Showing papers on "Harmonics published in 1970"

Power System Dynamic Equivalents

Abstract: This paper describes a method for determining a simplified equivalent mathematical representation of portions of a power system for transient stability analysis The method leads to equations that do not correspond directly to a system composed of normal power system components Conditions under which it is possible to obtain such an equivalent are given, and the results of applying the method to the 118-bus IEEE test system are reported

Nonlinear Effects in Surface Acoustic Waves

Abstract: Experimental results on harmonic generation and parametric mixing of surface acoustic waves are reported. Harmonics of signals at 615 MHz and 1.69 GHz propagating on YZ LiNbO3 substrates were observed: the experiments on parametric mixing used two surface acoustic waves at f1=490 MHz and f2=1.09 GHz. Optical probing technique was used to observe directly the spatial variations of the harmonics, the sum, and difference frequency signals. It will be shown that the nonlinear interactions can be phenomenologically described by coupled amplitude equations. The nonlinear coupling constants are determined by comparing the experimental results with the calculations.

Generation of Harmonics and Subharmonics of the Josephson Oscillation

Abstract: The observation of harmonics and subharmonics of the Josephson oscillation is shown to be in agreement with a rather simple model of the junction. The generation of harmonics provides an explanation of induced steps in the current‐voltage characteristic which occur at submultiples of the usual induced step voltages. The subharmonic oscillation is seen to be a relaxation‐like process which can be easily understood in terms of a mechanical analog.

Analytical, numerical, and experimental investigation of guided waves on a periodically strip-loaded dielectric slab

Abstract: The electromagnetic waves guided by a periodically strip-loaded dielectric slab were investigated. The determinantal equation was obtained by assuming that the strips are narrow as compared to all other linear dimensions. Numerical results involving different combinations of the linear and dielectric parameters are presented in terms of k-\beta diagrams. The amplitudes of the space harmonics were computed and are discussed in connection with the characteristic phenomena such as radiation and coupling. In particular, the relations between the attenuation of the guided waves and the space-harmonic amplitudes are pointed out. As an interesting phenomenon, real solutions have been found to occur in the complex-wave region and this new result has been explained in the light of the space-harmonic amplitudes. The numerical results in the backward-radiation region have been verified experimentally by two different methods: by measuring the phase and amplitude variation in the near field and by calculation from radiation patterns. In both cases, good agreement with the theoretical results has been obtained.

Temperature Effects on High‐Frequency Beam Plasma Interaction

Abstract: The dispersion equation corresponding to the interaction of an electron beam with a Maxwellian plasma has been solved in quasistatic and infinite geometry approximations. Two representative beams are considered: a parallel beam with isotropic velocity spread and a helical beam with different longitudinal and transverse temperatures. The aim of the work is to predict the frequency, growth rate, and wavenumbers of the most unstable waves as functions of the basic beam and the plasma parameters. The results of the calculations are presented in graphs suitable for comparison with the experiments. The effect of plasma and beam temperatures on the spectrum of the instabilities is discussed in detail. It is shown that the plasma temperature reduces the growth rate of the instabilities at cyclotron harmonic frequencies while a velocity spread in the helical beam suppresses the instabilities everywhere, except in the vicinity of the cyclotron harmonics.

Audibility of high harmonics in a periodic pulse.

Abstract: A periodic pulse consisting of sufficiently narrow pulses has a frequency spectrum which contains all harmonics with equal amplitude. Owing to the limited resolving power of the hearing organ, only the low harmonics can be perceived separately. The high harmonics are heard together as one complex signal. We have found that harmonics above a certain number are audible when spectrally absent (the other harmonics being present at normal amplitude). The solution of this seeming paradox is to be found in an analysis of the time structure of the signal. This time analysis of the stimulus is (in a limited way) possible at the basilar membrane because of its limitation in frequency‐resolving power.

Optical probing of acoustic surface‐wave harmonic generation

Abstract: The growth of nonlinearly generated harmonics of acoustic surface waves in LiNbO3 substrates has been observed directly by an optical probe. The attenuation of acoustic surface waves as a function of the level of input power and loss of energy to the nonlinearly generated harmonics is measured. The large nonlinear coupling to the high harmonics of surface acoustic waves, which is an encouraging sign for parametric amplification, may impose some limitations on linear devices at high power levels.

Octave jumper for musical instruments

Abstract: A bass or other guitar has a transducer for each of its strings, and each transducer is connected to an octave jumping circuit which lowers the musical tone produced by the individual string, all without loss of either harmonics or amplitude variations. The wave form of the fundamental frequency of each musical tone is squared, divided by two and then amplitude modulated to follow the amplitude envelope of the original tone. The modulated square wave contains only odd harmonics of the lowered frequency fundamental. The missing even harmonics are restored by combining with the modulated square wave the original tone containing all of its harmonics.

Nonlinear Effects in Microwave Acoustic LiNbO3 Surface‐Wave Delay Lines

Abstract: Nonlinear effects have been observed in LiNbO3 acoustic surface‐wave delay lines operating at a fundamental frequency of 905 MHz. Second‐, third‐, and fourth‐harmonic generation, and their buildup and subsequent decay with distance, have been measured using laser‐light deflection. The acoustic power entering these harmonics can be made comparable to that in the fundamental, since surface‐wave attenuation has been seen to be dependent on input power. In fact, under certain conditions harmonic power is returned to the fundamental causing a region of negative attenuation or “gain.” Similar effects have been observed for the sum and difference frequencies (mixing) when two input frequencies are used. For linear operation at 905 MHz, surface‐wave devices using Y‐cut Z‐propagating LiNbO3 should be limited to power densities of 10 mW/mm.

Calculation of transfer functions in grid-controlled convertor systems. With special reference to h.v. d.c. transmissions

Abstract: In high-power grid-controlled convertor systems large parallel capacitor batteries are usually installed and connected to the a.c. busbar at the same point as the convertor. They can be used either for filtering harmonics, e.g. as parts of tuned filters, or for the generation of reactive power, or both. The capacitive components introduced complicate the dynamic behaviour of the convertors considerably, and thus the system cannot be described by simple convertor theory. In the paper, the frequency response of such a system is deduced, using the concept of ‘conversion functions’ introduced to systematise and simplify the calculations. The frequency response for the current-control loop is deduced with reference to h.v. d.c. transmissions, but the results are applicable to any kind of rectifier load. The numerical calculations are laborious and require the use of a digital computer. The comparison between calculated and simulator-measured frequency responses for two practical h.v. d.c. transmissions shows satisfactory agreement. The calculated transfer functions are useful for the synthesis of the current-control system and allow an inexpensive study of the effects of system changes on the achievable speed of response.

Pulse width modulated inverter adaptive logic

Abstract: A pulse width modulated inverter is disclosed wherein adaptive logic is provided to control conduction of the switch means in the inverter. This logic controls the inverter switching rate and modulating pulse and notch width so that the power inverter section does not overheat because of a switching rate or fail because of a narrow modulating pulse. The adaptive logic is responsive to pulse width, notch width and a maximum or minimum carrier frequency all controlling the change of the ratio of carrier frequency to fundamental frequency. A three-phase system is described wherein the ratio of carrier to fundamental frequency is capable of being maintained at 3:1, which establishes a non-symmetrical wave with second harmonics in the fundamental output frequency yet which establishes a higher output voltage than a ratio of 6:1 of the carrier to fundamental frequencies and eliminates a large step of voltage when changing from a carrier to fundamental frequency ratio of 6:1 up to an unmodulated six-step output voltage from the inverter.

Input Generators for Digital Sound Synthesis

Abstract: A fast method is described for generating a periodic discrete‐time signal with harmonics of equal amplitude and a fundamental frequency which is not necessarily an integral fraction of the sampling frequency (as with ordinary pulse generators) Such a signal can be used as input to digital filters for the synthesis of speech and music

Field-harmonic theory of slip-ring motor taking multiple armature reaction into account

Abstract: The voltage equations of the slip-ring motor including the multiple armature reaction, i.e. the primary, secondary and tertiary armature reaction, are derived and presented in matrix notation. The theory put forward is valid for integral-and fractional-slot windings. With integral-slot windings and equal numbers of phases in the stator and the rotor, the current and field harmonics are neither influenced by delta connection nor by parallel branches of the winding (unlike the squirrel-cage motor). A system of n complex equations, for which, in general, n = 14, …, 30 suffices, is used to determine the n unknown stator-and rotor-current harmonics. The field harmonics, losses, torques etc. are obtained from the current harmonics. As an illustrative example, the system of simultaneous equations with n = 18 is solved for a 4-pole 70kW motor having 48 stator 36 rotor slots. The magnitudes and frequencies of the stator-and rotor-current harmonics for several coil pitches and slot skewings are given, and the resulting flux-density harmonics in the air gap are determined. The results are compared with measurements and are in agreement with them.

New 3-phase winding of low m.m.f.-harmonic content

Abstract: A new method of connection for 3-phase windings is described. It is shown that a conventional 60° phase-spread winding can be subdivided into two components, one of which is connected in delta and the other in star, the two winding components being connected in parallel to a 3-phase supply. Theoretically, the new principle is only applicable where the number of slots per phase is infinite, but it is demonstrated that entirely satisfactory results can be achieved with reasonably small numbers of armature slots. Simplicity of construction is considered to be very important, and, in each of the windings discussed, all the coils are identical and carry currents of equal magnitude. Theoretical examination shows that the new method gives a higher fundamental spread factor than for a conventional 3-phase winding, and a superior m.m.f. waveform, as well as providing a means of reducing the effective number of turns in series per phase. The theoretical studies were verified by tests on a 3-phase squirrel-cage induction motor.

A Method of Improving Power System Transient Stability Using Controllable Parameters

Abstract: Controllable parameters in a power system include generator terminal voltage, generator input power, and network admittances. These parameters can be controlled to damp mechanical rotor oscillation in the generators and thereby improve system transient stability. Explicit equations are derived for the control of these parameters to introduce damping uniformly throughout a large power system. These equations are derived on the basis of minimizing a positive definite error function. Decision functions are included which inhibit damping action when it leads to system instability. This method can be used to coordinate the application of locally based damping techniques.

Theory of the Generation of Harmonics and Combination Frequencies in a Plasma

Abstract: Publisher Summary This chapter discusses the theory of generation of harmonics and combination frequencies in the current density in plasma, emphasizing the kinetic approach to these problems rather than the elementary phenomenological approach considered by earlier reviewers. Vilenskii and Wetzel have investigated in detail the effect of the interaction of an electron density gradient with a microwave field on the time dependence of the first two components of the distribution function. The homogeneous and inhomogeneous plasmas are treated separately. Further, among homogeneous plasmas, a distinction is made between the neutral plasmas and plasmas with induced excessive ionization. Sodha and Kaw had investigated the simpler problem of the generation of the second harmonic in the current density in an inhomogeneous magnetoplasma. The problem of the generation and propagation of harmonic and combination frequency waves in an inhomogeneous plasma, when two plane-polarized electromagnetic waves of frequencies are propagating with their electrical vectors along the direction of the density and temperature gradients, has been investigated in detail by Sodha and Kaw. High-mobility semiconductors at low temperatures also hold great promise.

Generation of Fractional Harmonics in a Resonant Ultrasonic Wave System

Abstract: The problem of a fluid‐filled cavity caused to resonate by an ultrasonic wave is described as a parametric phenomenon. Variation of the cavity resonance frequency as a result of the periodic change of length produces the condition for parametric resonance. As a result, fractional harmonics of the driver transducer frequency are generated. The wave equation describing the system is transformed into an ordinary differential equation with periodic coefficients. The solution of this differential equation (Mathieu's equation) predicts frequency doublets which have been observed experimentally. A threshold condition of parametric excitation is derived from the region of unstable solutions of Mathieu's equation. This threshold condition relates the amplitude and frequency of the driver transducer to the cavity length and to the absorption per wavelength of the medium. Reasonable agreement between theory and experiment is obtained.

Apparatus for producing a low-distortion pulse width modulated inverter output

Abstract: The invention comprises apparatus for comparing the filtered output of a pulse width modulated inverter circuit with an AC reference voltage waveform and generating output voltage signals to control the inverter drive circuit to the extent necessary to produce an inverter output waveform substantially duplicating the reference voltage waveform and substantially void of low-order harmonics.

Multiple Pulse Modulation in Static Inverters Reduces Selected Output Harmonics and Provides Smooth Adjustment of Fundamentals

Abstract: It is the problem of the inverter designer to design a unit whose cost is low and whose reliability is high, consistent with all other application requirements This suggests that a minimum of major switching elements be used, that conservatively rated components be employed, and that circuit redundancy be incorporated in the design Another major problem facing the inverter designer is that of maintaining the output voltage of the inverter within an allowable band of values This problem arises due to the normal voltage drops within the inverter It also is aggravated by the voltage drops in the rectifier supplying power to the inverter or by the battery voltage variation Multiple pulse modulation provides more than one polarity reversal per half-cycle The amplitude of the input voltage to the inverter is equal to that of the source and is essentially fixed for small intervals of time The freedom to reverse polarity is the freedom to change the harmonic structure of the output By selecting the number and location of the reversals in polarity, the fundamental amplitude may be varied while eliminating low-order harmonics This technique offers a unique utilization of power handling components

Microwave bandpass filter with higher harmonics rejection function

Abstract: A rectangular waveguide bandpass filter for transmitting fundamental electromagnetic waves f 0 in a fundamental mode TE101 and attenuating second harmonic waves 2f 0 therein, comprising two susceptance elements spaced apart a distance of one-third waveguide wavelength in a lengthwise direction interiorly of the waveguide to form a resonant cavity for passing a frequency band including the fundamental wave f 101, attenuating the second harmonic wave 2f 101, and preventing resonant frequencies of modes higher than the fundamental mode TE101 from decreasing into a frequency region below the second harmonic; and one or two adjustable screws disposed between the two susceptance elements in one or both waveguide wide walls to project into the interior of the cavity at a position which is one-twelth of the one-third waveguide wavelength susceptance element spacing and which is from an adjacent narrow waveguide wall one-third of the overall distance between the two narrow waveguide walls whereby the screws are restricted to function as one or two capacitive elements only for the TE101 mode.

Input Filter Design with Static Power Converters

Abstract: Most static power converters are nonlinear systems which produce undesired harmonics in the three-phase input lines of the supply power system. These harnonics cause distorted voltage waveforms and must be reduced specially in large power applications. The methods of reducing undesired hannonics with special emphasis on designing input filters to reduce the undesired harmonics are discussed. The design of the input filters in general affects the performance of the converter. These effects are discussed for a single-phase voltage controller with an input filter.

Analysis of single-phase rectified thyristor-controlled load with integral-cycle triggering

Abstract: A rectified-voltage waveform caused by integral-cycle triggering of thyristors is found to contain most subharmonics and harmonics, odd and even, from zero to infinity. For a control period (on-plus-off time) of T supply cycles, the lowest subharmonic has a frequency of 1/T of the supply frequency. Subharmonics and higher harmonics can have amplitudes exceeding that of the average load voltage, dependent on T and the number of conducting cycles N. The ripple factor is a function of N/T and exceeds unity for N/T < 1/9. Average load voltage and load power both vary in proportion to N/T. In connection with electromagnetic interference, a method is developed for estimating the amplitude of high-order harmonic components.

Efficient power extraction at TRAPATT harmonics

Abstract: Using silicon planar diodes in a coaxial cavity that closely approximates to- Evans's TRAPATT circuit, microwave power up to the fourth harmonic has been extracted efficiently with a very low subharmonic content. The efficiency at the fundamental (1 GHz) and the third harmonic (3 GHz) were almost identical at 35% and 34%, respectively.

The response of the Fabry-Pérot interferometer to rapid changes in optical length

Abstract: The response of the Fabry-Perot etalon to changes in optical length is analysed. The optical length is initially fixed and then allowed to change at a constant rate. The analysis is therefore applicable to experimental situations such as plasma refractive index measurements or spectral line profile investigations. Two time constants of interest, td and tc, are obtained. td is the time lag between changes in the optical length and subsequent changes in the output intensity; it is equal to either the single or double transit time within the cavity, depending on the method by which the optical length is changed. tc is the time during which transients occur and is related to the energy decay time within the cavity. Under certain conditions at high frequencies, the output exhibits harmonics and the necessary and sufficient conditions for this to occur are established. A physical explanation for the generation of these harmonics is given and the relevance of these harmonics to the experimental use of the Fabry-Perot etalon at high frequencies is discussed.

Receivers for phase comparison radio navigation systems

Abstract: In a phase comparison radio navigation system in which a receiver may be operated with signals from a number of different chains of transmitting stations, each chain using radiations on a number of different harmonics nf of a common fundamental frequency f, the different chains using different fundamental frequencies, the receiver is provided with an oscillator and divider chain feeding a syntheizer matrix to form a frequency syntheizer to provide heterodyne signals of frequency n Delta for changing the frequencies of the received signals from harmonics of f to harmonics of F where F a fixed frequency used in the receiver for all chains. This oscillator and divider chain also provides timing signals for effecting a digital phase comparison between multiple frequency signals radiated in turn for short periods from the various stations to provide lane identification (for resolving ambiguities in the much more highly accurate but ambiguous normal position line determination).

Sine wave static inverter

Abstract: A sine wave static inverter produces a sine waveform from the output of a step wave generator by removing the higher harmonics from a step waveform. A first embodiment short circuits the higher harmonic signals across the secondary winding of a transformer thus permitting only the first harmonic sine wave to reach the output. A second embodiment applies only higher harmonic signals from a generated step waveform 180* out of phase with a second generated step waveform so that only the first harmonic of the second step waveform appears at the output.

Fourier analysis of cardiovascular events

Abstract: The theory and application of the method of Fourier analysis has been reviewed with specific reference to the applications of this technique to analysis of signals related to cardiovascular functions. Mathematics have been developed that relate the sampling rate of a function to the accuracy of harmonic amplitude resolution of the function. Specifically, the mathematical scheme was developed for the purpose of designing criteria for determining the minimum sampling rate of a function without introducing aliasing errors, and for elucidating the basis for the false indications resulting from selecting too few ordinates for the Fourier analysis. The application of Fourier methods to the analysis of cardiovascular functions has been studied. A thoracic aorta pressure pulse, the coronary artery flow pulse, and the electrocardiogram of a normal anesthesized mongrel dog have been examined in terms of the maximum sampling frequency required to yield the most dependable results. It was found that by sampling the arterial pressure pulse from 6 to 96 times/cycle, the absolute value of each harmonic amplitude for the first ten harmonics approaches asymptotically constant value at the higher sampling rates, suggesting that little or no further frequency information can be obtained by increasing the sampling rate >96 per second. At the lower sample rates (6–12 per cycle) the harmonic values were generally larger than the final steady value. The same type of asymptotic behavior is observed for the phase angle of each harmonic component as a function of the sample rate. The normal arterial pressure pulses appear to be fit adequately with ten harmonics. Sampling rates of about four times the largest significant frequency component in the wave form appear to produce the best analytical results. For the arterial pressure pulse, coronary flow pulse, and electrocardiogram, this turned out to be about 100 per second.

A Method for Harmonic Analysis of Cycloconverters

Abstract: Harmonic analysis of direct ac-to-ac frequency converters has been discussed in a few publications. A method of applying Fourier analysis and Boolean techniques to predict the harmonic content of the input and output currents of cycloconverters is described. The method is used to analyze an idealized threephase to single-phase frequency converter whose output frequency fo is a multiple or nonmultiple of the input frequency fi. The results obtained by this method are essential for the design of input filters and in determining amplitudes of subharmonics and beat frequencies with various cycloconverters.

An analysis of Alouette I plasma resonance observations

Abstract: Alouette 1 plasma resonance observations, analyzing electron density measurements in sheath region and cyclotron harmonic resonant frequencies