harmonic to radiate, while the fundamental wave and other spatial harmonics are suppressed in slow wave mode. In order to validate the design effectiveness, two examples for broadside beam and conical beam radiation are fabricated and measured. The measurement results show good agreement with the simulation results. The broadside beam LWA shows a gain of 9.75 dBic and the conical beam LWA with a beam angle of 13° has a gain of 7.93 dBic. The proposed LWA presents promising radiation performance and is a good candidate for wireless communication applications.

Design and analysis of concave‐core stator direct‐drive permanent magnet motor

AbstractTo solve the problems mechanically caused by parallel direct‐drive permanent magnet motors (DD‐PMSM). This paper proposes a concave‐core stator direct‐drive permanent magnet motor (CCSDD‐PMSM) structure. In this study, an auxiliary yoke structure is proposed to optimise the magnetic circuit and analyse the cogging torque to achieve the minimum detent force. Based on the unit motor and combined with the magnetomotive force to analyse the symmetry of different winding distributions, the stability characteristics of the motor are studied. The magnetic field distribution of the motor load air gap is calculated using the finite element method. The contribution of different spatial order harmonics to the motor output torque is calculated using the Maxwell tensor method. The torque calculation expression of the CCSDD‐PMSM is given. Finally, an experimental prototype is made to verify the accuracy of the analysis in this paper.

Improved Coreless Axial Flux Permanent-Magnet Machine With Nonuniformly Distributed Winding

The windings of coreless axial flux permanent-magnet machine (CAFPM) are exposed to the rotor magnetic field, where each back electromotive force (EMF) harmonic is induced not only by several different spatial field harmonics but also by the winding distribution. In order to reduce the time harmonics of back EMF for CAFPM with non-overlapping winding, one new winding structure with non-uniform distributed coils is proposed in this paper, in which the coils are arranged in a non-uniform way with annular distribution in the stator. Firstly, the relationship between uniform and non-uniform distributed windings is analyzed based on the phasor diagram of each coil EMF, and the analytical expression of back EMF under non-uniform distributed windings is established. Secondly, key performance indexes under different working states, like no-load, are investigated by three dimensional (3-D) finite element analysis (FEA). Finally, comprehensive experiments are carried out to verify related theoretical analysis, which demonstrate that the non-uniform distributed windings can effectively reduce the time harmonics and increase the working efficiency.

Properties of the multipole fields formed by round electrodes

The aim of the work is to study the properties of multipole electric fields formed by round rods. We consider the problem of finding the convergence radius of the series obtained by expansion of the potential into spatial harmonics, as well as the calculation of the complex potential for the case of the optimal configuration of cylindrical electrodes. A method is given for finding the real potential, which allows to obtain expansion of potential into power series with high precision.

An Influence of Spatial Harmonics on an Electromagnetic Torque of a Symmetrical Six-Phase Induction Machine

The analyses of the influence of spatial harmonics on the electromagnetic torque of the multi-phase induction machine and reducing this influence are important tasks to ensure the high efficiency of the induction machine. Designing the machine to consider the influence of spatial harmonics is essential to ensure the desired mechanical and energy characteristics. In the case of the sinusoidal winding supply of the induction machine, the magnetomotive force has high spatial harmonics, which are caused by the machine-winding design. The interaction between the 5th, 7th, 11th and 13th spatial harmonics of the winding function and the first time-harmonic of the winding supply causes the appearance of the 6th and 12th harmonics in the electromagnetic torque of the machine. A prototype of the symmetrical six-phase induction machine and the experimental study for the influence of spatial harmonics on the harmonic content of the stator currents in different machine modes are given in this paper. The mathematical model of the six-phase induction machine has been developed using the average voltages in integration step method. The introduction of the harmonic components into the magnetization inductance in the mathematical model of the six-phase induction machine for taking into account the spatial harmonics of the machine-winding function is proposed in this paper. The adequacy of the mathematical model was confirmed by comparing the simulation and experimental results. The harmonic content of the electromagnetic torque, which is caused by spatial harmonic influence, is analyzed.

Study of Winding Structure to Reduce Harmonic Currents in Dual Three-Phase Motor

Dual three-phase motors have the problem of a large generation of harmonic currents while driving due to small inductance for certain harmonics. The purpose of this paper is to theoretically clarify the effect of the winding structure of dual three-phase motors on harmonic currents. Analytical calculations considering the spatial harmonics of the magnetomotive force are used to formulate the inductance that depends on the winding structure and the harmonic order. The validity of the formulated theoretical expression of the inductance is confirmed by finite element analysis. In addition, drive simulations of the coil pitch 5/6 dual 3-phase motor and the coil pitch 1 dual 3-phase motor are performed, and it is found that the magnitude of the generated harmonic currents can be explained using the formulated inductance values. In conclusion, it is found that dual three-phase motors with large winding factors for fifth and seventh order spatial harmonics can reduce the harmonic currents.

Improved Mathematical Model and Modeling of Permanent Magnet Synchronous Motors Considering Saturation, Spatial Harmonics, Iron Loss and Deadtime Effect

Improved Mathematical Model and Modeling of Permanent Magnet Synchronous Motors Considering Saturation, Spatial Harmonics, Iron Loss and Deadtime Effect