Showing papers on "Harmonics published in 1978"

Relationship between Benjamin–Feir instability and recurrence in the nonlinear Schrödinger equation

Abstract: A simple relationship between the Benjamin–Feir instability associated with uniform solutions of the nonlinear Schrodinger equation and the long time evolution of the unstable solution is reported. The number of modes which actively participate in the energy sharing process associated with the instability is governed by the number of harmonics of the initial disturbance which lie within the unstable region as predicted by the Benjamin–Feir analysis. Generalization of this observation implies that equations which possess high wavenumber cutoffs in the instability characteristics should not thermalize in the conventional sense when undergoing such an instability, since active modes are confined to a finite range of wavenumbers.

Theory of electron cyclotron maser interaction in a cavity at the harmonic frequencies

Abstract: A theory of the cyclotron maser interaction between an annular electron beam and the standing electromagnetic wave in a cavity structure is formulated on the basis of the relativistic Vlasov equation and the Maxwell equations. Detailed analytical expressions for the beam‐wave coupling coefficient, beam energy gain, and threshold beam power have been derived for the fundamental and higher cyclotron harmonics. Physical interpretations of these results and comparison with cyclotron maser interactions in a waveguide structure are presented. Methods of parameter optimization and their applications to experiments are illustrated through numerical examples.

Low-frequency harmonic acceleration as a test of labyrinthine function: basic methods and illustrative cases.

Abstract: : The present studies were predicated on research results employing the rhesus monkey as a model for responses to low-frequency harmonic (sinusoidal) acceleration. Data from these previous efforts showed that measures of the phase relationships between the input stimulus and the resulting eye movement output were highly repeatable and not influenced by changes in arousal level. It was also found that the sudden loss of a labyrinth (in this case by surgical destruction) could be detected by low-frequency harmonic acceleration and that the animals could not compensate for this loss, especially at the lower frequencies of stimulation.

Real-time harmonic pitch detector

Abstract: A real-time harmonic pitch detection algorithm has been developed on the Lincoln Digital Voice Terminal (LDVT). The algorithm was designed to be fast and to perform well when the input speech is degraded (i.e., telephone quality) or corrupted with acoustically coupled noise. The algorithm determines the fundamental frequency from the spacing between harmonics in a selected portion of the spectrum. The algorithm was incorporated into a real-time linear prediction vocoder and compared favorably in informal listening tests with the Gold-Rabiner time-domain detector under a variety of adverse conditions.

Spread F bubbles: Nonlinear Rayleigh-Taylor mode in two dimensions

Abstract: The paper discusses long-wavelength developed bottomside spread F which has been attributed to the Rayleigh-Taylor instability. The nonlinear saturation amplitude and the k spectrum of the inertia-dominated Rayleigh-Taylor instability is found in two directions: east-west and vertical. As in the collisional case (Chaturvedi and Ossakow, 1977), the dominant nonlinearity is found to be two-dimensional. It is found that the linearly most unstable modes, which are primarily horizontal, saturate by the nonlinear generation of vertical spatial harmonics. The harmonics are damped by diffusion or recombination. The resulting amplitude spectrum indicates that bubbles are vertically elongated in both inertial and collisional regimes.

Tensor harmonics on the 3‐sphere

Abstract: The scalar, vector, and tensor harmonics on the 3‐sphere are developed by its identification with SU(2), enabling familiar angular momentum techniques to be employed. The application to spatially homogeneous cosmology is discussed. In this context the classic work of Lifshitz and the recent approach of Hu are bridged. Finally spinor harmonics are introduced.

SU2 monopole harmonics

Abstract: For a particle of I‐spin I in an SU2 monopole field in five‐dimensional Euclidean space, the monopole harmonics are found. They belong to the irreducible representation (p,q)5 where p =q+2I. They form a complete set of wave sections.

The power spectrum of the solar wind speed for periods greater than 10 days

Abstract: The use of the more than 11 years of solar wind speed data obtained by Vela 2-6 and Imp 6-8 to study the power spectrum of speed variations in the range near the solar rotational frequency is discussed. The broad bands of power near periods of 27 days (corresponding to the rotational period of the sun), 13.5 days, and higher harmonics are characterized, and it is suggested that the described individual peaks in both the solar wind and the geomagnetic spectra are probably not due to differential rotation. The alternate explanation is that the multipeak nature of the power spectra are explained by a wave packet concept in which recurring highspeed streams are described as a series of pulses (separated by a constant period) that last for a varying number of solar rotations.

Estimation of Higher Frequency Network Equivalent Impedances by Harmonic Analysis Natural Waveforms

Abstract: A digital method of analysing harmonics in a power system has been developed which permits the equivalent network impedance to be estimated by means of the switching of capacitor banks. The method records voltage and current digitally and by data processing computes the amplitude and phase of the harmonics. By comparing results before and after the switching of a capacitor bank on one phase, the equivalent network impedance is estimated at the odd harmonics. Precision of results is acceptable in amplitude but less accurate in phase.

Harmonic cancellation for multi-bridge, three-phase converters

Abstract: All harmonics of an order less than (6·N-1) are cancelled from the fundamental signal presented in each output phase of a three-phase converter as the sum of corresponding phase angle fundamental signals from an N number of converter bridges, where N is a non-power of two

Three phase ac to dc voltage converter with power line harmonic current reduction

Abstract: A three phase AC to DC voltage converter includes separate single phase AC to DC converters for each phase of a three phase source with the DC voltage output of the three converters paralleled and controlled to provide necessary regulation Each of the single phase AC to DC converters includes a full-wave bridge rectifier feeding a substantially resistive load including an inverter and a second single phase full-wave bridge rectifier To the extent that each inverter and second single phase full-wave bridge rectifier approximate a resistive load, the source current harmonics are reduced Additionally, the triplen harmonics produced in the three phase source lines by each of the three AC to DC converters are cancelled by the triplen harmonics produced in the three phase source lines by the remaining two AC to DC converters

Multi-harmonic electron cyclotron instabilities

Abstract: The reported investigation constitutes an extension of studies conducted by Ashour-Abdalla and Kennel (1975, 1976, 1978) with respect to a basic plasma model of Young et al. (1973). The model involves a combination of a cold Maxwellian background plasma, a hot plasma, and a 'loss cone' type of free energy source. Previous results on the first cyclotron harmonic bands are extended to multiharmonics. The significance of the obtained relations is discussed and tentative conclusions are presented. Given that the spatial growth rates of the convective modes are comparable, and that simultaneous nonconvective instability (NCI) is possible, it is concluded that multiharmonic emissions ought to be a common feature of the magnetospheric electrostatic wave observations. Since the volume of parameter space for which the first harmonic is NCI, and the volume for which the convective first harmonic mode has significant spatial growth rates, exceed those for the higher harmonics, first harmonic waves should be the most commonly observed and the higher harmonics should usually be accompanied by the first harmonic.

Satellite observation of discrete VLF line radiation within transmitter‐induced amplification bands

Abstract: Narrow-band VLF signals with a frequency separation of 100–130 Hz have been detected by a receiver aboard the S3-3 satellite. The observations were made at L = 2.9 at an altitude of 5700 km. Satellite nadir was 45°N and 151°E. The radiation has the same characteristics as those reported for ground-based observations of magnetospheric lines resulting from the nonlinear amplification of power line radiation. As is seen in ground-based observations, the lines are not exact harmonics of the power system frequency, nor are they spaced at exactly 2 or 3 times that frequency. The frequencies of the three dominant lines were typically 7364, 7494, and 7598 Hz. During the time period of these observations the transportable very low frequency (TVLF) transmitter was performing magnetospheric wave injection experiments from a site in Central Otago, New Zealand. The modulation was 0.5 Hz frequency shift keying between 7350 and 8780 Hz. The narrow-band signals detected by the S3-3 satellite were observed in the 250-Hz band above the lower frequency. The narrow-band magnetospheric lines were apparently observed because power line harmonic radiation was amplified to detectable levels by a nonlinear interaction involving the TVLF signal. The most likely sources of the power line radiation are the 50-Hz power grids in Tasmania, southeastern Australia, or New Zealand.

The theory of hydromagnetic stability of a tokamak plasma

Abstract: The author considers the stability of a plasma with a fixed boundary in a toroidal column of circular cross-section under the usual tokamak conditions and shows the effect of the non-local nature of the associated harmonics coupled with the fundamental mode. It is demonstrated that the stability conditions deteriorate with a rise in the pressure gradient, and this proves the inadequacy of the earlier known local criteria, according to which there is no instability when q2 > 1.

Microstrip open ring resonator oscillators

Abstract: A microstrip circuit which features a pair of open ring resonators sections adapted to oscillate independently in their even mode. In a preferred form, the ring resonator sections are each driven by a TRAPATT diode, and include a load circuit which combines the individual power outputs to a common load. Tuning stubs and the like may be provided to reactively trap harmonics in order to initiate the desired TRAPATT mode, and additional ring resonators may be interposed between the driving circuit and the load to filter the fundamental frequency, if desired. Other configurations permit power to be combined from two or more sets of dual ring resonators.

Harmonics produced by direct current in convertor transformers

Abstract: Test and analytical procedures are described that determine the relationship between direct current and resultant harmonics in a convertor transformer. It is shown that a linear relationship exists between lower-order harmonics and direct current. The effect of `fluxing' the transformer is also shown, and it is found that `under-fluxing' a transformer in the presence of direct current has little effect.

The effect of harmonics on the capillary instability of liquid jets

Abstract: The instability of a inviscid liquid jet was investigated in both the linear and nonlinear regime. Sound vibrations were used to break up the jet of water into a row of spheres. At small amplitudes, the growth of variations in the jet radius agreed with the calculations of Lord Rayleigh. The distribution of droplets was related to the Fourier coefficients of the periodic vibration. Harmonics and the fundamental component of the vibration grow at different rates which determine the shape of the unstable jet. The analysis of Lord Rayleigh was extended into the nonlinear regime to second order to predict the coupling between the fundamental mode and the second‐harmonic mode.

Power harmonic radiation enhancement during the sudden commencement of a magnetic storm

Abstract: THE enhancements of power harmonic radiation that occurred at the same time as a sudden commencement of a geomagnetic storm (ssc) and with geomagnetic pulsations that followed the ssc are described and discussed here. The power harmonic radiation was detected by an ELF–VLF wave receiver with two loop antennas and a vertical whip at Riverton, while geomagnetic variations were observed by three induction magnetometers distributed at Thompson (55.9° N, 97.4° W), Riverton (51.0° N, 97.0° W) and Star Lake (50.1° N, 95.2° W), Manitoba, Canada. The power harmonic enhancements are accounted for in terms of the geomagnetically induced telluric current that was possibly shunted through transformer neutrals and a transmission line of a power system, giving rise to a near saturation of the transformer core material. The important role which the enhanced power harmonics may have in stimulation of emissions in the magnetosphere is considered.

Musical tone generator with time variant overtones

Abstract: There is described a tone generator in which waveform amplitude data is generated from a table of sinusoid values in an addressable memory by changing the addresses as a function of time in a periodic or sinusoidal manner. The effect is to produce a sequence of sinusoidal values from the table which correspond to a series of points on a frequency modulated carrier signal. By making the effective modulation frequency equal to the carrier frequency, the resulting frequency modulated signal corresponds to a carrier with side bands that correspond to harmonics of the carrier. The relative amplitudes of these harmonics can be varied as a function of time to produce the sliding formant effect of a synthesizer.

Convertor control with selective reduction of line harmonics

Abstract: In the paper, a new method of controlling the power of a d.c. series motor drive using the forced-commutation principle is proposed and investigated. In this method, it is possible to reduce any one unwanted harmonic and its multiples to a low value. However, only the reduction of triplen harmonics is investigated in the paper. A power circuit to realise the proposed method is also suggested. A slight modification of the proposed control circuit yields symmetrically pulsewidth modulated and sinusoidally modulated schemes with two chops per halfcycle. These two and the recently reported scheme using symmetrical pulsewidth modulation with a single chop per half-cycle are investigated and are compared with the proposed new method with regard to the line side harmonic components, power factor and the motor performance characteristics. Experimental verification of the basic principles involved is made. The experimental values closely agree with the theoretical results.

Phase balance monitoring system incorporating voltage and phase sequence monitoring

Abstract: A phase unbalance detecting system that includes also low-voltage detection and wrong-phase-sequence detection. The system can be packaged in a small volume because it is a solid state type that uses a minimum of electronics and does not require transformers for obtaining signals from the several phases of the plural-phase power line but only one transformer for the D.C. power supply circuit for the detection system. The system incorporates means for allowing it to be used at 50 or 60 Hz without separate adjustment, for making it insensitive to noise and harmonics of the power line, and for providing a good estimate of the negative sequence voltage caused by a phase unbalance. It provides external terminals whereby it can be adapted for use at different power line voltages.

Synchronized receiver power system

Abstract: A portable radio receiver powered by a battery includes an RF amplifier, an IF amplifier and an audio amplifier powered by a first regulated, switched, DC power converter that derives a first DC voltage. A frequency synthesizer, including varactor diodes, is powered by a second regulated, switched DC power converter that derives a second DC voltage. Digital circuitry included in the synthesizer is powered by opposite polarity, third and fourth power converters. A synchronizing source for switching all of the power converters simultaneously has a fundamental and harmonics outside of the bandpasses of the audio and IF amplifiers to minimize the injection of spurious signals by the power converters into the amplifiers. The synchronizing source is FM modulated by an audio source so that harmonics of the synchronizing source are spread over a predetermined spectrum and the harmonics have noise-like characteristics spread over relatively wide frequency ranges.

Apparatus for detecting faults to be occurred or initially existing in a running electric rotary machine

Abstract: Apparatus for detecting possible changes or variations in the dimension of an air gap of a running electric rotary machine during operation thereof. Detector coils are each accommodated within respective slots formed in the stator core of the machine, the coils being geometrically separated from one another at an angular distance corresponding to the distance between poles or its integral multiple. The detector coils are electrically connected in series with each other to produce a voltage for detection. The detector coils are so connected that the fundamental waves of the voltages induced in two detector coils will cancel each other and a synthesized value of higher harmonics induced in both detector coils is picked up as the detection voltage signal. The number of slots of the rotor of the electric rotary machine is predetermined to a limited number in order to get a detection signal of higher quality.

Estimates of oceanic surface wind speed and direction using orthogonal beam scatterometer measurements and comparison of recent sea scattering theories

Abstract: The wind direction properties of radar backscatter from the sea were empirically modelled using a cosine Fourier series through the 4th harmonic in wind direction (referenced to upwind). A comparison with 1975 JONSWAP (Joint North Sea Wave Project) scatterometer data, at incidence angles of 40 and 65, indicates that effects to third and fourth harmonics are negligible. Another important result is that the Fourier coefficients through the second harmonic are related to wind speed by a power law expression. A technique is also proposed to estimate the wind speed and direction over the ocean from two orthogonal scattering measurements. A comparison between two different types of sea scatter theories, one type presented by the work of Wright and the other by that of Chan and Fung, was made with recent scatterometer measurements. It demonstrates that a complete scattering model must include some provisions for the anisotropic characteristics of the sea scatter, and use a sea spectrum which depends upon wind speed.

Noise and Transfer Properties of Harmonically Synchronized Oscillators

Abstract: A theoretical model of a harmonically synchronized oscillator is developed. Using this model output power, stability conditions, noise, and transfer properties of a harmonic frequency divider are calculated and discussed.

Approximations in sinewave generation and synthesis

Abstract: Linear segment approximation to a sine wave is almost exclusively used in the modern function generator signal source. This paper offers an in-depth treatment of the question of breakpoint selection. Computer-aided analysis is used to obtain required data for design purposes according to two criteria of minimizing either the number of harmonics or the total harmonic distortion by appropriate positioning of breakpoints. The results obtained indicate that values for total harmonic distortion of less than 0.1% lead to undue amounts of hardware and this value represents a practical limit for this technique.