Showing papers on "Harmonics published in 1969"

A circular-harmonic computer analysis of rectangular dielectric waveguides

Abstract: This paper describes a computer analysis of the propagating modes of a rectangular dielectric waveguide. The analysis is based on an expansion of the electromagnetic field in terms of a series of circular harmonics, that is, Bessel and modified Bessel functions multiplied by trigonometric functions. The electric and magnetic fields inside the waveguide core are matched to those outside the core at appropriate points on the boundary to yield equations which are then solved on a computer for the propagation constants and field configurations of the various modes. The paper presents the results of the computations in the form of curves of the propagation constants and as computer generated mode patterns. The propagation curves are presented in a form which makes them refractive-index independent as long as the difference of the index of the core and the surrounding medium is small, the case which applies to integrated optics. In addition to those for small index difference, it also gives results for larger index differences such as might be encountered for microwave applications.

Harmonic reduction in multiplex convertors by triple-frequency current injection

Abstract: Conventionally, harmonic filters have hitherto been used to reduce the very undesirable effects of current harmonics in the input current to convertor equipment. The present paper describes an investigation into a new method of eliminating these current harmonics at the source, this being a more fundamental method than merely suppressing their consequences. The cost of the new method is not likely to be more expensive than elaborate filter equipment. The process consists of modifying the primary current waveform by the injection of triple-frequency currents into the convertor. An explanation of the fundamental action is presented, together with an analysis of the effects of triple-frequency current injection upon the harmonics generated by duplex convertor equipment.

Finite-Element Postbuckling Analysis of Thin Elastic Plates

Abstract: reflects the Fourier stiffness distribution profile (A convergence trend is exhibited because the higher-order harmonics of the solution diminish in magnitude) The total deflection obtained by summing the Fourier contributions is plotted along the plane of symmetry (6 = 0-180°) in Fig 5 Also shown are the deflections obtained for axisymmetric shells with uniform stiffness distributions corresponding to the magnitude of the stiff and weak sides As expected, these results bracket the solution for the variable-rigidity shell The same problem was a run with only three and five terms retained in the stiffness series expansions Variation in the third harmonic of deflection (w%) along the meridian is plotted in Fig 6 for the cases where K is set equal to 3, 5, and 10 The higher harmonic coupling effects appear to diminish as more terms are retained in the solution (ie, as K increases) For economic purposes, the number of integration points used in obtaining the preceding numerical results was N = 26 The basic character of the solutions is illustrated for the relatively coarse grid Additional studies have shown increased accuracy when a finer finite-difference mesh is taken; this should be considered when the results presented in this paper are interpreted

Wave Propagation in Microstrip Transmission Lines

Abstract: With the growing popularity of integrated circuits the microstrip transmission line has received wide attention from the microwave community. A common feature that most known analytic solutions share is an assumption that the fundamental mode of propagation resembles a TEM wave closely enough to permit various electrostatic approximations such as conformal mapping, relaxation method, and variational principle. Such solutions although quite useful at low frequencies neglect the fact that the actual propagating modes cannot be TEM. The dispersion of non-TEM waves causes, at microwave frequencies, considerable deviations in effective dielectric constant and velocity of propagation from those values obtained by the electrostatic approximation. In this paper it is shown that the modes that exist on a microstrip transmission line must be hybrid in order that all boundary and continuity conditions be satisfied. In this rigorous analysis the hybrid modes are decomposed into sums of TE and TM (or LSE and LSM) space harmonics, each satisfying the wave equation and the external boundary conditions and their total satisfying the continuity conditions and boundary conditions on the strip. The final outcome of the analysis is a pair of coupled integral equations that are solved numerically. The results indicate that the fundamental hybrid mode is propagating at all frequencies and approaches the known static solutions at low frequencies. However, the correct solution deviates from the static approximation at microwave frequencies. Of particular interest is the fact that as the dielectric constant of the substrate increases the frequency range at which the TEM approximation is valid decreases. The results obtained show close agreement with available experimental data.

Second-Harmonic Generation of Light at the Boundary of an Isotropic Medium

Abstract: Measurements of second-harmonic generation of light from liquid-air interfaces are reported. A physical model is proposed in which the observed harmonics arise from the electric double layer at the surface. The experimental results from the surfaces of various liquids and solids are discussed in the light of this model.

Harmonic generation and submillimeter wave mixing with the josephson effect

Abstract: By observing constant‐voltage steps from Josephson junctions at voltages as high as 17 mV we deduce that junctions can generate harmonics up to frequencies as high as 8200 GHz. In consonance with this, submillimeter wave laser detection, harmonic generation, and mixing are demonstrated. These results suggest a model for the upper frequency limit of the Josephson effect.

Nonlinear Effects and Turbulent Behavior in a Beam-Plasma Instability

Abstract: Continuing experimental studies of beam‐plasma interactions in a magnetic field have shown an assortment of nonlinear effects to be present during a well‐developed instability. Observations have been made of: the vanishing of the spatial growth rate; electron cross‐field diffusion in synchronism with the unstable electric field; generation of harmomics of the fundamental interaction frequency up to the seventh; similarities in the spatial behavior of all seven harmonics; and the existence of a wavenumber power spectrum whose average behavior over the domain of the harmonic peaks is proportional to k−5±0.5, in agreement with certain theories of plasma turbulence. The data suggest that the large‐amplitude fundamental electric field is the driving force for the nonlinearity that generates the harmonics, and that the fundamental, and the harmonics as well, represent waves traveling with a phase velocity equal to that of the slow space‐charge wave on the electron beam. An interpretation is offered in terms of ...

Eddy-current and hysteresis effects in rotating machines

Abstract: Hysteresis in the magnetic circuit of a rotating machine is represented by an approximate method which neglects harmonics and enables the hysteresis motor to be analysed by the equivalent Kron primitive machine. The method is extended to hysteresis and eddy-current effects in hysteresis, induction and synchronous machines; steady-state equivalent circuits are derived for the hysteresis motor and induction machine.

Observations of the Directional Characteristics of Sea Waves

Abstract: Summary Simultaneous records of orbital velocity and pressure disturbance in wind generated waves have been analysed by power spectral methods, to obtain the first five angular harmonics of the directional spectrum. The observations were made at a coastal site, offshore from a gently sloping beach, where the bottom topography was sufficiently simple to permit corrections for the effects of refraction. The orbital velocities were measured by an electromagnetic flowmeter and the pressure disturbance by an N.I.O. pressure recorder. A capacitance probe was also available for recording the surface elevation. A computer program has been developed which computes the auto and cross-spectra of the pressure and velocity components, the angular harmonics and a smoothed estimate of the directional spectrum directly from data which were recorded digitally on punched paper tape. Estimates of the mean direction and the width of the directional spectrum and its skewness, have been obtained for a wide range of frequencies and related to wind conditions in the generating area. After correction for refraction, the mean direction of the waves was found to correspond well to the mean wind direction. For waves generated by a reasonably constant wind field, the spectrum width exhibits a general tendency to increase with frequency. At low frequencies the spectrum width corrected for refraction is not inconsistent with the resonance angle given by Phillips’ theory, while at frequencies just above the transition frequency defined by the combined Miles-Phillips theory, the spectrum is appreciably narrower than the resonance angle. The smoothed directional spectrum estimate based on five harmonics gives no indication of bimodality in the spectrum. A method of obtaining improved angular resolution using an array of three flowmeters to obtain four additional harmonics was only partially successful on account of turbulent interference generated by the pier structure to which the sea units were attached. The surface power spectrum was found to fit the equilibrium power law at high frequencies under saturation conditions. A spectrum obtained under conditions very similar to those in the SWOP project has been compared with the SWOP spectrum. Marked differences between the two suggest that bottom friction is a major influence on waves in coastal waters. The attenuation of the waves in depth was determined from the ratios of the surface elevation and pressure spectra. No significant departure

A General Approach to Harmonic Current Generation by HVDC Converters

Abstract: A general approach to the computation of current harmonics is presented for the ac side of HVDC transmission installations considering both normal and abnormal harmonics that can arise from harmonic distortion of the supply waveform and perturbations in the control firing pulses. Attention is given to 12- pulse converter operation and to alternative types of automatic control. A comprehensive digital computer program is described and examples of computed harmonics are given.

Digital Generation of Low-Frequency Sine Waves

Abstract: Generation of approximately sinusoidal waveforms by a digital method is described. Very low frequencies (below 1 Hz) are easily obtained without the use of large inductors or capacitors, and the method is fully compatible with integrated circuit techniques. A process equivalent to nonrecursive digital filtering is used to remove the majority of harmonics from a binary waveform generated by a feedback shift register, leaving the fundamental together with only a few high-order harmonics of small amplitude.

Analysis and Simplified Representations of Rectifier - Inverter Reluctance-Synchronous Motor Drives

Abstract: Methods of analyzing six-step and pulse-width- modulated (PWM) types of rectifier-inverter reluctance-synchronous motor drive systems are set forth. In this development the harmonic components due to the switching of the rectifier are neglected, and the operation of the inverter is expressed in a reference frame rotating in synchronism with the fundamental frequency of the inverter output voltages. In the case of the PWM inverter, the Fourier series expansion of a pulse train is used to express the operation of this type of inverter in the synchronously rotating reference frame. Simplified representations are obtained by neglecting the harmonics due to the inverter switching. These simplified representations are verified by comparing the results obtained from a computer study using these representations to those obtained using a detailed simulation of the system. The analysis set forth and the simplified representations that are developed can be used to determine small-displacement system stability, as well as provide a simple and direct technique of predicting the dynamic and steadystate performance of these involved systems. Moreover, the equations established for the PWM inverter can also be used in conjunction with an induction motor drive.

Distribution pattern of cochlear harmonics.

Abstract: This study is designed to determine whether or not traveling waves accompany harmonic distortion products generated in the cochlea, and also to describe the amplitude distribution of these nonlinear components. Cochlear microphonics were monitored with the differential electrode technique from the first and third turns of guinea pig cochleas. Cancellation of the distortion components was attempted by introducing bone‐conducted pure tones of the frequency of the harmonic and of controllable magnitude and phase. It was demonstrated that harmonic components can never be canceled simultaneously throughout the cochlea. It was shown that the reason for this inability to cancel is that harmonics are not distributed in the cochlea as their own frequency would indicate, but instead they are prominent in the region where their fundamentals are strong.

Core losses in magnetic materials at very high flux densities when the flux is not sinusoidal

Abstract: Presently, insufficient material data is available to predict core losses at high flux densities with complex flux waveforms. A steel tester is described whereby this data can be obtained from electrical steel at densities in excess of 20 kG. The flux wave-form can be selected and controlled to study the influence of harmonics and to simulate actual flux conditions existing in magnetic circuits. An electromechanical waveform generator is capable of synthesizing waveforms of 30 to 90 Hz fundamental with phase and amplitude selected odd harmonics up to the eleventh. This signal is amplified to excite Epstein sample strips placed in a water-cooled test yoke up to 140 kA/m. Feedback technique is applied to keep total distortion between input signal and flux waveform below 4 percent at peak excitation. The flux density is measured with air-flux compensated search coils. A calorimetric method is used to measure core losses by recording the temperature rise of thermistors placed between sample strips. Some test results are presented to demonstrate the flexibility and usefulness of the steel tester.

Equivalent Circuits for Single-Phase Squirrel-Cage Induction Machines with both Odd and Even Order MMF Harmonics

Abstract: The special winding connections used in certain dual voltage or multiple-speed single-phase induction motors lead to large, even order MMF harmonics. The calculation procedures used to evaluate machines of this type must include proper representation of these harmonics. This paper develops the general describing equations for a two-phase machine with arbitrary MMF distributions. These equations are then specialized to yield harmonic equivalent circuits for steady-state operation. Proper interconnection of these harmonic circuits yields equivalent circuits representing actual machine windings. Examples are given, including circuits for representation of consequent pole windings. A numerical example of a machine operating with only its north poles excited is also included.

Optimum Second‐Harmonic Generation in Nondegenerate Semiconductors using dc Electric Fields

Abstract: In this paper the author has analytically investigated the use of dc electric fields of arbitrary strength, for the generation of second harmonics of high‐frequency electromagnetic waves in a nondegenerate semiconductor. Boltzmann equation techniques have been employed to describe the motion of free carriers inside the semiconductor; the only form of carrier scattering considered is acoustic phonon scattering. The curve of second‐harmonic intensity vs dc field exhibits a maximum, thus illustrating that there is an optimum value of the dc field for which the generation can be most efficient.

A General Theory of Commutated Networks

Abstract: A state-space approach is used to derive an exact closed-form solution for the steady-state and transient response of a general commutated network terminated in a multiport. By expanding the time-varying transfer function N(p, t) in a Fourier series, the transfer function at input frequency N_{0}(p) , and the transfer functions at harmonic frequencies N_{m}(p) are then calculated. A necessary and sufficient condition for the recovery of the input signal, without distortion due to the harmonics, is given. From the general analysis, we immediately obtain previously available results on comb filters, n -path filters, sample-data filters, etc., as special cases. The resulting closed-form solutions in terms of element values are most suitable for computer simulation in which the performance of the commutated network is to be evaluated as the element values are varied.

Microstrip High-Power High-Efficiency Avalanche-Diode Oscillator

Abstract: A simple microstrip oscillator circuit has been designed and operated satisfactorily with high-power high-efficiency avalanche diodes. The power output obtained from a single diode chip is ahout 100 watts at 1 GHz with efficiencies of 25 to 30 percent. Mechanical tuning capability of a few hundred megahertz and a combined power output from series-connected diodes have been demonstrated using the circuit. An essential part of the circuit is a low-pass filter tuning section which enables the circuit to support high-order harmonics including the transit-time frequency and prevents them from getting to the load. Probe measurements of the electric field show strong second as well as third harmonics inside the circuit.

Extra low‐frequency terrestrial radio‐wave field calculations with the zonal harmonics series

Abstract: Use of the zonal harmonics series for calculating the terrestrial wave guide fields directly is described. The analysis is extended to include radio waves propagating into sea water or below the earth's surface. A sample calculation of ELF radio waves is analyzed into a direct wave and a wave that has traveled the circumference of the earth. The location of the ripples in the standing wave pattern is compared with the locations predicted by less exact but simpler mathematical models. It has been found that approximate formulas check within a few percent of the exact analysis when used to estimate positions of maxima and minima near the antipode. It is concluded that the exact analysis can be used to check various approximate formulas. Where possible the extension of the analysis to more complex models should be accomplished with the exact solution.

Transformation of Spherical Harmonics Under Change of Reference Frame

Abstract: Summary The problem of transforming spherical harmonics under a linear change of reference frame is solved analytically and numerically. In contrast to other methods both translation and rotation are treated with the same background theory which is comparatively straightforward and is formulated in geophysical terms; the directions of translation and rotation are arbitrary; and generally, combinations of harmonics of the same order can be dealt with equally as readily as individual harmonics. It is found that the expansion coefficients of a translated spherical harmonic are themselves spherical harmonics in the co-ordinates of the translation vector. As a special case, the potential of an eccentric dipole is briefly discussed. Very useful byproducts of this paper are the ways in which the given numerical algorithms can be used to evaluate any linear combination of harmonics.

Analysis of the Hysteresis Machine - Part I

Abstract: A theoretical model has been developed for the hysteresis motor by solving Laplace's equation for the field in the air gap and the rotor ring subject to appropriate boundary conditions. The hysteresis phenomenon is accounted for through the use of an elliptical approximation for the hysteresis loop. The relation between the magnitude of the fundamental components of the B and H waves is assumed to be linear and the phase shift between them, due to hysteresis, is assumed to be constant. However, an iteration procedure is described to account for the nonlinearity in the actual machine. A similar approximation is used to represent the minor loops described by the harmonic components of the field, and the effect of MMF and slot harmonics on machine performance is thus estimated. Rigorous analysis predicts and evaluates the "gap leakage field," which constitutes a part of the main field without penetrating the rotor material. The inclusion of this field in the model is shown to eliminate the nonrealistic assumption that the B and H waves in the rotor material are in phase. The model is used to evaluate the output torque and the EMF and power factor of the stator windings. A simple equivalent circuit is developed, in which the three fields present inside the machine, two in the air gap and one in the rotor, are represented by individual elements. The nonlinearity of the rotor material is represented in the equivalent circuit by a nonlinear impedance whose characteristics are directly predictable from the shape of the B-H curve. A comprehensive model has been obtained which is flexible enough to handle the different nonlinearities. It has been rigorously derived from the field equations, and therefore is expected to be very useful in further investigations of the hysteresis machine.

Tunable L-band high-power avalanche-diode oscillator

Abstract: An avalanche-diode oscillator that has achieved pulsed power output of 180 W at 1.3 GHz with 40% efficiency will be discussed. Frequency is tunable from 1.0-1.6 GHz with power variations less than 1 dB.

Three-phase inverter

Abstract: A three-phase inverter for producing a stepped voltage approximating to a sinusoidal form, and largely free of odd harmonics, wherein, for the purpose of producing each phase voltage a basic and two additional rectangular impulses are summed, the basic impulse being shortened in relation to a halfwave and occupying substantially the entire amplitude-time area of the phase voltage, and the additional impulses having a considerably smaller amplitude and shorter duration than the basic impulse. One of the additional impulses procedes and the other is superimposed on a basic impulse of the same polarity.

Error reduction logic network for harmonic measurement system

Abstract: The fundamental period of a complex periodic signal may be determined by measuring the periods of individual harmonics of the periodic signal and finding their smallest common multiple. A useful display of harmonics and their submultiples is called a period histogram. Since the fundamental period in a period histogram is an integral multiple of a number of harmonics and is characterized by a maximum amplitude pulse, the time of occurrence of the first maximum pulse may be taken to represent the fundamental period of the complex periodic signal. However, because the largest peak of the histogram does not always correspond to the fundamental frequency of a wave, occasional errors in the indication of pitch may result. Such errors may be obviated by examining the pitch signal developed from a histogram measurement, applying logical tests to determine its acceptability and, if the indicated pitch is found to be unacceptable, by substituting a more acceptable value.

Aircraft Antenna-Coupled Interference Analysis

Abstract: A mathematical model specifically for aircraft antenna-to-antenna electromagnetic interference analysis has been developed. Basically, the model consists of a two-level analysis: 1) frequency coincidence to indicate potential interference and 2) a detailed analysis involving power levels and receiver thresholds. A receiver and transmitter are selected from the input data, and their frequency bands are compared for coincidence. The frequency comparison includes the fundamental and significant harmonics as specified for the transmitter. If frequency coincidence is found, indicating potential interference, the worst-case power level at the receiver from the transmitter is computed using the shortest path along the aircraft surface. When the path is around the fuselage, allowance is made for shading (diffraction) effects. The power received is compared with the receiver threshold to obtain an EMI margin. Each case with an EMI margin above a specified value is listed in the computer output as are the frequencies involved and the computational method used. Margins are computed for each antenna combination of the two systems. This process is repeated for each transmitter and receiver on the aircraft. The method of analysis is presented with particular emphasis on the techniques used to obtain propagation paths and shading factors.

One‐Center Molecular Calculations with Unlimited Radial Basis. H2, HeH+, and LiH Centered on One Nucleus

Abstract: As a prelude to one‐center studies of the coordination center in ligand‐field problems, this paper gives results for LiH, HeH+, and H2 in their ground states. In each case the Hamiltonian and the orbital functions are expanded in series of spherical harmonics about the largest nucleus, the orbital expansions are truncated, and the resulting coupled integro‐differential equations are solved numerically for the radial function associated with each orbital harmonic. The result is a Hartree–Fock solution with limited angular basis but unlimited radial basis. The results for energy, quadrupole coupling constant, and other properties are reasonably close to the limiting Hartree–Fock results, and certain properties determined by the wave‐function at the nucleus are exact within the accuracy of the numerical method. For H2 at R = 1.4 bohr, the best calculated total energy is − 1.104 hartree for an expansion truncated after four spherical harmonics, s + p + d + f(− 1.128, extrapolated to many harmonics; − 1.133, H...