Odd Harmonics Research Articles

Using degenerate parametric interaction of intense acoustic beams to amplify weak signals

The paper considers the degenerate parametric interaction of an intense acoustic pumping beam and a weak signal beam at the subharmonic. The use of a special emitter system with independent signal emission at the harmonic and subharmonic made it possible to study the features of nonlinear interaction both for different amplitude levels and arbitrary phase relations of the fields at these frequencies. Just as predicted in the theory, the experiment showed that signal amplification at the subharmonic hardly occurs at all. It is shown that the use of odd field harmonics, which are absent for a zero amplitude of the signal wave, makes it possible to substantially increase the efficiency of isolating a weak signal wave. The interaction of beams for large and small acoustic Reynolds numbers of the signal wave is studied.

Using higher order harmonics in MTF calculations

Scanning a bar pattern image along the direction perpendicular to the bars produces a periodic wave. This wave can be decomposed into a sum of harmonics by means of its Fourier series. Oversampling bar pattern images produces output waves with a high signal to noise ratio (SNR), and this high SNR allows the use of several harmonics of the wave for MTF calculations. However, increasing the order of the harmonic used for the calculation entails a loss of accuracy. In this work, some limiting factors to the use of these harmonics are investigated and their effects are quantified. Also, a criterion to discern if a given harmonic should be used is presented. Synthetic phantom images with several bar groups of different frequencies are generated through a process that simulates blurring, sampling and noise addition. Then, an output wave is obtained for each group of bars, and the MTF at the frequencies of its first odd harmonics are calculated. Five noise levels were simulated spanning an exposure range from 0.02 to 200 mR. Spatial sampling introduces errors in the estimation of the wave period resulting in underestimates of the MTF calculations. An error of 2% in the wave period produces underestimates of 0.0%, 0.4%, 1.2% and 2.4% in the MTF values obtained from the 1st, 3rd, 5th, and 7th harmonics of the output wave. Also, a bound for the aliasing error derived from spatial sampling is presented. This bound is inversely proportional to the square of the number of samples per period in the output wave. Increasing the noise level leads to increasing uncertainties in the MTF calculations, being larger at high frequencies and for high order harmonics. In all situations, the SNR of a harmonic can be used to determine the accuracy of the MTF estimation.

Hearing the transformation of conical to closed-pipe resonances

The harmonics for an open cone with slant length are the same as the harmonics for an open pipe with length . When the cone is transformed through phases of closed–open conical frusta into a cylinder of length closed at one end, the fundamental halves and only odd harmonics remain. A simple approach using boundary conditions is presented in order to understand this remarkable fact. A new free interactive HMTL5 application is provided which enables the user to hear the resonances of a complete cone transform into the pitches of a conical frustum closed at the small end, and eventually into the odd harmonics of a closed cylindrical pipe.

The shift of harmonics with different initial vibrational states in the H molecular ion

Molecular high-order harmonic generation of H and its isotopes is investigated by numerical simulations of the non-Born–Oppenheimer time-dependent Schrödinger equations. The general characteristic of the typical high-order harmonic generation (HHG) spectra for the H molecule indicates that only the odd harmonics can be generated. Here we show that how the initial vibrational states and nuclear dynamics break down this standard characteristic, i.e. a redshift or blueshift of the harmonics appears. We investigate the effect of the initial vibrational states on the redshift or blueshift of the HHG spectrum under trapezoidal laser pulses. The ionization probability and time-frequency analysis are used to illustrate the physical mechanism of the shift of the harmonics. We also show the HHG spectra from the different isotopes of H molecule with different initial vibrational states.

Comparative Measurements on Loudspeaker Distortion: Current vs. Voltage Control

Abstract Modulation and harmonic distortion produced by ordinary moving-coil direct-radiator drive units are measured under current control and voltage control. A realistic two-tone test signal is used to investigate the detrimental effect of the voice coil electromotive forces on the voltage-to-current conversion that is critical with voltage control. Dramatic improvements in distortion performance are obtained with current control. Current nonlinearities in voltage-controlled speakers are shown to be the dominant source of modulation and odd harmonic distortions at signal frequencies above the fundamental resonance region. Currents in conductive voice coil formers also seem to be significant sources of distortion; with current control and non-conductive formers, odd harmonics and related modulation products virtually vanished in the upper midrange.

Parallel structure general repetitive controller for general grid‐connected PWM converters

This study investigates parallel structure general repetitive control (PSGRC) and its error convergence rate by using exponential function properties. PSGRC offers a general repetitive control solution for power converters to mitigate power harmonics distortions. PSGRC with appropriate settings will lead to various RCs with various error convergence rates at interested harmonic frequencies, e.g. conventional RC, dual-model RC, and odd harmonics RC. As application examples, PSGRC was applied into general grid-connected pulse-width-modulation (PWM) converter systems. Experimental results show the effectiveness and advantages of PSGRC: three/single-phase grid-connected PWM converters can achieve zero-error current tracking and very fast current error convergence rate upon demand.

The warm, rich sound of valve guitar amplifiers

Practical solid state diodes and transistors have made glass valve technology nearly obsolete. Nevertheless, valves survive largely because electric guitar players much prefer the sound of valve amplifiers to the sound of transistor amplifiers. This paper discusses the introductory-level physics behind that preference. Overdriving an amplifier adds harmonics to an input sound. While a moderately overdriven valve amplifier produces strong even harmonics that enhance a sound, an overdriven transistor amplifier creates strong odd harmonics that can cause dissonance. The functioning of a triode valve explains its creation of even and odd harmonics. Music production software enables the examination of both the wave shape and the harmonic content of amplified sounds.

High harmonic generation in ZnO with a high-power mid-IR OPA

We generate high-order harmonics in a-cut (11–20) ZnO at a high repetition rate of 50 kHz, using the tunable mid-infrared pulses (3–4 μm wavelength) from a high-power optical parametric amplifier. For driving laser pulses with 3.8 μm central wavelength, we observe nonperturbative harmonic spectra that well exceed the material band gap. The harmonic spectra depend strongly on the orientation of the crystal with respect to the laser polarization, with odd harmonics exhibiting periodicities of π/2 for a polarization within the (11–20) crystal plane. Energy conversion efficiencies of ∼10−6 per harmonic are measured for the 9th–13th harmonics, yielding an average power of more than 0.2 μW for the 13th harmonic.

Odd Harmonics in Exoplanet Photometry: Weather or Artifact?

Photometry of short-period planetary systems allows astronomers to monitor exoplanets, their host stars, and their mutual interactions. In addition to the transits of a planet in front of its star and the eclipses of the planet by its star, researchers have reported flux variations at the orbital frequency and its harmonics: planetary reflection and/or emission and Doppler beaming of starlight produce one peak per orbit, while ellipsoidal variations of a tidally distorted star and/or planet produce two maxima per orbit. Researchers have also reported significant photometric variability at three times the orbital frequency, sometimes much greater than the predictions of tidal theory. The reflected phase variations of a homogeneous planet contains power at even orbital harmonics-important for studies of ellipsoidal variations-but cannot contain odd orbital harmonics. We show that odd harmonics can, however, be produced by an edge-on planet with a time-variable map, or an inclined planet with a North-South (N-S) asymmetric map. Either of these scenarios entail weather: short-period planets are expected to have zero obliquity and hence N-S symmetric stellar forcing. North-South asymmetry in a giant planet would therefore suggest stochastic localized features, such as weather. However, we find that previous claims of large-amplitude odd modes in Kepler photometry are artifacts of removing planetary transits rather than modeling them. The only reliable claims of odd harmonics remain HAT-P-7b and Kepler-13Ab, for which the third mode amplitude is 6-8% of the planetary flux. Although time-variable albedo maps could in principle explain these odd harmonics, upper-limits on the infrared variability of hot Jupiters make this hypothesis unlikely. We urge theorists to study the effects of close-in planets on stellar atmospheres, as this remains the only plausible hypothesis.

Internuclear distance R-distribution of high-order harmonic generation from H2+ and its isotopes

Internuclear distance (R) distribution of high-order harmonic generation from H2+ and its isotopes have been theoretically investigated. We found that in the presence of the few-cycle pulse, the harmonics mainly produce from R=2.0a.u. to R=4.5a.u. and the odd harmonics can be found in the harmonic spectra. With the increase of the pulse duration, the harmonics can be generated from R=2.0a.u. to the larger internuclear distance (e.g. R=15.0a.u.) and the even/odd harmonics can be obtained in the below/above-threshold harmonic regions. Moreover, the intensities of the harmonics can be enhanced in the presence of the multi-cycle pulse, but the intensities of the below-threshold harmonics can be reduced with the increase of the nuclear mass (e.g. D or T). The time-dependent nuclear motions, the ionization probabilities, the time-frequency analyses of the harmonic spectra and the R-dependent time-dependent wave functions have been shown to explain the R-distribution of the harmonic spectra from H2+ and its isotopes.

Nonlinear properties of multiphase high-temperature superconductors of the Bi–Sr–Ca–Cu–O system in the temperature range of the superconducting transition

The nonlinear characteristics of high-temperature superconductors of the Bi–Sr–Ca–Cu–O system have been experimentally investigated in the temperature range of the superconducting transition under the influence of a harmonic alternating magnetic field. The effect of the generation of odd harmonics in the signal of response to a harmonic alternating magnetic field for multiphase high-temperature superconductors containing regions with different values of the critical temperature in their bulk has been observed for the first time. The mechanism of harmonic generation in a superconductor in the resistive state, which is associated with the switch effect, i.e., with the redistribution of eddy current density between the local regions of the superconductor, has been considered.

Light bullets formation accompanied by odd harmonics generation under Mid-IR femtosecond filamentation in LiF

The formation of light bullets in mid-IR femtosecond filamentation is investigated numerically by means of the unidirectional pulse propagation equation (UPPE). A general approach for light bullets formation is presented for condensed media under anomalous GVD. The main parameters of the light bullets are evaluated. The features of super continuum and odd harmonic generation accompanying the light bullets formation are analyzed.

Scattering to Higher Harmonics for Quarter-Wave and Helmholtz Resonators

The nonlinear response of acoustic resonators is investigated over a broad range of frequencies and amplitudes. Helmholtz resonators with a symmetric neck and an asymmetric neck, respectively, as well as quarter-wave resonators are considered. Describing functions for impedance and the reflection coefficient of a Helmholtz resonator at various sound pressure levels are determined from compressible flow simulation and validated against experimental data. The particular focus of the present study is the nonlinear scattering to higher harmonics. For the Helmholtz resonator with a symmetric neck, a distinct pattern in the amplitudes of the higher harmonics is observed, where the odd harmonics dominate the response, whereas the even harmonics are almost negligible. Such an “odd-harmonics-only” pattern, which was observed previously in an experiment at the orifices, is explained by a quasi-steady analysis based on the Bernoulli equation, assuming a symmetric flow pattern at the neck. For the Helmholtz resonator with an asymmetric neck, it is observed in computational fluid dynamics simulations that even harmonics contribute noticeably to the resonator response, such that the odd-harmonics-only pattern is less pronounced. For the markedly asymmetric geometry of the quarter-wave resonator, the second harmonic is dominant and the odd-harmonics-only pattern vanishes completely. The quasi-steady analysis is extended successfully to also describe nonlinear scattering to higher harmonics for asymmetric configurations and flow patterns. Overall, the scattering to higher harmonics remains on a moderate level, even at very high excitation levels for the Helmholtz resonator configurations. For the quarter-wave resonator, the scattering is more pronounced and contributes perceptibly to the response at high excitation amplitudes.

Application of Monte Carlo simulation for estimation of uncertainty of four-point roundness measurements of rolls

Large-scale rotors in the paper and steel industry are called rolls. Rolls are reground at regular intervals and roundness measurements are made throughout the machining process. Measurement systems for roundness and diameter variation of large rolls (diameter <2000mm) are available on the market, and generally use two to four sensors and a roundness measurement algorithm. These methods are intended to separate roundness of the rotor from its movement. The hybrid four-point method has improved accuracy, even for harmonic component amplitudes. For reliable measurement results, every measurement should be traceable with an estimation of measurement uncertainty. In this paper, the Monte-Carlo method is used for uncertainty evaluation of the harmonic components of the measured roundness profile under typical industrial conditions. According to the evaluation, the standard uncertainties for the harmonic amplitudes with the hybrid method are below 0.5μm for the even harmonics and from 1.5μm to 2.5μm for the odd harmonics, when the standard uncertainty for the four probes is 0.3μm each. The standard uncertainty for roundness deviation is 3.3μm.

Extending Geobandwidth using the Multipulse Configuration

Measurement bandwidth is an important feature of a geophysical system. Bandwidth allows detection of very resistive features (such as some kimberlites) and very conductive targets (like massive sulphides). In electromagnetic systems, bandwidth is not simply the sample rate of the data acquisition system or the earliest time channel, but also depends on transmitter spectrum, distance to target and processing. Optimising a system to detect a feature or measure a specific signal requires design considerations and trade-offs for different targets. The choice of excitation waveform in electromagnetic systems is one such trade-off. A square-pulse allows high-frequency energy to be excited, but, because of electronic limitations, has only limited dipole moment. A half-sine waveform efficiently generates energy at the base frequency and first few odd harmonics (low-frequency energy) and less high-frequency energy. Here, we describe the Multipulse configuration, an option on the Helitem system which employs both a half-sine and a trapezoid waveform to efficiently generate high- and low-frequency energy. Using survey data, we show the resolution power of the combined system compared to a single waveform. The combined data is better able to resolve near-surface features and deep structure than data from either waveform alone.

Discrete-Time Domain Modeling of Voltage Source Inverters in Standalone Applications: Enhancement of Regulators Performance by Means of Smith Predictor

The decoupling of the capacitor voltage and inductor current has been shown to improve significantly the dynamic performance of voltage source inverters in standalone applications. However, the computation and pulse width modulation delays still limit the achievable bandwidth. In this paper, a discrete-time domain modeling of an LC plant with consideration of delay and sample-and-hold effects on the state feedback cross-coupling decoupling is derived. From this plant formulation, current controllers with wide bandwidth and good relative stability properties are developed. Two controllers based on lead compensation and Smith predictor design, respectively, are obtained. Subsequently, the voltage regulator is also designed for a wide bandwidth, which permits the inclusion of resonant filters for the steady-state mitigation of odd harmonics at nonlinear unbalance load terminals. Discrete-time domain implementation issues of an antiwind up scheme are discussed as well, highlighting the limitations of some discretization methods. Extensive experimental results, including a short-circuit test, verify the theoretical analysis.

High-harmonic generation from an atomically thin semiconductor

Observations of high-harmonic generation from a single layer of a transition metal dichalcogenide opens the door to studying strong-field and attosecond phenomena in two-dimensional materials. High-harmonic generation (HHG) in bulk solids permits the exploration of materials in a new regime of strong fields and attosecond timescales1,2,3,4,5,6. The generation process has been discussed in the context of strongly driven electron dynamics in single-particle bands7,8,9,10,11,12,13,14. Two-dimensional materials exhibit distinctive electronic properties compared to the bulk that could significantly modify the HHG process15,16, including different symmetries17,18,19, access to individual valleys20,21 and enhanced many-body interactions22,23,24,25. Here we demonstrate non-perturbative HHG from a monolayer MoS2 crystal, with even and odd harmonics extending to the 13th order. The even orders are predominantly polarized perpendicular to the pump and are compatible with the anomalous transverse intraband current arising from the material’s Berry curvature, while the weak parallel component suggests the importance of interband transitions. The odd harmonics exhibit a significant enhancement in efficiency per layer compared to the bulk, which is attributed to correlation effects. The combination of strong many-body Coulomb interactions and widely tunable electronic properties in two-dimensional materials offers a new platform for attosecond physics.

Condition assessment of outdoor porcelain insulator based on dielectric dissipation factor evaluated from non‐linear equivalent circuit

This study presents a novel technique for estimation of contamination level as well as flashover voltage of outdoor insulators based on dielectric dissipation factor evaluated from the applied sinusoidal excitation and corresponding surface leakage current. Existing literature shows that surface leakage current of insulator is infested with odd harmonics though the applied voltage is sinusoidal in nature. The presence of harmonic contents in leakage current is due to non-linear characteristics of the insulator surface owing to formation of dry bands. The nonlinear characteristic of the insulator surface depends on its contamination level which in turn affects the corresponding flashover voltage. Therefore, the harmonic configuration in leakage current can be correlated with the contamination level on insulator surface and corresponding flashover voltage. Considering the fact, in this contribution, a non-linear equivalent circuit of insulator has been proposed based on harmonic components of the leakage current. For each harmonic component of the leakage current flowing through the insulator system, energy lost and energy stored in the system is calculated, which eventually enables to calculate dielectric dissipation factor. The proposed technique is applied for experimental investigation on 11 kV disc porcelain insulator artificially contaminated in the laboratory under controlled environmental conditions.

Nonlinear Behavior Analysis of GaAs PHEMT Transconductance to Design Active Frequency Multipliers

This paper discusses the nonlinear behavior of the transconductance of a GaAs PHEMT device and its dependence with the harmonic generation. The analytic study and simulations show that when the gate bias is close to the pinch-off voltage, the transconductance is zero and the extracting of the even harmonics occurs, besides, when this bias is around 0 V, the transconductance is maximized and the odd harmonics are generated. As an example to validate this dependence, a frequency quadrupler based on 0.15 μm PHEMT from UMS foundry using ADS software from Agilent is presented in this work.

Analysis of Three-Phase Transformer Response due to GIC Using an Advanced Duality-Based Model

In this paper, the behavior of three-phase transformers in the presence of geomagnetically induced current (GIC) is investigated. The associated phenomena involve very slow transients, in the millihertz range, while representing significant magnitudes of even and odd harmonics of power frequency. As a result, the transformer response involves nonlinear and frequency-dependent effects. This paper considers the impact of variations in the transformer core construction and design parameters on its saturated behavior and the resulting reactive power absorption, when subjected to GIC. A detailed transformer model is described including air-gap and tank effects. The study results highlight significant parameters that can affect transformer reactive power and promote them as being important parameters for GIC studies. Furthermore, the transformer dynamics during the slow transient of the GIC variations and polarity reversal are discussed.