Showing papers on "Harmonic published in 1968"

The Determination of Kinematic Properties of a Wind Field Using Doppler Radar

Abstract: A technique is proposed for the measurement of kinematic properties of a wind field in situations of widespread precipitation, using a single Doppler radar to sense the motion of the precipitation particles. The technique is an extension of ideas put forward by Probert-Jones, Lhermitte, Atlas, Caton and Harrold, and is based upon the Velocity-Azimuth Display (VAD) obtained by scanning the radar beam about a vertical axis at a fixed elevation angle. Harmonic analysis of the VAD permits divergence to be obtained from the magnitude of the “zeroth” harmonic, wind speed and direction to be obtained from the amplitude and phase of the first harmonic, and resultant deformation and the axis of dilatation to be obtained from the amplitude and phase of the second harmonic. Although limitations to the accuracy of this technique are imposed by inhomogeneities in the horizontal distribution of precipitation fall speed and, in the presence of strong vertical wind shear, by elevation angle errors and reflectivi...

Period Histogram and Product Spectrum: New Methods for Fundamental‐Frequency Measurement

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.

Polyphase Induction Motor Performance and Losses on Nonsinusoidal Voltage Sources

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.

The Phase-Locked Oscillator - A New Control System for Controlled Static Convertors

Abstract: Static convertors for high-voltage direct-current transmission links, whether based on mercury-arc valves or thyristors, are controlled by accurately timed firing pulses from a control system. With conventional control systems it has not so far been practicable to operate a convertor on a very weak (high impedance) ac system; one principal reason is inherent harmonic instability caused by the direct dependence of the control system on ac line voltage and its distortion.

Second Harmonic Generation from Short Pulses

Abstract: The second harmonic pulse shape generated from ultrashort pulses is calculated In long dispersive crystals the pulse width may be much broader than the incident pulse and the power conversion ratio may saturate at a low value These effects should be prominent in LiNbO3 with 4 × 10−13 sec pulses

Induction-motor losses due to nonsinusoidal supply waveforms

Abstract: The paper presents an analytical and experimental study of the additional losses which occur in induction motors supplied with nonsinusoidal waveforms. Measurements on an inverted induction motor are used to show the importance of losses due to skew-leakage and end-leakage fluxes, and to verify the methods developed for calculating these components. Computed losses are compared with test results obtained on a variety of machines and supply waveforms, and the agreement is shown to be consistently good. The manner in which the losses are related to the machine design and to the supply harmonic content is described.

Transverse Vibrations of Tapered Cantilever Beams with End Support

Abstract: Free vibrations of nonuniform cantilever beams with an end support have been investigated, using the equations of Bernoulli‐Euler. Two configurations of interest are treated: (a) constant width and linearly variable thickness, and (b) constant thickness and linearly variable width. Charts have been plotted for each case from which the fundamental frequency, the second harmonic, and the third harmonic can be easily determined for various taper ratios. The Tables from which these charts were plotted are also included.

Generation of Abnormal Harmonics in High-Voltage AC-DC Power 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.

Reflection of Finite‐Amplitude Ultrasonic Waves. I. Phase Shift

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.

Impatt oscillator performance improvement with second-harmonic tuning

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.

Efficient cw second harmonic generation to 2573 å

Abstract: Efficient cw second harmonic conversion to 2573 A has been achieved in an argon laser cavity by means of the nonlinear materials ADP and KDP. Peak SH power was 415 mW which represented 50% efficiency. Trace impurities in the crystals prevented the realization of theoretical efficiency. An increase in cavity loss was observed during the simultaneous presence of fundamental and SH beams.

Higher harmonic oscillations in heteronomous non-linear systems with one degree of freedom

Abstract: Higher harmonic oscillations in systems governed by Duffing-type differential equations are investigated by the harmonic balance method and by an analog computer analysis. Theoretical resonance curves of the first and third harmonic components of the response, the amplitudes and phase angles of which vary with the frequency of external force, are analyzed and compared with analog computer results. The stability problem is analyzed by solving a corresponding variational Hill-type equation. Regions of anomalous generation of the third harmonic component and of even and odd higher harmonic components, termed higher order resonances, as found through analog computer techniques are found, and phenomena analogous to that at the main resonance (“jump” and hysteresis effects) are observed.

Absorption in a Hot Plasma near the Second Harmonic of the Electron Cyclotron Frequency

Abstract: Analysis is presented of 4‐mm microwave propagation in the extraordinary mode (for propagation angles of 76°, 90°, and 104° to the external magnetic field), near the second harmonic of the electron cyclotron frequency, across reasonably uniform, highly ionized cylindrical plasma columns (approximately 3, 4, and 5 in. in diameter) confined in a homogeneous (0.05%) magnetic field in the Model C stellarator. Reasonably good agreement with the general predictions of the conventional collisionless hot‐plasma theory is obtained. In particular, the measured values of the width, the depth, and the strength of the experimentally detected absorption resonances fall within ±50% of the corresponding theoretically expected values. For these experiments the electron densities are typically in the range of 1011 to 1013 per cm3; the electron temperatures are in the range of 5‐35 eV; and the electron collision frequencies ν are such that ν/ω ≲ 5 × 10−5, where ω is the angular frequency of the incident microwave beam.

Effect of harmonic components on frequency discrimination.

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.

Nonlinear Interactions of Cyclotron Harmonic Plasma Waves

Abstract: Experimental and theoretical evidence of resonant and nonresonant mode coupling of cyclotron harmonic plasma waves is presented.

Charge storage frequency multipliers

Abstract: Frequency multiplication by means of a nonlinear charge storage element is investigated This element is assurmed to have an abrupt transition from an infinite to a zero capacitance An analysis of a frequency multiplier circuit utilizing such an element is carried out with certain limitations imposed on the mode of operation in order to make possible an algebraic solution; namely that 1) only a fundamental and one harmonic current be applied to the nonlinear element, 2) only particular conduction angles be permitted, and 3) the fundamental and harmonic be subject to a particular phase relationship These limitations permit an algebraic solution for circuit performance for any multiplication factor and for a range of conduction angles The analysis yields directly the input and output resistances of the multiplier, in terms of which the conversion efficiency and power handling capability are derived Design data are presented for circuits with muitiplication factors of between 2 and 20

Nonlinear Propagation of a Moderately Strong Electromagnetic Wave in a Fully Ionized Plasma

Abstract: The nonlinear effects resulting from the propagation of a moderately strong electromagnetic wave in a fully ionized plasma are investigated; a detailed study of the case, when the incident frequency is in the vicinity of the plasma frequency, has been made. The nonlinear contributions to the absorption of the wave and to the reflected components from a plasma‐free space interface, have also been obtained. It is shown, in contrast with earlier work, that under some conditions the nonlinear effects can increase the absorption. The generation of harmonic components in the current density and the reflected wave has also been studied.

Forced Oscillations of the van der Pol Oscillator with Delayed Amplitude Limiting

Abstract: Forced oscillations of the van der Pol oscillator with delayed amplitude limiting are analyzed using the derivative-expansion method. The forcing function is taken to be either sinusoidal or white noise. The oscillator's output depends on whether the excitation is "hard" [i.e., excitation amplitude is O(1) ] or "soft" [i.e., excitation amplitude is O(\mu) , \mu is a small parameter], and whether the excitation is resonant (i.e., excitation frequency is near natural frequency) or not. Explicit first-order expressions are obtained for the output in the nonresonant case. If the excitation is soft, the steady-state output is a combination of terms having frequencies equal to those of the natural and excitation frequencies, with the forced response being dominated by the natural response. On the other hand, if the excitation is hard, the natural response fades away as time increases over a wide range of frequencies and excitation amplitudes. Consequently, the output is harmonic, having a frequency equal to the excitation frequency. In the resonant case, the steady-state output is synchronized at the excitation frequency, irrespective of whether the excitation is soft or hard. The frequency response equation is a family of curves that depends on the excitation amplitude and the delay time as parameters. The stability of these harmonic oscillations is determined. For the noise perturbed oscillator, the conditional probability distribution for the deviations from the stationary stable state is presented.

Signal generator for producing a set of signals at baseband frequency and with adjustable phase slope

Abstract: This disclosure describes a signal generator for producing a family of signals of common frequency and of uniformly stepped phase progression with the rate of progression or phase slope adjustable. Signal sets of this character find application for control of beam direction in electronically steered array radiators of radar, sonar and communications systems, and in frequency selective filters of the kind tunable to scan through a band of frequencies. The signal generator as described comprises a reference harmonic spectrum generator and a steering harmonic generator provided with basic frequency inputs of common frequency value but with a phase difference made adjustable as by coupling one such input through an adjustable phase shifter. Each harmonic of the spectrum produced by one generator is mixed with a harmonic of different order from the other generator to provide a group of signals all of common frequency, corresponding to the difference in order of the two harmonics from which each is derived, and with each of the signals phase-displaced from the next by a phase difference equal to the phase shift introduced through the input phase shifter and adjustable thereby. These signals then are again mixed with steering signals and output sidebands selected to yield the desired set of output signals all of common frequency and of phase slope dependent upon the setting the adjustable phase shifter.

Finite‐Amplitude Acoustic Waves in Dielectric Crystals

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 ...

Phase-lock circuit for a 100 MHz nuclear magnetic resonance spectrometer.

Abstract: In heteronuclear double resonance experiments the observing and irradiating radio frequencies are fed into the same nuclear magnetic resonance probe. In many cases a stable relationship between the two radio frequencies is essential. A system meeting this requirement is described whereby the observing frequency of a 100 MHz spectrometer is phase-locked to a harmonic of the 100 kHz reference of a frequency synthesizer, the synthesizer being the source of irradiation. The locking system has a hold-in range of 350 Hz.

Regulated harmonic generator

Abstract: A harmonic generator employing an emitter-coupled monostable multivibrator with a feedback loop including a field effect transistor responsive to variations in the amplitude of a selected harmonic output signal to vary the input bias to the multivibrator. Varying the input bias to an emitter-coupled monostable multivibrator modifies the duty cycle of its rectangular output waveform and thereby regulates the amplitude of the selected harmonic in response to variations in the output signal.

Harmonic-rejecting ac-to-dc converter

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.