Showing papers on "Harmonic published in 1972"

Transverse Vibrations of Double‐Tapered Cantilever Beams

Abstract: The differential equation is developed from the Bernoulli‐Euler equation for the free vibrations of a double‐tapered cantilever beam. The beam tapers linearly in the horizontal and in the vertical planes simultaneously. From a computer solution of this equation, a table has been developed from which the fundamental frequency, second, third, fourth, and fifth harmonic can easily be obtained for various taper ratios. Charts are plotted for selected taper ratios in the vertical plane to show the effect of taper ratios on frequency.

Nonlinear waves in a Kelvin-Helmholtz flow

Abstract: Nonlinear waves on the interface of two incompressible in viscid fluids of different densities and arbitrary surface tension are analysed using the method of multiple scales. Third-order equations are presented for the space and time variation of the wavenumber, frequency, amplitude and phase of stable waves. A third-order expansion is also given for wavenumbers near the linear neutrally stable wave-numbers. A second-order expansion is presented for wavenumbers near the second harmonic resonant wavenumber, for which the fundamental and its second harmonic have the same phase velocity. This expansion shows that this resonance does not lead to instabilities.

On the rippling of small waves: a harmonic nonlinear nearly resonant interaction

Abstract: We show that the rippling often observed on small progressive gravity waves can be explained in terms of a nearly resonant harmonic nonlinear interaction. The resonance condition is that the phase speeds of the two waves must be nearly identical. The in viscid analysis is generalized to any order in a small parameter proportional to the wave steepness. Wave tank measurements provide experimental evidence for most of the predicted results. The phenomenon of resonant rippling is further shown to be not just peculiar to capillary-gravity waves, but in fact possible for any weakly nonlinear dispersive wave system whose dispersion relation has discrete pairs of solutions nearly satisfying the resonance conditions.

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.

Relative Positions of Fundamental and Second Harmonic Type III Bursts

Abstract: Observations of the relative positions of fundamental and second harmonic bursts can be used to study refraction and scattering effects in the corona. Smerd, Wild and Sheridan have pointed out that the observed positions of type II bursts can be interpreted as favouring the backward emission of the second harmonic in a smooth corona. In this case the harmonic is seen after reflection from near the fundamental plasma level. Several other examples of type II and type III bursts have been reported which show this effect. We wish to present further evidence from a recent study of a large number of type III bursts observed with the 80 MHz heliograph and 158 MHz interferometer.

Computor organ using harmonic limiting

Abstract: Harmonic limiting is employed in an electronic musical instrument of the type wherein notes are produced by computing the amplitudes at successive sample points of a musical waveshape and converting these amplitudes to notes as the computations are carried out in real time. Each amplitude is computed by accumulating as many as W individually calculated waveshape discrete Fourier components. In accordance with the present invention, harmonic inhibit means are provided for limiting the Fourier components included in each amplitude computation only to those having frequencies below a certain value preferably within the normal human hearing range.

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.

Ultrasonic Harmonic Generation in Piezoelectric Semiconductors

Abstract: Second‐harmonic generation of ultrasound in piezoelectric semiconductors is investigated using a quantum treatment which is valid at high frequencies and in strong magnetic fields. The effects of collisions are neglected so that our treatment is valid only for ql≫1. It is shown that the amplitude of the second harmonic can be expressed in terms of the fundamental using the linear and nonlinear conductivity tensors. The latter quantities are related to the current densities which are linear and nonlinear in the piezoelectric fields generated by the ultrasound. The linear and nonlinear conductivities are calculated using the parabolic and nonparabolic models for the energy bands of a semiconductor. It is found that only those sound waves which induce longitudinal electric fields will contribute appreciably to second‐harmonic generation. For waves propagating parallel to a magnetic field, we find that the amplitude of the second harmonic is independent of the magnetic field for the parabolic model. It is also found that the acoustic flux in the second harmonic will peak at sound wave vectors of the order of the Debye wave vector. In contrast, for the nonparabolic model it is found that the amplitude of the second harmonic depends upon magnetic field. The results of the calculation are applied to n‐type InSb, and the magnitude of the second‐harmonic generation is estimated for ultrasonic frequencies in the microwave region. It is found that the magnitude of the second harmonic is considerably enhanced using the nonparabolic model over what would be predicted using the parabolic model.

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.

Accurate and stable encoding with low cost circuit elements

Abstract: This accurate and stable analog to digital conversion system and circuits useful therewith is based upon selective counting of high frequency electrical signal oscillations generated by a phase locked frequency multiplication network The network contains only low cost components Accuracy and stability derive from maintenance of predetermined phase locked relationship between the signal derived through frequency division of the network output signal and a cyclic reference signal which is also the reference for gating the encoding counts (ie the reference for measurement of the analog parameter which is to be encoded) The network output frequency is a harmonic of the frequency of the reference signal Feedback phase control is developed through interaction of the frequency divided network output with the reference signal in a phase comparator circuit A novel circuit arrangement for generating the reference signal in the form of ramp oscillations is also disclosed

Synchronous vibrational analyzer for rotating machinery

Abstract: A pulse signal is generated which is a precise multiple of the rotation frequency of a machine to be tested. A sensor is utilized to generate an electrical signal in accordance with vibration developed in the machine with its rotation. Low frequency components of this signal are filtered out therefrom and these filtered signals fed to a pair of switching circuits. The pulse signals in accordance with the rotation of the machine are fed to a switching signal generator where quadrature related signals synchronized with the machine rotation are developed. These quadrature related signals are fed to the switching circuits as the switching control therefor, so as to provide samplings of the vibration signals in quadrature relationship. The outputs of the switching circuits are each integrated and squared, the squared signals then being summed. These summed output signals are then fed to an indicator which provides the indication of the amplitude of vibrational components at the machine rotation frequency or a harmonic thereof.

Surface Elastic‐Wave Velocity and Second‐Harmonic Generation in an Elastically Nonlinear Medium

Abstract: We report the derivation of a closed‐form expression for the acoustic surface‐wave velocity in an isotropic medium which is elastically nonlinear. An expression is given for the particle displacement of the second harmonic generated, and its variation with distance is shown. The amplitude of the harmonic is proportional to the power density of the fundamental frequency input. Numerical results are given for fused quartz.

Phase matched optical wave generator for integrated optical circuits

Abstract: A phase matched optical wave generator is described wherein a harmonic optical wave is generated by the interaction of a fundamental optical wave with a non-linear polarizing material. The harmonic wave is coupled to a thin-film optical waveguide which is tuned to the wavelength of the harmonic optical wave. The separation of the fundamental and harmonic waves in different optical waveguides facillitates phase matching over the length of the interacting region to produce a harmonic of enhanced intensity. Several embodiments are shown and described.

Measurement System for Derivative Studies

Abstract: A system for measuring I‐V, dI/dV, and d2I/dV2 characteristics of two‐terminal devices is described. An operational amplifier integrator is used to produce a sweep voltage. For derivative measurements the dc bias voltage is modulated by a constant ac voltage signal. Current is detected by a near‐zero input impedance circuit with adjustable gain. A simple circuit utilizing an IGFET at zero drain voltage as a voltage controlled resistor compensates for harmonic content in the oscillator signal. It also enhances the detectability of weak harmonic signals in the presence of a strong fundamental signal by rejecting more than 90% of the strong signal. The system has been used to measure devices with impedances from a few ohms to over 105 Ω.

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.

Multiplex decoding system

Abstract: A decoder circuit for stereophonic FM broadcast receivers adapted for construction by integrated circuit techniques. A local oscillator arranged to operate at an even harmonic of the 19 KHz stereo pilot signal is locked in phase and frequency to the pilot signal by means of an automatic frequency and phase control (AFPC) loop. The AFPC loop includes frequency dividing means coupled to the oscillator output and balanced synchronous detection means coupled to the output of the frequency dividing means and to a source of composite stereophonic signals (including the pilot signal) for producing oscillator control signals. Additional synchronous detection means are coupled to the source of composite signals and to further frequency dividing means for producing indications of pilot signal presence and above-band noise and for demodulating the difference channel (LR) information. Matrixing and sterophonic-monophonic switching means are also incorporated in the decoder system.

Transient radiation field of a circular loop antenna

Abstract: For a circular loop antenna excited by a frequency-hand-limited rectangular voltage pulse, the time variation of the electric field at remote points in various directions has been computed. The computations are for a loop of radius b made from wire of radius a , for which the thickness parameter \Omega = 2 \ln (2\pi b/a) = 15 . The moment method was used in obtaining the current distribution on the loop due to each harmonic component in the excitation. Then the transient field is obtained by using the harmonic current distribution due to each frequency component of the exciting voltage pulse.

Power amplifier klystrons operating in wide frequency bands

Abstract: Klystrons of the invention comprise resonant cavities tuned to frequencies higher than the maximum frequency of the frequency band B of operating in order to improve the efficiency at frequencies higher than the centre frequency Fo of the band B, and harmonic cavities tuned to frequencies slightly below the frequency 2 Fo - B, in order to improve the efficiency at frequencies of less than Fo

Method and apparatus for measuring distance to target using frequency-modulated continuous waves

Abstract: An improvement of a method for measuring distance to target using transmitted and reflected frequency-modulated continuous waves is provided. A low frequency wave produced by mixing a transmitted wave and a wave reflected from the target is separated into frequency components such as a Doppler signal component, a fundamental wave component and its harmonic components. Then, Doppler signals are obtained from the fundamental wave and harmonic components. The ratio in intensity between at least two Doppler signals is calculated to measure the distance to the target. Since the phase of Doppler signal is reversed depending upon whether the target is moving toward or away from the distance measuring apparatus, the direction of the relative movement between the target and the apparatus may be detected. Furthermore, the relative speed between the target and the distance measuring apparatus may be detected from the frequency of each Doppler signal. When the ratio of the distance to the target to the relative speed reaches a predetermined value, a command signal to actuate a device is produced.

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.

Analysis of evoked responses in man elicited by sinusoidally modulated noise

Abstract: For two subjects responses at the cortex, elicited by sinusoidally modulated white noise, have been measured. The influences of the modulation frequency, in a region around 9 Hz, and of the modulation depth are investigated. For one subject an undistored sine wave was measured at frequencies between 8 and 11 Hz, with a maximum amplitude of 3 μV at about 9 Hz. For the other subject a distorted wave was found. This wave has been analysed into its harmonic components. The spectrum consists mainly of the first and the second harmonic.Plotting the amplitudes of the different spectral components as a function of the modulation frequency gives a characteristic for the first harmonic which is comparable with that for subject 1, although less sharp. For the second harmonic the greatest amplitudes are found at lower frequencies. By varying the modulation depth a saturation effect was found at about 25% modulation depth for both subjects.The characteristics found with evoked response techniques are very different fr...

Harmonic composite grinding of tires

Abstract: A method and apparatus for grinding tires to reduce the force reaction between the tire and load wheel to predetermined limits both as to the fundamental of the force reaction and a harmonic of the fundamental. Automatic switching from one to the other modes of grinding is provided.