Frequencies, range

The objective of impedance measurements is typically to capture the frequency response of the system under study. To that end, the measured frequency range should include frequencies sufficiently large and frequencies sufficiently small to reach asymptotic limits in which the imaginary impedance tends toward zero. In some cases, for example, blocking electrodes, the low-frequency as5onptotic behavior does not exist. In other cases, a true dc limit is not achievable due to nonstation- 

Solution For a system that follows Tafel behavior, the current density response to a potential perturbation 

The mean value of the current i t) is, for T equal to an integer number of cycles, 

To have a variation of the dc current lower than 1 percent, AV must be lower than 0.2/b. 

Evaluation cfthe harmonics erf the nonlinear current response can be achieved by introduction of the trigonometric expressions 

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The technique presented above has been extensively evaluated experimentally using ultrasonic data acquired from a test block made of cast stainless steel with cotirse material structure. Here we briefly present selected results obtained using two pressure wave transducers, with refraction angles of 45° and 0°. The -lOdB frequency ranges of the transducers were 1.4-2.8 MHz and 0.7-1.4 MHz, respectively. The ultrasonic response signals were sampled at a rate of 40 MHz, with a resolution of 8 bits, prior to computer processing. 

By employing this technique, the frequency range best suited for a particular material can be automatically estimated and utilized for inspection, without the need to employ a tailor-made transducer. Consequently, a single wide-band transducer can be used to get near-optimal inspection results for a wide range of materials. 

During the inspection of an unknown object its surface is scanned by the probe and ultrasonic spectra are acquired for many discrete points. Disbond detection is performed by the operator looking at some simple features of the acquired spectra, such as center frequency and amplitude of the highest peak in a pre-selected frequency range. This means that the operator has to perform spectrum classification based on primitive features extracted by the instrument. 

In this section, two illustrative numerical results, obtained by means of the described reconstruction algorithm, are presented. Input data are calculated in the frequency range of 26 to 38 GHz using matrix formulas [8], describing the reflection of a normally incident plane wave from the multilayered half-space. 

On the other hand, one current upper limit of the frequency range of instruments is 4 MHz So, it is theoretically impossible to digitally demodulate a 4 MHz ET signal. 

The ultrasound system should have more independent channels and allow the transmitter pulse to be individually adjustable in width and amplitude, and an increased frequency range for the logarithmic amplifier was desired. The digitization should be improved both with respect to sampling rate and resolution. 

HILL-SCAN type Highlights Frequency range... 

For special applications such as air coupled testing a special programmable transmitter board was developed. This transmitter generates rectangular and burst signals, which increase the acoustical power in an optimized frequency range, and provides a superior signal-to-noise ratio. 

The UT-Acquisition system hardware consists of a 1 channel ultrasonic board, for puls/echo, one or two crystal probes It operates within a frequency range of 0,5 - 15 Mhz and with variable sampling frequencies in steps of 20,40 or 80 MHz... 

Electromagnetic earthquake forerunners show themselves like the electromagnetic phenomena, including electromagnetic emission (EME) in a radio frequency range. This emission caused by collective exiting of the set of local mechano-electrical transformers (MET). The excitation mechanism inside the crust is determined by the fact that elastic tension ranges up to the threshold level within the source area. 

The principal part of the integral is taken and the integration must be done over all frequencies. In practice, the integration is often tenninated outside of the frequency range of interest. Once the frill dielectric fiinction is known, the reflectivity of the solid can be computed. 

An alternative perspective is as follows. A 5-frmction pulse in time has an infinitely broad frequency range. Thus, the pulse promotes transitions to all the excited-state vibrational eigenstates having good overlap (Franck-Condon factors) with the initial vibrational state. The pulse, by virtue of its coherence, in fact prepares a coherent superposition of all these excited-state vibrational eigenstates. From the earlier sections, we know that each of these eigenstates evolves with a different time-dependent phase factor, leading to coherent spatial translation of the wavepacket. 

The quantity introduced above is the spectral density defined as the energy per unit volume per unit frequency range and is... 

The foremost of the modem teclmiques is tlie use of lasers as spectroscopic tools. Lasers are extremely versatile light sources. They can be designed with many usetlil properties (not all in the same instmment) such as high intensity, narrow frequency bandwidth with high-frequency stability, tunability over reasonable frequency ranges, low-divergence beams which can be focused into very small spots, or pulsed beams with... 

The spectral frequency range covered by the central lobe of this sinc fiinction increases as the piilselength decreases. For a spectrum to be undistorted it should really be confined to the middle portion of this central lobe (figure B 1.12.2). There are a number of examples in the literature of solid-state NMR where the resonances are in fact broader than the central lobe so that the spectrum reported is only effectively providing infonnation about the RF-irradiation envelope, not the shape of the signal from the sample itself... 

The interpretation of MAS experiments on nuclei with spin / > Fin non-cubic enviromnents is more complex than for / = Fiuiclei since the effect of the quadnipolar interaction is to spread the i <-> (i - 1) transition over a frequency range (2m. - 1)Vq. This usually means that for non-integer nuclei only the - transition is observed since, to first order in tire quadnipolar interaction, it is unaffected. Flowever, usually second-order effects are important and the angular dependence of the - ytransition has both P2(cos 0) andP Ccos 9) terms, only the first of which is cancelled by MAS. As a result, the line is narrowed by only a factor of 3.6, and it is necessary to spin faster than the residual linewidth Avq where... 

The easily accessible frequency range of sound and ultrasound waves confines the range of applicability of... 

Direct time-dependent detection is limited by the response time of detectors, which depends on the frequency range, and the electronics used for data acquisition. In the most favourable cases, modem detector/oscilloscope combinations achieve a time resolution of up to 100 ps, but 1 ns is more typical. Again, this reaction has been of fiindamental theoretical interest for a long time [59, 60]. 

Tetralluoroethylene polymer has the lowest coefficient of friction of any solid. It has remarkable chemical resistance and a very low brittleness temperature ( — 100°C). Its dielectric constant and loss factor are low and stable across a broad temperature and frequency range. Its impact strength is high. 

This copolymer has useful properties from cryogenic temperatures to 180°C. Its dielectric constant is low and stable over a broad temperature and frequency range. 

A variety of commercial instruments are available for the determination of the viscoelastic behavior of samples. Figure 3.15 shows one such apparatus, the Rheovibron Viscoelastometer. This instrument also takes advantage of the complementarity that exists between time and temperature It operates at four frequencies over a 175°C temperature range. With accessories, both the frequency range and the temperature range can be broadened still further. 

If energy of the proper frequency is supplied, a transition between these quantum states occurs with the absorption of an amount of energy equal to the separation of the states. The frequency of the absorbed radiation lies in the radio-frequency range and depends on the local magnetic field at the atom in question. 

In the microwave region tunable monochromatic radiation is produced by klystrons, each one being tunable over a relatively small frequency range, or a backward wave oscillator, tunable over a much larger range. Both are electronic devices. Absorption experiments are usually carried out in the gas phase, and mica windows, which transmit in this region, are placed on either end of the absorption cell, which may be several metres in length. Stark... 

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