Showing papers on "Harmonics published in 1968"
TL;DR: Several methods of fundamental frequency and period measurement, based on these concepts, are described and the results of computer simulations and analog instrumentations indicate that these new methods compare favorably with, and in some cases exceed, the capabilities of cepstrum analysis.
Abstract: The fundamental frequency of a periodic signal whose fundamental component is not available for measurement can be determined by measuring the frequencies of its higher harmonic components and computing the largest common divider of these frequencies. Similarly, the fundamental period can be determined by measuring the periods of individual harmonics and finding their smallest common multiple. Several methods of fundamental frequency and period measurement, based on these concepts, are described in this paper. The results of computer simulations and analog instrumentations indicate that these new methods. at a considerable reduction in complexity, compare favorably with, and in some cases exceed, the capabilities of cepstrum analysis.
312 citations
TL;DR: In this article, a method for calculating the harmonic currents and losses of induction motors excited with static frequency converters is presented, and experimental data are included to substantiate it. But, the authors do not consider the effect of motor load on the performance of inductive motors.
Abstract: Induction motors excited with static frequency converters almost invariably are subjected to nonsinusoidal voltage waveforms, and the presence of time harmonics in the applied voltage results in currents at the harmonic frequencies. These currents result in additional and sometimes rather large losses. A method for calculating these harmonic currents and losses is presented, and experimental data are included to substantiate it. The losses are separated into various components and it is shown that the largest loss is usually in the rotor bars as a result of deep bar effect. Harmonic losses are shown to be nearly independent of motor load and the fundamental magnetizing current is found to increase over that which would be present for the same rms fundamental voltage. These observations are explained on a theoretical basis. The encouraging correlation between test and calculated data confirms that the important elements which differ between motor performance on sinusoidal and nonsinusoidal waveforms have been identified and accounted for.
152 citations
TL;DR: The high-frequency temporal behavior of the human visual system has been shown to have some of the properties of a linear low-pass filter, and predictable behavior is found at high frequencies, and it leads to discovery of hitherto unobserved pseudoflash and real flash phenomena.
Abstract: The high-frequency temporal behavior of the human visual system has been shown to have some of the properties of a linear low-pass filter. For such a system it is appropriate to consider a repetitive stimulus as having separable Fourier harmonic components. The direct-current component or average luminance is important in that it sets the adaptation level. It is therefore convenient to keep it constant when varying other stimulus parameters, such as frequency or wave form. Of the alternating-current components, only the fundamental is important at high frequencies, the higher harmonics being relatively more attenuated. Any linear low-pass filter system responds in a predictable way to sinusoidal stimulation, whether continuous or of short duration. In the case of the visual system, predictable behavior is found at high frequencies, and it leads to discovery of hitherto unobserved pseudoflash and real flash phenomena. Measurement of a new characteristic time is suggested. At low frequencies the use of half and whole-sinusoidal flashes leads to the discovery of some interesting relations with flicker thresholds, but these remain for future discussion.
74 citations
01 Nov 1968
TL;DR: In this paper, a general method is established for the evaluation of the driving point admittance of a radiating aperture, fed by a waveguide of the same cross section as the aperture, in an infinite periodic planar phased array.
Abstract: A general method is established for the evaluation of the driving point admittance of a radiating aperture, fed by a waveguide of the same cross section as the aperture, in an infinite periodic planar phased array. The array may have an arbitrary element lattice and it may be covered by a dielectric layer. The coefficients of the waveguide modal expansion and of the Floquet series representing the electromagnetic field in the waveguide and in the radiation half-space, respectively, are determined by approximately enforcing the boundary conditions in the array plane through an application of Galerkin's method. By eliminating from the set of equations thus obtained the complex amplitudes of the waveguide modes and of the Floquet harmonics, the driving point admittance can be expressed as the ratio of two determinants of order N and N-1 (N being the number of the waveguide modes utilized), whose elements contain truncated bidimensional series, structurally similar to the well-known grating-lobe series. The expression allows relatively simple numerical computations if the Fourier transforms of the waveguide vector mode functions are known in closed form (as they are for rectangular or circular elements). The variation of the power reflection loss with scan angle has been numerically calculated for various array configurations. The results are in some cases substantially different from those predicted through the conventional grating-lobe series technique, which is based on the assumption of one-mode elements.
65 citations
TL;DR: In this article, the shape of the smallest characteristic unit of a fold profile, a “quarter” wavelength, can be matched by a curve made up from suitable combinations of the first and third harmonics of a sine series called an F-T curve.
56 citations
TL;DR: In this paper, the effect of unbalances in the altemating voltages and the valve firing angles on the ac waveform was analyzed for six and 12-pulse dc conversion.
Abstract: Unbalance in the operation of high-voltage dc convertors gives rise to unusual or uncharacteristic harmonics in the ac waveform not expected from the existing theory relating to balanced operation. Analysis of the effect of unbalances in the altemating voltages and the valve firing angles is provided together with selected characteristics illustrating the variations in the harmonics with unbalance as determined by a comprehensive digital computer program. Six-pulse and 12-pulse operation is considered.
47 citations
TL;DR: In this article, the possibility of abnormal harmonic generation in an ac system feeding a converter load is examined from the standpoint of automatic control systems used in modern HVDC transmission systems.
Abstract: The possibility of abnormal harmonic generation in an ac system feeding a converter load is examined from the standpoint of automatic control systems used in modern HVDC transmission systems. It is shown that with certain types of automatic controls, the firing angles of converter valves may sustain some errors, which in turn could generate abnormal harmonic currents in the three- phase ac system feeding the converter. A criterion for predetermining the type and extent of abnormal harmonic generation is defined, and numerical examples given. Methods of reducing abnormal harmonic generation are discussed, and some experimental data supporting the theoretical calculations are also included.
44 citations
TL;DR: In this article, the damping power system swings have been studied by analog and digital simulation, and the authors proposed a damping scheme based on analog simulation and analog simulation techniques.
Abstract: Techniques for damping power system swings have been studied by analog and digital simulation.
38 citations
TL;DR: In this paper, the effects of space harmonics in multi-winding double cylindrical structures are analyzed and the terminal characteristics of the machine are obtained by solving the dynamical equations of motion using certain linear transformations.
Abstract: The effects of space harmonics in multiwinding double cylindrical structures are analyzed. Terminal characteristics of the machine are obtained by solving the dynamical equations of motion using certain linear transformations. The equivalent circuits are derived from the transformed equations of motion and the effects of current-sheet space harmonics are included. An example is considered and numerical calculations are made and compared with experimental results. For completeness, pertinent definitions and theorems relating to linear algebra are included.
30 citations
TL;DR: In this article, the dispersion curves of the Bernstein modes were calculated numerically for hybrid frequencies in the vicinity of the thirtieth to fortieth harmonic of the gyrofrequency.
Abstract: The electrostatic modes for which k is perpendicular to the impressed field B 0 (the ‘Bernstein modes’) have been examined, and dispersion curves ( w vs. k ) have been calculated numerically for hybrid frequencies in the vicinity of the thirtieth to fortieth harmonic of the gyrofrequency. Although the calculations were performed for the lower hybrid case (ion branch), they also apply to the upper hybrid cases in which the plasma parameter The structure of the dispersion curves for these large values of plasma parameter differs from that for smaller values investigated by others, in that broad bands in wave-number space have very small group speeds in narrow frequency bands close to many of the gyrofrequency harmonics. All of the Bernstein modes examined have group speeds less than 37 % of the ion thermal speed, and can be classified as very slow waves. Furthermore, the spectrum of propagating Bernstein modes is broadened as becomes large, with an effective total transmission region from the gyrofrequency up to several harmonics of gyrofrequency above the hybrid frequency.
30 citations
TL;DR: In this paper, the phase angle between the fundamental and second-harmonic components in the distorted wave was measured by using a pulse technique and agreement between theory and experiment was established for the phase shift upon reflection from water copper, from water duralumin, and from water mica-glycerin interfaces when correction is made for finite-amplitude effects between the interface and the receiving transducer.
Abstract: When an ultrasonic wave is reflected from an interface, a phase shift that is dependent on the angle of incidence may occur. If the wave is nonsinusoidal, this phase shift causes relative spatial shifting of the Fourier harmonic components. The assumption of independent reflection of the Fourier harmonics allows the use of linear theory to calculate the change in the phase angle between the fundamental and the second‐harmonic components in the distorted wave. A pulse technique is used to measure this change in phase angle. Agreement between theory and experiment is good for the phase shift upon reflection from water‐copper, from water‐duralumin, and from water‐mica‐glycerin interfaces when correction is made for finite‐amplitude effects between the interface and the receiving transducer.
01 Sep 1968
TL;DR: In this paper, the Impatt oscillators are operated so that the second harmonic lies in the frequency range for classical Read operation, in addition to the required tuning at the output frequency.
Abstract: Improvements in power, efficiency, and FM sensitivity are achieved experimentally with Impatt oscillators which are operated so that the second harmonic lies in the frequency range for classical Read operation. The improvement in performance is accomplished by providing a trapped resonance at the second harmonic, in addition to the required tuning at the output frequency.
TL;DR: In this paper, a method for investigating the seismic response of single-story elastic structures situated on elastic foundation media which are represented by an elastic half-space is presented, where the dynamic properties of the halfspace are defined only for steady-state motion.
Abstract: A method for investigating the seismic response of single-story elastic structures situated on elastic foundation media which are represented by an elastic half-space is presented. The dynamic properties of the half-space are defined only for steady-state motion. This requires a solution of the equations of motion for the structure-foundation system subjected to a psuedo strong motion earthquake by a method similar to harmonic analysis, with the foundation properties redefined for each harmonic component. By inspecting the frequency dependent nature of these properties, it is found that good approximations to the seismic response of the interaction system may be obtained by taking the average values for the foundation properties in the range of the harmonics frequencies of the earthquake excitation. The results indicate that the response of the structure may be increased or decreased when compared to the response of the same structure on rigid foundation. An interpretation of this behavior is offered by means of the spectral velocity curves.
TL;DR: For signals of fundamental frequency greater than approximately 2000 cps, harmonic components have little or no effect on the ability of observers to discriminate differences in frequency, however, below approximately2000 cps differences in the frequency of signals containing harmonically related components are more readily discriminated than differences inThe frequency of sinusoidal signals.
Abstract: The effect of the presence of harmonics on frequency discrimination is measured as a function of the frequency of the fundamental component of the signal. For signals of fundamental frequency greater than approximately 2000 cps, harmonic components have little or no effect on the ability of observers to discriminate differences in frequency. Below approximately 2000 cps, however, differences in the frequency of signals containing harmonically related components are more readily discriminated than differences in the frequency of sinusoidal signals. These findings relate to the dependence of frequency discriminability on frequency.
TL;DR: In this paper, a set of ultrasonic measurements which were designed to test the theory of reflections of harmonics generated by finite amplitude waves at stress free boundaries in solids have been made.
Abstract: Ultrasonic measurements which were designed to test the theory of reflections of harmonics generated by finite amplitude waves at stress free boundaries in solids have been made. The results are found to be in agreement with theoretical expectations.
TL;DR: In this article, the effect of a skin high frequency field polarized along the magnetostatic field, on the onset of the drift-cyclotron instability of an inhomogeneous plasma with warm ions was studied.
Abstract: A study is made of the effect of a skin high frequency field polarized along the magnetostatic field, on the onset of the drift-cyclotron instability of an inhomogeneous plasma with warm ions. It is found that an h.f. field of this sort removes instability on the low harmonics of the ion cyclotron frequency but that instability arises on all the higher harmonics.
TL;DR: In this article, Bragg diffraction of light from the harmonic components of the acoustic wave was used to obtain direct harmonic analyses of the waves without the need for calibrated broad-band transducers.
Abstract: Acoustic waves at microwave frequencies show significant nonlinear effects at power densities of 10 W/cm2. These effects have been studied using Bragg diffraction of light from the harmonic components of the acoustic waves. With this technique, direct harmonic analyses of the waves have been obtained without the need for calibrated broad‐band transducers. The following effects of finite amplitude waves propagating in quartz have been observed: variation of the attenuation of the fundamental with power level; the presence of the second through fifth acoustic harmonics; the growth and decay of these harmonics as a function of the distance traveled by the acoustic wave; and the behavior of the second harmonic after reflection from a stress‐free surface. The growth of the harmonics assures that they were generated in the bulk of the solid. Similar effects have been observed in MgO and MnF2. The experimental observations have been compared with theoretical predictions and estimates of the relevant third‐order ...
TL;DR: In this paper, a mechanical chopper which discriminates against all even harmonics and against third harmonics is discussed and the use of eddy currents to precisely align a sample in a null measurement of magnetization is described.
Abstract: In order to eliminate the sensitivity to field noise and microphonics of a vibrating sample magnetometer it is sufficient to add trimming coils which are adjusted to produce no signal when the applied field is deliberately driven at the frequency ω0 which is to be used for vibrating the sample. A mechanical chopper which discriminates against all even harmonics and against third harmonics is discussed. The use of eddy currents to precisely align a sample in a null measurement of magnetization is described.
01 Apr 1968
TL;DR: In this article, the annual variation of rainfall at 131 stations distributed all over Central America is subjected to harmonic analysis, where the authors present the total variance of the mean monthly rainfall, the percentage variance of first three harmonics, the residual contributed by the higher harmonics.
Abstract: The annual variation of rainfall at 131 stations distributed all over Central America is subjected to harmonic analysis. Maps present the total variance of the mean monthly rainfall, the percentage variance of the first three harmonics, the residual contributed by the higher harmonics, the amplitudes and phase angles of the first three harmonics, and the ratio of the amplitudes of the first to te second harmonics. Annual rainfall curves are in most areas adequately reproduced by the first three harmonics.
Patent•
09 Jul 1968
TL;DR: In this article, an AC-DC conversion system which reduces sensitivity of the conversion to selected harmonics of the input AC wave is described, where the absolute value signal is formed of the AC wave and compared with the output of the system to provide gating signals.
Abstract: An AC-DC conversion system which reduces sensitivity of the conversion to selected harmonics of the input AC wave. The absolute value signal is formed of the input AC wave and compared with a DC level which is the output of the system to provide gating signals. The latter are used to time-gate the absoluted AC signal through an averaging device. The time-gating is explicit, gating signals being generated whenever the absolute value of the input potential exceeds a fraction of the output DC.
01 Sep 1968
TL;DR: In this paper, a dispersion relation involving all space-time harmonics has been obtained for electromagnetic wave propagation in an infinite dielectric medium whose permittivity is modulated by a high-intensity pump wave containing two harmonics.
Abstract: A dispersion relation involving all space-time harmonics has been obtained for electromagnetic wave propagation in an infinite dielectric medium whose permittivity is modulated by a high-intensity pump wave containing two harmonics. A solution for the modal amplitudes has been obtained in the form of continued fractions and the convergence criterion has been postulated.
TL;DR: In this paper, the effects of MMF and permeance harmonics on the N-phase to two-phase slip ring transformation are considered and simplifications occur if MMFs higher than the Nth can be neglected.
Abstract: The effects of MMF and permeance harmonics on the N-phase to two-phase slip ring transformation are considered. Considerable simplifications occur if MMFs higher than the Nth can be neglected. Particular attention is given to both three-phase and squirrel-cage windings. Practical factors influencing the ?,s,O transformation and the choice of coefficients result from the former and the basis and limitation of the harmonic equivalent circuits of the squirrel cage induction motor result from the latter.
TL;DR: In this article, the resonance curve for a clarinet is automatically plotted on a chart for external excitation with sound of constant pressure amplitude, and the harmonic structure of sound pressure in the mouthpiece of the instrument when sounded by blowing with an artificial embouchure.
Abstract: Equipment has been constructed that will automatically plot on a chart the resonance curve for a clarinet as produced by external excitation with sound of constant pressure amplitude. On the same chart are plotted for comparison the frequencies of the harmonics of the lowest resonance. The harmonic structure of the sound pressure in the mouthpiece of the instrument when sounded by blowing with an artificial embouchure is also plotted for further comparison. It is found for the lowest notes on the clarinets used that the resonances lie at frequencies progressively lower than the harmonic frequencies. Even harmonics are present in the standing wave in the instrument when sounded, although the odd ones predominate out to the fifth harmonic; only the second is completely absent. As the scale is ascended, the resonances get more out of tune with the harmonics and decrease in number until for the (written) note B♭4, before the change to the next register, there are only two strong resonances. In the next regist...
Patent•
23 May 1968
TL;DR: In this article, the authors describe a system for generating polyphase odd harmonics of a fundamental frequency derived from but one phase of a high power polyphase source, both the magnitude and relative phase of the harmonics with respect to the fundamental being variable and controllable.
Abstract: : The patent describes a system for generating polyphase odd harmonics of a fundamental frequency derived from but one phase of a high power polyphase source, both the magnitude and relative phase of the harmonics with respect to the fundamental being variable and controllable. The harmonic may be injected into a polyphase aircraft power system to both evaluate the response thereto and provide harmonics of equal magnitude but opposite phase relation to balance out inherent aircraft system harmonics.
Patent•
16 Jul 1968
TL;DR: In this paper, a high power radio transmitter is improved by selectively shifting the parasitic resonant frequency in the output network as a function of the transmitter operating frequency, where inductance means is switchably inserted in the network to accomplish the shift in parasitic frequency.
Abstract: Operating efficiency of a high power radio transmitter is improved by selectively shifting the parasitic resonant frequency in the output network as a function of transmitter operating frequency. Inductance means is switchably inserted in the output network to accomplish the shift in parasitic resonant frequency.
01 Dec 1968
TL;DR: In this article, the semimajor axis of an artificial satellite can undergo long term variations if its mean motion and the rotational speed of the Earth are nearly commensurable.
Abstract: The semimajor axis of an artificial satellite can undergo long term variations if its mean motion and the rotational speed of the Earth are nearly commensurable. A theoretical expression for this variation is obtained for satellites with a twelve to one such commensurability by considering twelfth order harmonics of degree twelve through fifteen. The TIROS IX satellite is in such a near resonant orbit. From this single satellite, only two pairs of resonant gravity harmonics of twelfth order can be estimated. One pair must be of even degree while the other is of odd degree. The values obtained were; 10 7 X 1412 =1.01.4 10 7 X 14,12 = 2.1 1.4 101xEl5,12 -1.71.2 10 7 x 515.12 = 2.1 ± .2 These values must be considered to be in some sense composite harmonics since all harmonics whose order is divisible by twelve are nearly rc 3onant. These values will however serve as estimates with widest application to orbit prediction for satellites with orbit characteristics similar to those of TIROS IX.
Patent•
10 Sep 1968
TL;DR: In this article, a phase-sensitive detector for a simple SINE-WAVE was proposed. But the phase-sensitivity of the detector was not considered. And the phase sensitive detector was used to adjust the phase of the INCOMING SINE WAVE with the SYNTHESIZED SINEWAVE.
Abstract: THERE IS PROVIDED A PHASE-SENSITIVE DETECTOR FOR A SIMPLE HARMONIC WAVEFORM INCLUDING MEANS FOR SYNTHESIZING A SINE-WAVE PLUS HARMONICS BY GENERATING A PULSE TRAIN IN WHICH THE PULSES ARE EFFECTIVELY WEIGHTED -E, O+E AND IN WHICH THE PULSE CLOCK RATE, NUMBER OF PULSES AND PULSE DISTRIBUTION ARE SO ARRANGED THAT THE AMPLITUDES OF SELECTED HARMONICS IN THE SYNTHESIZED SINEWAVE ARE MINIMIZED, MEANS FOR MULTIPLYING THE INCOMING SINE-WAVE WITH THE SYNTHESIZED SINE-WAVE, MEANS FOR INTEGRATING THE RESULTANT AND MEANS RESPONSIVE TO THE VALUE OF THE INTEGRATED RESULTANT FOR ADJUSTING THE PHASE OF THE SYNTHESIZED SINE-WAVED RELATIVE TO THE PHASE OF THE INCOMING SINE-WAVE.
TL;DR: In this paper, the authors considered a transistorized synthesizer or harmonic generator with a 400-Hz reed oscillator, binary divided, which controlled the master square-wave generator at 50 Hz.
Abstract: The paper considers in detail a transistorized synthesizer or harmonic generator. It is driven by a highly stable 400-Hz reed oscillator, binary divided, which controls the master square-wave generator at 50 Hz. Each harmonic channel consists of two selective amplifier modules separated by a limiter and has amplitude and phase control. A complex wave is formed of harmonics up to and including the forty-ninth. This is fed to a 1-kVA power amplifier via an adding stage. Connected to the output of the amplifier is an excitation coil containing the single Epstein sample under test. On the sample is wound a B -search coil whose waveform is made sinusoidal. The Hall plate is positioned in the center of the excitation coil perpendicular to the air flux. The B coil is connected to the Hall plate buffered by an amplifier. The current through the Hall plate is proportional to the induced voltage, Hence the output from the Hall plate is a measure of the iron losses of the sample. Losses have been measured up to 24 kG for sinusoidal flux density and at several frequencies using the harmonics as fundamentals.
TL;DR: In this paper, a simple method was developed for computer experiments on the disc model of the confined electron beam, and the a.c. beam current components of the lowest harmonics (lω, 2ω, 3ω) in the two-resonator klystron were studied.
Abstract: A simple method is developed for computer experiments on the disc model of the confined electron beam. The a.c. beam current components of the lowest harmonics (lω, 2ω, 3ω) in the two-resonator klystron are studied. A number of hollow and solid beam geometries are investigated. The maximum obtainable relative a.c. current amplitudes are in general larger: (a) in thin beams than in wide beams, (b) in beams inside a conducting tube than in beams without tube, (c) in solid beams than in hollow beams. The largest fundamental frequency current amplitude obtained is about l.25i0.