Odd Harmonics Research Articles

A Class E/Fodd Power Oscillator Incorporating a Distributed Active Transformer

A power combined high-efficiency oscillator is proposed using a hybrid class E and class F tuning, where the odd harmonics are shorted: the class E/Fodd. The oscillator is achieved by adding a high-pass feedback network to a class E/Fodd amplifier, where the output’s odd harmonics are used to construct the required square-like wave at the input. Furthermore, two class E/Fodd oscillators can be power combined using a distributed active transformer, where magnetic coupling to the high-pass feedback network can be realized using a third transformer winding. Two power combined class E/Fodd oscillators designed using this method have an oscillation frequency of 10.1 MHz, a total output power of 324 W and dc-to-RF conversion efficiency of 75%.

Enhanced Odd-Harmonic Repetitive Control of Nanopositioning Stages Using Spectrum-Selection Filtering Scheme for High-Speed Raster Scanning

Odd-harmonic repetitive control (ORC) has been successfully applied to improve the triangular trajectory tracking performance of nanopositioners. However, the conventional ORC tends to amplify the tracking errors at frequencies other than the odd-harmonic components, mainly the even harmonics of the fundamentals of the intended triangular trajectory to be tracked. Due to the influence from the hysteresis nonlinearity of the piezoelectric actuator, this would result in significant tracking errors. To overcome this limitation, this article proposes an enhanced odd-harmonic repetitive control (EORC) using the spectrum-selection filtering scheme to improve the loop-shaping property of the ORC. This effectively eliminates the problem of amplifying the tracking errors while preserving the advantages of the conventional ORC, such as fast convergence speed and low computation cost. The EORC is combined with a proportional–integral tracking controller to improve the tracking performance. The controller design, stability analysis, and performance evaluation are presented. The experimental results demonstrating the effectiveness of the proposed EORC-based control scheme are presented showing the excellent tracking of triangular trajectories with fundamental frequencies up to 1000 Hz. Moreover, a reduction in rms tracking errors by up to 52% is achieved. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The high-speed atomic force microscopy (AFM) plays an increasingly vital role in observing and manipulating objects at the nanoscale. In the raster scanning of AFMs, the most challenging issue is the triangular trajectory tracking of nanopositioning stages with high precision. Although the odd-harmonic repetitive control (ORC) has been successfully applied to improve the tracking performance, the conventional ORC would amplify the tracking errors distributed at the frequencies other than the odd harmonics, especially those at the even harmonics, resulting from the inherent complicated hysteresis nonlinearity. This problem of amplifying the tracking errors would lead to larger tracking errors, deteriorating the performance of AFM imaging. To address this issue, this article proposes an enhanced ORC using the spectrum-selection filtering scheme to improve the loop-shaping property of the ORC, so as to eliminate the problem of amplifying the tracking errors while preserving the advantages of the conventional ORC, such as fast convergence speed and low computation cost. The experimental results show that, with this simple modification, the positioning errors are reduced greatly, all-the-while preserving the benefits of the conventional ORC scheme– fast convergence speed and low computation cost. In terms of tracking accuracy and the simple structure, this development can be easily implemented to other systems that challenge from the tracking accuracy under ORC scheme.

Jupiter's Interior as Revealed by Juno

Jupiter is in the class of planets that we call gas giants, not because they consist of gas but because they were primarily made from hydrogen-helium gas, which upon gravitational compression becomes a metallic fluid. Juno, in orbit about Jupiter since 2016, has changed our view: The gravity data are much improved, and the simplest interpretation of the higher order even harmonics implies that the planet may have a diluted central concentration of heavy elements. Jupiter has strong winds extending to perhaps ∼3,000-km depth that are evident in the odd zonal harmonics of the gravity field. Jupiter's distinctive magnetic field displays some limited local structure, most notably the Great Blue Spot (a region of downward flux near the equator), and some evidence for secular variation, possibly arising from the winds. However, Juno is ongoing; it has not answered all questions and has posed new ones. ▪ Juno's mission reveals Jupiter's interior. ▪ A core exists but is diluted by hydrogen. ▪ The mission revealed wind depth and magnetic field.

Multi-section branch-line crossover/coupler optimization for wideband applications and higher-order harmonics suppression

In this paper, we propose an optimization-driven framework for the design of wideband multi-section branch-lines that exhibit varying branch impedances. Even-odd mode analysis is performed utilizing transmission lines theory to derive the expressions of the S-parameters. Then, an error function is developed to control the electrical characteristics of the branch-lines considering predefined physical constraints including impedance matching and machining tolerance. By modifying the error function, cascaded branch-lines can operate as crossovers or couplers. To validate the proposed concept, wideband crossover and coupler prototypes are designed, simulated and measured. Simulations and measurements agree well and show improved fractional bandwidths. Moreover, odd harmonics are suppressed in the proposed designs due to enforcing the desired electrical characteristics over a given frequency band.

Determination of the corrosion resistance of low alloyed steels by magnetic method

An innovative method of measuring and control of the steel corrosion rate by changing magnetic characteristics is developed. The impact of heat treatment on the corrosion rate of the samples of high-carbon steels (maximum corrosion loss is observed at a tempering temperature of 400°C) is attributed to the appearance of micro-galvanic pairs (MGP) between the phase components of the material. MGP undergo redistribution under heat treatment thus changing conditions of the galvanic current flow. The structural phase composition, in turn, determines the magnetic properties of steel and correlation between the magnetic properties and corrosiveness. The goal of the study is demonstration of the possibility and expediency of using the magnetic parameters of steel for determination of the steel corrosion rate. A close correlation dependence is observed between the coercive force and the electrochemical potential (relative to the silver chloride electrode) which are direct indicators of the corrosiveness. Case study of a pipeline made of 09G2S steel along which change in the coercive force attained 25% revealed rather high risk of developing micro-galvanic pairs. A rapid method of scanning magnetic parameters is proposed to detect potentially corrosive zones. A multi-parameter approach can be used to solve the problem of the ambiguity of the relationship between the corrosiveness and magnetic parameters. Harmonic decomposition of magnetic hysteresis loops of 45Kh steel samples is used to obtain a number of odd harmonics. Some of them weakly correlate with the corrosion loss, whereas complexes of several harmonics correlate to a greater extent. The results can be used in technical diagnostics and prediction of the corrosion activity of steel structures before their operation. The results can be used in technical diagnostics and forecasting of the corrosiveness of steel structures prior to their operation.

Impact of Statistical Fluctuations on High Harmonic Generation in Liquids.

High harmonic generation (HHG) from gases and solids has been studied extensively. Whereas for liquids, it is far more challenging to understand the ultrafast dynamics with conventional methods. From a statistical perspective, we investigate the liquid-phase HHG theoretically by using a disordered linear chain. Our results reveal that (i)the harmonic spectra are characterized by a transition energy that separates the spectra into a low-energy region containing only odd harmonics and a high-energy region containing both even and odd harmonics with low yields; (ii)the transition energy depends on the fluctuation of structure and the field strength, but independent of the laser wavelength; (iii)the occurrence of dephasing is a natural result of the electron dynamics modulated by the long-range disorder. Furthermore, a simple formula is proposed to identify the transition energy, from which we correctly reproduce the experimental cutoff energies of HHG from liquid ethanol. Our results pave the way to better understand and control the HHG in liquids as another compact HHG source.

Computation-Efficient Position Estimation Algorithm for Permanent Magnet Synchronous Motor Drives Under Distorted Conditions

This article proposes a computationally efficient position-sensorless control scheme for medium- and high-speed permanent magnet synchronous motor (PMSM) drives under distorted conditions. An adaptive comb observer (ACO) is designed for accurate position estimation by eliminating primary distortions simultaneously, including dc offsets from current measurement, odd harmonics caused by inverter nonlinearity, and even harmonics due to the modulation. A frequency-locked loop based on the Lyapunov stability theory is embedded in the ACO to ensure the observer’s stability and fast convergence of the estimated variables. Compared with conventional adaptive position observers that usually require high-order filtering networks, the proposed scheme only consists of four delay operators and does not require complicated discretization. Therefore, it can simplify digital implementation and reduce the computational burden of the sensorless algorithm. To validate the effectiveness of the proposed observer, comparative experiment tests of the proposed ACO and conventional methods are performed on a 15-kW PMSM setup.

Ellipticity control of high-order harmonic generation with nearly orthogonal two-color laser fields

Elliptically polarized high-order harmonics opens a path toward the study of ultrafast dynamics in circular dichroism of magnetic materials, chiral molecules, and electronic spin motion. Recently, efficient high-order harmonic generation with controllable ellipticity has attracted considerable attention in experiment and theory. Here, we experimentally demonstrate a scenario using cross-linearly-polarized two-color fields consisting of a fundamental field and its second harmonic (SH). Through adjusting the relative phase, crossing angle, and intensity ratio of the cross-linearly-polarized two-color field, we obtain ellipticity-tunable high-order harmonics, with ellipticity up to $\ensuremath{\varepsilon}=0.73$. Meanwhile, the elliptically polarized high-order harmonics preserve high efficiency. Furthermore, when the intensity of the SH field is stronger than that of the fundamental field, the even order harmonics will become several times stronger than the odd order harmonics with opposite helicity.

A Broadband Millimeter-Wave Continuous-Mode Class-F Power Amplifier Based on the Deembedded Transistor Model

In this letter, a broadband millimeter-wave (mm-wave) continuous-mode Class-F power amplifier (PA) based on the deembedded transistor model is proposed for the fifth-generation (5G) applications. To design the output matching network at the intrinsic current-generator plane, an $S$ -parameter fitting method is proposed to extract the parasitic parameters of nonpackaged transistors over a wide frequency range. The PA is implemented in the 0.13- $\mu \text{m}$ SiGe BiCMOS process, which occupies only 0.42 mm2. By controlling the even and odd harmonics impedance, the PA achieves a 78.2% −3-dB small-signal gain fractional bandwidth from 21.1 to 48.2 GHz. The −1-dB $P_{\mathrm {sat}}$ bandwidth covers 21–43 GHz (68.8% fractional bandwidth) and the saturated output powers are 17.2–18.1 dBm. Meanwhile, the designed PA provides a 24.1%–32.1% peak power-added efficiency (PAE) over the band.

High-harmonic generation at particle–hole multiphoton excitation in gapped bilayer graphene

A microscopic nonlinear quantum theory of the interaction of coherent electromagnetic radiation with gapped bilayer graphene is developed. The Liouville-von Neumann equation for the density matrix is solved numerically at the multiphoton excitation regime. The developed theory of interaction of charged carriers with the strong driving wave field is valid near the Dirac points of the Brillouin zone. We consider the harmonic generation process in the nonadiabatic regime of interaction when the Keldysh parameter is of the order of unity. On the basis of numerical solutions, we examine the rates of odd and even high harmonics at the particle–hole annihilation in the field of a strong pump wave of arbitrary polarization. The obtained results show that the gapped bilayer graphene can serve as an effective medium for the generation of even and odd high harmonics in the terahertz and far-infrared domains of frequencies.

Control Design and Experimental Validation of a HB-NPC as a Shunt Active Power Filter

This work presents the design of a control law based on the average model of a shunt active power filter considering an H-bridge neutral point clamped topology and its experimental validation. Therefore, the proposed controller is formed by three control loops, namely current (inner), regulation (outer), and balance control loops. The current loop aims to compensate both the displacement power factor and the harmonic distortion produced by nonlinear loads connected to the point of common coupling. To deal with harmonic current distortion, the current loop involves an adaptive mechanism based on a bank of resonant filters tuned at odd harmonics of the fundamental grid frequency. The regulation and balance loops are aimed to maintain the voltage of the capacitors forming the DC-link at a desired constant level. For this, proportional-integral controllers are designed. The design of all three loops considers the average model of the system. The performance of the proposed multi-loop control law is evaluated through numerical results and real-time experimental implementation, both considering a 2 kW academic benchmark with a constant switching frequency of 7 kHz. In order to provide harmonic distortion, a nonlinear load based on an uncontrolled diode bridge rectifier is considered. Additionally, step-load changes from 0.5 kW to 1 kW are considered for the nonlinear load. As a result, a suitable current tracking, voltage regulation, and balance are observed despite parametric uncertainties, load variations, and harmonic distortion. As a consequence, in steady state, simulation results indicate that the compensated grid current THD is 1.75%; meanwhile, the nonlinear load current THD is 52.5%. Experimental results indicate that the compensated grid current THD is 2.32%; meanwhile, the nonlinear load current THD is 53.8%.

Differential configuration of 180° anti-phase-modulated nonlinear magnetoelectric effect of parallel-placed dual FeNiMoSiB/Pb(Zr1−xTix)O3 composites for magnetic field sensing

Magnetic sensors based on nonlinear magnetoelectric (ME) effect can be used to measure weak dc and ac magnetic fields at room temperature. The focus of this paper is to present the nonlinear ME effect of parallel-placed dual FeNiMoSiB/PZT/FeNiMoSiB composites with small size which are operated in 180° anti-phase modulated mode and differential output configuration. In this design, the strong ME voltage at even order harmonics due to frequency doubling effect of magnetostriction is greatly attenuated. This is of great benefit to the design of the sensor signal conditioning circuit because strong even order harmonics limit the magnification of the first stage amplifier. Due to the nonlinear ME effect, the induced ME voltage of the odd order harmonics is modulated by a weak dc/ac magnetic field to be measured. The wideband frequency of weak magnetic field from dc-0.9f (f is the frequency of the driving field) can be recovered from the 1 st harmonic response by the lock-in demodulation method. The sensitivity and limit of detection of the anti-phase modulated differential ME dual-unit are 176.1 μV/μT and 2 nT/√Hz at 10 Hz, respectively.

Simulation of source current harmonic elimination technique using phase shifting transformer

This paper presents design of phase shifting transformer to reduce source current harmonic generated by using of variable speed drive (VSD) in textile industry. Nine VSDs are used in a stenter machine of a selected textile industry. Each of these VSD generates source current total harmonic distortion (THD) in range of 43.91% to 50.34%, which contains all odd order harmonics except the triplen ones. The first method to reduce this source current harmonic is by using arrangement of three phase shifting transformers, which requires one Yy three-phase winding connection to produce 0° phase shifting, one Yz(+) three-phase winding connection to produce 20° phase shifting and one Yz(-) three-phase winding connection to produce –20° phase shifting. The second method is by using arrangement of nine phase shifting transformers, which requires one Yy three-phase winding connection with 0° phase shifting, four Yz(+) three-phase winding connections with 6.67°, 13.34°, 20° and 26.67° phase shifting respectively and four Yz(-) three-phase winding connections with –6.67°, –13.34°, –20° and –26.67° phase shifting respectively. Simulation results using MATLAB SIMULINK show that source current THD successfully reduced to 1.99% and 1.74% respectively when arrangements of three phase shifting transformers and nine phase shifting transformers are used.

Multiharmonic Toroidal Standing Alfvén Waves in the Midnight Sector Observed During a Geomagnetically Quiet Period

AbstractExcitation of toroidal mode standing Alfvén waves in the midnight sector of the inner magnetosphere in association with substorms is well documented, but studies are sparse on dayside sources for the waves. This paper reports observation of midnight toroidal waves by the Van Allen Probe B spacecraft during a geomagnetically quiet period on 12–13 May 2013. The spacecraft detected toroidal waves excited at odd harmonics below 30 mHz as it moved within the plasmasphere from 2100 magnetic local time to 0030 magnetic local time through midnight in the dipole range 4.2–6.1. The frequencies and the relationship between the electric and magnetic field components of the waves are consistent with theoretical toroidal waves for a reflecting ionosphere. At the time of the nightside toroidal waves, compressional waves were observed by geostationary satellites located on the dayside, and the amplitudes of both types of waves varied with the cone angle of the interplanetary magnetic field. The nightside toroidal waves were likely driven by fast mode waves that resulted from transmission of upstream ultralow frequency waves into the magnetosphere. Ground magnetometers located near the footprint of the spacecraft did not detect toroidal waves.

Integrated Battery Charger for EV by Using Three-Phase Induction Motor Stator Windings as Filter

This article presents an on-board charger for the electric vehicles (EVs) by integrating the drive-train components into the charging process. The stator windings of three-phase induction motor (IM) can be used as a grid interfacing inductor with the constraint that the rotor should be in the stationary position during the charging mode. This article proposes the stator winding configurations of three-phase IM split into two equal parts at zero electrical degree for the on-board integrated battery charger. The effective filtering with these two three-phase windings combination, either in series or parallel while the rotor is in a stationary position, is analyzed. The equivalent inductance provided by the stator windings for filtering is increased by generating the pulsating magnetic field (PMF) in the motor. However, it results in the unbalanced impedances in filter causing odd harmonics in the grid current. This is resolved by using a modified double synchronous reference frame control algorithm, which maintains the balanced current operation with the unity power factor at the grid interface during the charging mode. This configuration is obtained by using the existing three-phase-based drive-train components, thereby providing the saving in space and reducing the weight of EV. Experimental results for the proposed winding configurations are presented with filter losses and system efficiency.

Geomagnetically Induced Currents and Harmonic Distortion: Storm‐Time Observations From New Zealand

AbstractLarge geomagnetic storms are a known space weather hazard to power transmission networks due to the effects of geomagnetically induced currents (GICs). However, research in this area has been hampered by a lack of GIC observations. Previous studies have noted that New Zealand is unusually fortunate in having a comparatively dense, high quality, set of GIC measurements, spanning &gt;60 transformers in &gt;20 substations. However, due to operational reasons these observations are clustered in the mid and lower South Island. In this paper we analyze space weather‐induced GIC impact patterns over the entire country by using a different set of sensors that monitor levels of harmonic distortion, with even and odd harmonics measured separately. GICs lead to half cycle transformer saturation and is one of the few ways in which even harmonics are produced in a well‐run power transmission network. We make use of harmonic distortion measurements at 377 circuit breakers made at 126 separate locations. Focusing on the intense geomagnetic storm activity during 6–9 September 2017, we show how the even harmonic distortion observations provide a useful new picture of GIC‐stressed transformers. These observations demonstrate how GIC effects can be monitored by using even harmonic distortion in locations where no GIC measurements are present (e.g., the most of the North Island). We understand that harmonic distortion measurements are fairly common in electrical networks and could provide a new tool for space weather researchers.

Performance comparison of series and parallel damped LCL filters using 5-level voltage source converter

The high harmonic content produced by conventional converters has resulted in the increased system size and cost, due to the need for large-sized low-order harmonic passive filters and cooling system requirement. Given that, multilevel inverters and special modulation techniques were developed to suppress or eliminate the low-frequency harmonics and the left behind high-order ones are eliminated using a high-frequency small-sized filter. Hence, this paper designs and compares the total harmonic distortion (THD) and efficiency values of three set of filters, namely LCL filter, LCL with series and parallel resistance on a novel five-level multilevel voltage source inverter topology. The novelty lies with the proposed inverter, which, apart from using a single direct current source, it can extend it elimination capability beyond the normal five level using the concept of multiple switching per step and an optimised selective harmonic elimination pulse width modulation. The converter can eliminate eleven lower-order odd nontriplen harmonics, hence making the 37th harmonic at 1.85 kHz to be the first dominant harmonic. At 2-kW loading, two of the filters have THD below 5%, therefore satisfying the IEEE 519 standard. The parallel resistance damped filter (LCL-P-R) has less THD value but poor efficiency due to the resistance introduced into the circuit. The study was carried out using PSIM and MATLAB software.

Design of multi-band miniaturized Bagley power dividers based on non-uniform coplanar waveguide

Power dividers, in general, suffer from higher order harmonics and large occupational area, especially at low frequencies. To overcome these drawbacks, we introduce the design of a three-way Bagley power divider (BPD) using non-uniform coplanar waveguide (CPW). The compact configuration is achieved by replacing the conventional CPW with its equivalent non-uniform counterpart. An optimization process incorporating a truncated Fourier series is used to design the optimum non-uniform CPW profiles. Odd harmonics are suppressed by enforcing the divider to operate only at the design frequencies based on a predefined error function. The proposed structure is compact and easy to fabricate. To validate the design approach, different 3-way BPDs (i.e., single-, dual-, and triple-band) are designed and simulated; whereas a single-band prototype is fabricated and tested. Measured results show excellent input port matching and an insertion loss around −5 dB at the design frequency.

Finer Granularity DFT Bins With Moving Window for Capacitance Sensing

In this article, the moving window discrete Fourier transform (MWDFT) with finer granularity bin indices is proposed for frequency estimation of periodic signals. The MWDFT structure is a cascade connection of comb filter and a complex resonator. The sign of comb filter is toggled between positive and negative using a multiplexer to select the integer and fractional bin indices. The sign of comb filter is chosen as negative for setting-up integer bin indices with certain resonator angle. The positive sign of comb filter rotates the zeros of the MWDFT to a specified angle in the anticlockwise direction in the z -plane. By selecting the positive feed forward coefficient, all odd harmonics of one-half of the fundamental frequency can be extracted from the MWDFT. This unique property of MWDFT with finer granularity bin indices is exploited to extract frequencies of finer resolution. A frequency locked loop is designed with MWDFT of finer granularity bins to estimate the frequency change of finer resolution. The proposed method is implemented on field programmable gate array (FPGA) as a capacitance measurement system. The method is able to provide better accuracy, wider frequency estimation range, and wider capacitance measurement range.

High Performance Single-Phase Single-Stage Grid-Tied PV Current Source Inverter Using Cascaded Harmonic Compensators

In this paper, a single-phase single-stage photovoltaic (PV) grid-tied system is investigated. The conventional pulse width modulated (PWM) voltage source inverter (VSI) is replaced by a PWM current source inverter (CSI) for its voltage boosting capabilities, inherent short-circuit proof and higher reliability features. Modeling, design, and analysis of the considered CSI are presented altogether with enhanced proposed control loops aided with a modified PWM technique. DC-link even current harmonics are commonly reflected as low-order odd harmonics in the grid resulting in a poor quality grid current. In order to overcome the latter, a high performance proportional resonant controller, applied in the inverter inner grid current loop, is proposed using cascaded resonant control units tuned at low-order frequencies to eliminate injected grid current harmonics. Hence, with a less-bulky smoothing inductor at the CSI DC-side, grid power quality and system efficiency are simultaneously improved. Simulation and experimental results verify the proposed controller effectiveness.