Showing papers on "Harmonics published in 1972"

Adaptation to square-wave gratings: inhibition between spatial frequency channels in the human visual system.

Abstract: 1. The observation that the detection threshold for a square-wave grating depends only on that of its fundamental was confirmed by showing that adapting to the fundamental spatial frequency caused elevation of the square-wave threshold, to the same extent as the fundamental threshold was elevated by the same adapting pattern. Adapting to the third harmonic frequency had no effect on the square-wave threshold.2. Adapting to a square-wave grating should elevate the thresholds for both the fundamental and third harmonic frequencies (Blakemore & Campbell, 1969), and the amount of elevation at each frequency should be predictable from the contrast of that frequency within the square-wave.3. It was found, however, that both the fundamental and third harmonic, when present in the square-wave, were much less effective as suprathreshold adapting stimuli than would be predicted from their effects when viewed in isolation.4. Adapting to a mixture of two sinusoidal gratings (with 3:1 frequency ratio) demonstrated that the fall in adapting power was not due to the higher harmonics of the square-wave nor to nonlinearities in the stimulus display. Similar effects were found when the phase relations of the adapting gratings were changed, showing that the interaction is not a special property of square-waves or of edges.5. It is suggested that the spatial frequency channels subserving the fundamental and third harmonic frequencies inhibit each other when the patterns are some way suprathreshold. At or near threshold, there is no such reciprocal inhibition.

Generalised method of harmonic reduction in a.c.-d.c. convertors by harmonic current injection

Abstract: The paper describes a general theory for a new method of current harmonic reduction in a.c.-d.c. convertors. The principle of the method is to modify the current waveforms on the d.c. windings of the convertor transformer by injecting harmonic currents at a particular frequency. Experimental results carried out prove that the new method is effective in reducing the alternating-current harmonics, and that it is applicable to any type of convertor.

Characterization of Equilibrium and Stability in Power Systems

Abstract: The evaluation of the stability of a power system during a transient requires that the dynamics of the subsystems be decomposed into relative and collective motions. This decomposition must establish a distinction between synchronous and frequency equilibria. Such a decomposition is made possible by specifying a system center of angle which is defined as the inertia weighted average of all rotor angles. The angular velocity of the center of angle accurately describes the frequency of the system. An angular coordinate of each rotating element in the system can be specified relative to the center of angle. In terms of these coordinates a simple expression is obtained for the exact transient kinetic energy of the system. A transformation relating center of angle referenced variables to the usual one machine reference allows the simultaneous use of both references each where best suited.

Summation of harmonics with random phase angles

Abstract: The magnitude of the sum of a number of harmonics, of the same order but with random phase angle, is derived, subject to certain assumptions regarding the phase distribution. Computation of the net magnitude is carried out for different types of individual harmonic amplitudes. When the number of individual harmonics is greater than about ten, it is shown that simplified expressions for the sum may be used. These lead to a simple approach, based on r.m.s. values, to the problem of determining an assessed level of harmonic content which would have a specific probability of being exceeded. Consideration is also given to the situation when just one or two harmonics are dominant, and a consequent simplification of an assessed level. The main results apply for instantaneous values of the net magnitude, but some subsidiary results given an indication of the likely behaviour over a continuous period of time.

Power loss and flux density distributions in the T-joint of a three phase transformer core

Abstract: A three phase transformer test facility has been used for measuring the localized power loss and flux distribution within the core. The flux and loss distributions in the T-joint of a core with simple double overlap joints have been investigated. The flux density distribution was measured by an array of search coils wound on individual laminations, and the localized power loss was found by measuring the initial rate of temperature rise using miniature thermocouples. For measurements made in the range of flux densities from 1.1 to 1.6 T, the inner edges of the yoke and limb laminations were the highest loss areas, up to 30% higher than the mean core loss. These regions of high power loss were found to be due to a high third harmonic flux density component being present. The fundamental component of flux density tended to follow the rolling direction of both yoke and limb laminations; however, some deviation from the rolling direction was present in the case of other harmonics.

Computor organ using parallel processing

Abstract: Parallel processing is used in a computor organ of the type wherein musical notes are produced by computing at regular time intervals the amplitudes at successive points of a musical waveshape, and converting the amplitudes to tones as the computations are carried out. Each amplitude is evaluated by concurrently calculating in parallel channels different subsets of the Fourier components for the same point, then combining the components to obtain the waveshape amplitude. In a typical embodiment, low order harmonic components are calculated in one channel and high order harmonics in another channel; in another embodiment, odd and even harmonics are calculated in separate, parallel channels. A recirculating shift register, shifted in unison with successive component calculations, advantageously stores the harmonic coefficients used in the amplitude calculations.

Parametric instability of plasma waves in a magnetic field, due to high-frequency electric fields

Abstract: We have observed experimentally the parameteric excitation of ion acoustic waves and cyclotron harmonic waves by a high-frequency electric field with frequencies near the harmonics of the cyclotron frequency. We have verified both the wave-vector and the frequency selection rules. The measured threshold fields and growth rates are in good agreement with theory.

Prediction of the Spectral Content of Combination Tone Noise

Abstract: Combination tone noise is generated by a pattern of rotating shock waves in the inlet of turbofan engines when the relative tip speed of the fan blades is supersonic. A method is presented for determining the expected distribution of sound power among the harmonics of engine rotation frequency, based on the spectral analysis of an almost periodic succession of pulses. The spectral distribution of combination tone noise is found to depend on two statistical — crfl, the standard deviations of the sequence of shock wave amplitudes; and cr£, the standard deviation of the sequence of time intervals between successive shock waves. The spectral distribution of sound power is found to depend more critically on

Theory of the Three Phase Salient Pole Type Generator with Bridge Rectified Output - Part II

Abstract: The theoretical equations, describing the characteristics of a three phase salient pole type AC generator with asymmetrical damperwindings and bridge rectified output are derived. All resistance and rectifier drops are neglected; only the first winding MMF's and the first two permeance harmonics are considered. All winding inductances are defined in detail in App. I and are expressed in absolute and per-unit values. A set of equations is derived, defining the mutual relations between DC output voltage and current, start and duration of commutation, commutation current, constant and variable field current, damper circuit currents and instantaneous DC voltage fluctuations. By the use of two simplifying assumptions, this set is converted into explicit equations for the above values. These show that the inductance, determining the length of the commutation period is the equivalent of the average between the direct and quadrature subtransient inductances. Both a Star as well as a Delta connected stator winding is discussed. All equations can be expressed in generalized machine parameters. A numerical example is included.

System for detecting an object within a magnetic field

Abstract: The specification discloses a system for detecting a marker secured to an object when the object is positioned within an interrogation zone having a magentic field periodically varying at a predetermined fundamental frequency. The magnetic field is generated by a coil unit including a plurality of loops of rigid hollow metal pipe which is electrically resonated by capacitors and energized by an electrical signal having a frequency equal to the resonant frequency of the electrical circuit. Phase-lock loop circuitry is provided to maintain the drive to the pipe loops at a frequency equal to the resonant frequency of the pipes, irregardless of variance in the load imposed in the magnetic field generated by the pipes. The transmitting pipe loops are also driven by electrical signals of less than full wave, such that the generated magentic field has improved distortion characteristics. The marker of the invention generates detectable signals containing harmonics of the fundamental frequency of the alternating magnetic field. Detection circuitry is provided to detect the harmonic signals generated by the marker. The detection circuit is gated in synchronism with the less than full wave driving signal applied to the transmitting coil. A dropout circuit is provided to disconnect the transmitting circuitry in case a heavy load is imposed upon the magnetic field.

Genetic meaning of zooecial chamber shapes in fossil bryozoans: fourier analysis.

Abstract: Fourier harmonic amplitudes quantitatively characterize chamber shapes of fossil tubular bryozoans. The odd-numbered harmonics, particularly the seventh, carry evolutionary information. The phenotypically plastic second and sixth harmonics measure zooecial orientation and packing, respectively. As a measure of crowding, the sixth harmonic reflects mechanistic growth response to paleoenvironmental conditions.

High‐frequency electromagnetic response of the Moon

Abstract: It is shown that the contribution of higher harmonics to the lunar transfer functions for the tangential components of the surface magnetic field is significant at frequencies greater than 0.01 Hz. The inclusion of the higher harmonics shows that there are two distinct transfer functions corresponding to the components of the tangential surface magnetic field perpendicular and parallel to the direction of the wave vector of the external disturbance forcing the lunar induction. The dependences of these transfer functions on frequency and location are determined. The effects of the higher harmonics can: (1) account for a hitherto unexplained feature in the Apollo 12-Explorer 35 transfer functions, namely the rolloff at high frequencies; and (2) offer a possible explanation for the frequency dependence of the difference between the transfer functions for the two orthogonal components of the surface magnetic field. The harmonic response of a simple current layer model of the moon is derived.

Eddy Current Losses in Solid Pole Shoes of Synchronous Machines at No-Load and on Load

Abstract: An improved method of calculation is described which the eddy current reaction and the variable permeability of the solid pole are taken into account. At no-load, the saturation of the stator teeth is fully considered and shows that tooth-ripple harmonics are increased by it. On load, the stator MMF harmonics of integral-slot windings are determined and added with due regard of their phase shift.

Harmonic Generation of Shallow Water Waves Over Topography

Abstract: We investigate the reflection and nonlinear interaction between the first and second harmonics of a two-dimensional Boussinesq wavetrain. Effects of topography are included, the depth departing from a constant in a finite region. It is found that topography can speed up or retard energy transfer between first and second harmonics. The reflection coefficient in the present context is significantly different from the one obtained by using linear theory. This is partly due to partitioning of energy between harmonics.

Analysis of Closed-Loop Conveyor Systems

Abstract: A closed-loop conveyor system having a single loading station, a single unloading station, and operating with time-varying input and output flow rates, is analyzed. The balance of flow on the conveyor is represented by a difference equation. Solutions of that difference equation appear naturally in terms of a Fourier series expansion. An important description of the system is its frequency response. Singularities in the frequency response represent cases of incompatibility. Incompatibility is shown to depend on the ratio T/P of conveyor period to work-cycle period, and on the presence of harmonics in input and output flow rates. Solutions for several specific cases are presented graphically.

Sum and Difference Frequencies in Vibration of High Speed Rotating Machinery

Abstract: A vibration incident on a gas turbine engine was noted where two major excitation frequencies were involved—an excitation synchronous with rotor rotation, associated with rotor unbalance, and an asynchronous excitation associated with fluid inadvertently trapped in the rotor. Spectral analysis of the vibration wave form revealed not only the two base excitation frequencies, but also a component at the difference frequency. A mechanism for generating such a difference frequency is hypothesized—the truncation of the basic “beat frequency” wave form by virtue of clearance in the rotor bearing system. Fourier analysis of the hypothesized excitation wave form indicates that components at difference frequency are indeed generated, and also at the sum frequency and a spectrum of higher harmonics and side band frequencies. The hypothesized wave form’s spectral analysis bears a remarkable resemblance to the measured spectrum, except that low frequencies appear to have been greatly amplified in the experimental case, and high frequencies attenuated. This latter fact is attributed to the transmission characteristics of the gas turbine stator system, and is probably responsible for the lack of precise correspondence between the measured and hypothesized wave forms.

A computer program for the geometrically nonlinear static and dynamic analysis of arbitrarily loaded shells of revolution, theory and users manual

Abstract: A digital computer program known as SATANS (static and transient analysis, nonlinear, shells) for the geometrically nonlinear static and dynamic response of arbitrarily loaded shells of revolution is presented. Instructions for the preparation of the input data cards and other information necessary for the operation of the program are described in detail and two sample problems are included. The governing partial differential equations are based upon Sanders' nonlinear thin shell theory for the conditions of small strains and moderately small rotations. The governing equations are reduced to uncoupled sets of four linear, second order, partial differential equations in the meridional and time coordinates by expanding the dependent variables in a Fourier sine or cosine series in the circumferential coordinate and treating the nonlinear modal coupling terms as pseudo loads. The derivatives with respect to the meridional coordinate are approximated by central finite differences, and the displacement accelerations are approximated by the implicit Houbolt backward difference scheme with a constant time interval. The boundaries of the shell may be closed, free, fixed, or elastically restrained. The program is coded in the FORTRAN 4 language and is dimensioned to allow a maximum of 10 arbitrary Fourier harmonics and a maximum product of the total number of meridional stations and the total number of Fourier harmonics of 200. The program requires 155,000 bytes of core storage.

An experimental study of the shapes of microwave spectral lines in gases at low pressures

Abstract: A spectrometer which has been used for studying the shapes of microwave spectral lines in gases is described. Radiation from a klystron was passed through a waveguide cell and detected with a crystal diode. The klystron frequency was modulated sinusoidally with a frequency of f/n, n being integral and in the range 1 to 5, and the detected output at frequency f was observed on an oscilloscope. In this way the first five harmonics of the modulation frequency were observed. The mean klystron frequency was swept slowly across the spectral line and the frequency separations between the various maxima and minima of the harmonic outputs were measured using frequency markers. The results were compared with those deduced from three theoretical lineshape models. Three cases were studied; the self broadened (J,K)=(6,6) line in the inversion spectrum of NH3 the same line broadened by He; and the self broadened J=1 to 2 line in the rotational spectrum of COS. In all cases the lineshape was represented to within the experimental error by a Lorentz shape corrected for the Doppler contribution.

The generation of sound in a Rijke tube using two heating coils

Abstract: By using one setting of the positions of two flat, spiral heating coils it is possible to generate only the even harmonics of a Rijke tube. For another setting it is possible to generate only the third, sixth, ninth harmonics, and so on. The experimentally determined positions are in agreement with those predicted from the Rayleigh criterion.

Flux penetration in a ferromagnetic material including hysteresis and eddy-current effects

Abstract: Hysteresis in a ferromagnetic material is represented by an idealized elliptical magnetization characteristic that neglects harmonics and enables flux density and magnetizing force, when expressed in terms of phasor vectors, to be related by complex permeability. This concept, together with the assumption that all field quantities have a linear relationship and vary sinusoidally in time and space, is then used to obtain steady-state solutions for electromagnetic field problems in materials including both hysteresis and eddy-current effects. Computed values are determined for the flux distribution and losses in semi-infinite and finite-thickness plates.

Cyclotron harmonic waves in an inhomogeneous plasma. II. Experiment

Abstract: For pt. I see ibid., vol. 14, no. 5, 473. Electrostatic cyclotron harmonic waves were excited in an inhomogeneous plasma column with axial magnetic field by means of an externally applied r.f. capacitor field. Amplitude and phase of the r.f.-potential inside the plasma were measured with a probe. For frequencies just above the harmonics of the electron cyclotron frequency forward waves were found in the low density region of the plasma where the local density omega p2 is less than the hybrid density omega pH2= omega 2- omega c2. For frequencies just below the harmonics backward waves were found in the dense core of the column, where omega p2> omega pH2. In the latter case standing waves (Buchsbaum-Hasegawa-modes) were found which are set up by two oppositely propagating backward waves with group velocities directed towards the dense plasma core. Phase measurements indicate an excitation near the hybrid layer and allow a direct determination of the phase condition for the Buchsbaum-Hasegawa resonances to occur. In applying a short microwave pulse to the capacitor plates short wave trains were excited in the plasma. Time of flight measurements show that both the forward and the backward waves are excited around the hybrid layers. Multiple reflection of backward wave trains at the hybrid layers were observed.

Stresses in a Semi-Infinite Body Subjected to Uniform Pressure on the Surface of a Cavity and the Plane Boundary

Abstract: In this paper, the three-dimensional solutions for the stresses and displacements in a semi-infinite body having a spherical cavity are given for the case of a uniform pressure applied to the plane boundary and to the surface of the cavity. In analysis, the method of Boussinesq's two harmonic stress functions are used. The two stress functions are given by simple expressions of the cylindrical and spherical harmonics. The boundary conditions both on the face of the plane and on the surface of a cavity are satisfied with the aid of Hankel transform and the relations between the two harmonics. Further, numerical calculations are carried out for four different values of the radius of a cavity.

An analysis of surface energy anisotropy data using lattice harmonics

Abstract: Measurements of thermally equilibrated grain-boundary grooves in wires exhibiting bamboo structure are numerically analysed and an analytical expression describing the complete γ-plot is obtained by a least-squares fit of a lattice harmonic series. The results are compared with those obtained using a Fourier analysis technique described in a previous paper. It is suggested that, with present experimental accuracies, a combination of both methods is required.

Emission of coherent microwave radiation from a relativistic electron beam propagating in a spatially modulated field.

Abstract: Intense electromagnetic radiation has been observed from the interaction of an intense relativistic electron beam and a spatially modulated magnetic field. An efficiency of conversion of electron kinetic energy into microwave radiation of the order of 1% has been achieved, with total rf power radiated greater than 30 MW. A parametric study has shown that the device has not reached saturation over the range of parameters tested. The experimental results show that the new device differs from conventional generators in several respects. For example, the frequency and the bandwidth of the rf radiation can be tuned over a wide range and the power at the harmonics of the fundamental frequency (∼ 1010 Hz) is the same order of magnitude as the power in the fundamental. Infrared radiation has also been observed; more than 1 MW has been found even for wavelengths under 10 μm.

This business of harmonics

Abstract: The rapid growth of thyristor-controlled loads is causing concern to the electricity-supply authorities. Methods of reducing the resulting harmonic effects are examined.

Frequency separation in structure of solar continuum radio bursts

Abstract: A plot of frequency separation in fine structure in solar continuum radio bursts against emission frequency indicates that the frequency structure cannot represent local proton plasma frequency modulation. However, the observations are consistent with the interpretation of the frequency structure as harmonics of the local electron cyclotron frequency and lead to reasonable estimates of the ratio between magnetic and kinetic pressures in stable coronal magnetic field configurations producing continuum radio sources.

Superlattice harmonic generator & mixer for electromagnetic waves

Abstract: The disclosure relates to a device for generating electromagnetic waves which have wavelengths different from an input wavelength to the device. The device consists of man-made superlattice structure fabricated by epitaxial deposition techniques to which at least one electromagnetic wave is applied. The input wave has an electric field component parallel to the longitudinal axis of the superlattice structure. Because of the special characteristic of the superlattice structure, it is possible to obtain as outputs all the odd harmonics of the input wavelength. By applying an electric field parallel to the longitudinal axis of the superlattice, it is possible to obtain both odd and even harmonics of the input wavelength. By switching the electric field, a gating action is obtained. To select the desired harmonic, appropriate filters are used. Mixing as well as harmonic generation is possible with the arrangements disclosed by applying a plurality of input wavelengths which by multiple photon processes produce outputs having relatively long wavelengths compared to the input wavelength. The mixed outputs in both the presence and absence of an applied electric field are obtainable by filtering. Thus, inputs in the visible range may be mixed to provide outputs in the far infrared region which are not easily obtainable using prior art arrangements.

Resonances of an Antenna Associated with the Excitation of Ion Bernstein Modes

Abstract: The impedance with respect to the plasma of a wire parallel to the magnetic field is studied theoretically and experimentally. The theoretical boundary‐value problem is solved through linearization and completed by numerical calculation. The wire impedance as a function of frequency is shown to exhibit peaks above the ion cyclotron harmonics corresponding to the passbands of ionic Bernstein waves. Experiments are performed in a single‐ended Q machine and led to results in good agreement with theory.

Reflection amplification in thin layers of n-GaAs

Abstract: Theoretical expressions are developed for the stability criterion and admittance of a thin coplanar GaAs reflection amplifier. The traveling-wave dispersion relation includes diffusion. The cathode boundary condition includes velocity modulation, injection, and distributed inhomogeneity effects. The admittance includes displacement currents running outside the semiconducting layer. The results show that the second to fifth harmonics may be more nearly unstable than the fundamental. Experiments on a coplanar epitaxial sample yield stable linear net gain at frequencies in the range 2 GHz-8 GHZ.