Response frequency

Once the probe is set into the target, the acquisitions consist of the peak to peak amplitude, the time of flight and the frequency response of the back-reflected echo. 

Given that the ultrasonic back-wall echo from the synthesized beam and from the single element output may differ due to the coherent summing, time and frequency response of synthesized beam outputs may be achieved. Therefore, flat wall must be in the far-field or at the focus point as recommended by the standard [1]. 

The sinc fiinction describes the best possible case, with often a much stronger frequency dependence of power output delivered at the probe-head. (It should be noted here that other excitation schemes are possible such as adiabatic passage [9] and stochastic excitation [fO] but these are only infrequently applied.) The excitation/recording of the NMR signal is further complicated as the pulse is then fed into the probe circuit which itself has a frequency response. As a result, a broad line will not only experience non-unifonn irradiation but also the intensity detected per spin at different frequency offsets will depend on this probe response, which depends on the quality factor (0. The quality factor is a measure of the sharpness of the resonance of the probe circuit and one definition is the resonance frequency/haltwidth of the resonance response of the circuit (also = a L/R where L is the inductance and R is the probe resistance). Flence, the width of the frequency response decreases as Q increases so that, typically, for a 2 of 100, the haltwidth of the frequency response at 100 MFIz is about 1 MFIz. Flence, direct FT-piilse observation of broad spectral lines becomes impractical with pulse teclmiques for linewidths greater than 200 kFIz. For a great majority of... 

The sharpness of the frequency response of a resonant system is conunonly described by a factor of merit, called the quality factor, Q=v/Av. It may be obtained from a measurement of the frill width at half maxuuum Av, of the resonator frequency response curve obtained from a frequency sweep covering the resonance. The sensitivity of a system (proportional to the inverse of tlie minimum detectable number of paramagnetic centres in an EPR cavity) critically depends on the quality factor... 

McMorrow D and Lotshaw W T 1990 The frequency response of condensed-phase media to femtosecond optical pulses spectral-filter effects Cham. Phys. Lett. 174 85-94... 

In this paper, we discuss semi-implicit/implicit integration methods for highly oscillatory Hamiltonian systems. Such systems arise, for example, in molecular dynamics [1] and in the finite dimensional truncation of Hamiltonian partial differential equations. Classical discretization methods, such as the Verlet method [19], require step-sizes k smaller than the period e of the fast oscillations. Then these methods find pointwise accurate approximate solutions. But the time-step restriction implies an enormous computational burden. Furthermore, in many cases the high-frequency responses are of little or no interest. Consequently, various researchers have considered the use of scini-implicit/implicit methods, e.g. [6, 11, 9, 16, 18, 12, 13, 8, 17, 3]. 

The frequencies responsible for suites IX and X are near the Fj and F2 modes of vibration of thiazole, respectively, and have been assigned to such oscillations. 

Because of its small size and portabiHty, the hot-wire anemometer is ideally suited to measure gas velocities either continuously or on a troubleshooting basis in systems where excess pressure drop cannot be tolerated. Furnaces, smokestacks, electrostatic precipitators, and air ducts are typical areas of appHcation. Its fast response to velocity or temperature fluctuations in the surrounding gas makes it particularly useful in studying the turbulence characteristics and rapidity of mixing in gas streams. The constant current mode of operation has a wide frequency response and relatively lower noise level, provided a sufficiently small wire can be used. Where a more mgged wire is required, the constant temperature mode is employed because of its insensitivity to sensor heat capacity. In Hquids, hot-film sensors are employed instead of wires. The sensor consists of a thin metallic film mounted on the surface of a thermally and electrically insulated probe. 

The frequency response or switching speed of the bipolar transistor is governed by the same processes which control the speed of thep—n junction, the capacitance associated with the movement of charge into and out of the depletion regions. To achieve high frequencies the dimensions of the active areas and parasitic circuit elements must be reduced. The two critical dimensions are the width of the emitter contact and the base thickness, W. The cutoff frequency,, is the frequency at which = 57 / - b /t > where is the emitter-to-coUector delay time and is the sum of the emitter... 

The PI controller is by far the most commonly used controller in the process industries. The summation of the deviation with its integral in the above equation can be interpreted in terms of frequency response of the controller (Seborg, Edgar, and Melhchamp, Process Dynamics and Control, Wiley, New York, 1989). The PI controller produces a phase lag between zero and 90 degrees ... 

A recent addition to the model-based tuning correlations is Internal Model Control (Rivera, Morari, and Skogestad, Internal Model Control 4 PID Controller Design, lEC Proc. Des. Dev., 25, 252, 1986), which offers some advantages over the other methods described here. However, the correlations are similar to the ones discussed above. Other plant testing and controller design approaches such as frequency response can be used for more complicated models. 

FIG. 8-64 Pneumatic controller a) example (h) frequency response characteristic,... 

FIG. 8-75 Frequency response curves for a pneumatic positioner/actuator (a) input signal to stem travel for a 69-inch spring and diaphragm actuator with a 1.5-inch total travel and. 3-15 psig input pressure (h ) dynamic stiffness for the same positioner/actuator. 

A frequency response technique was tried first and some results were received. The useful frequency domain was less than one order of magnitude, while in electrical problems five orders of magnitude can be scanned. The single pulse technique was more revealing, but evaluation by moments had the usual accumulation of errors. Fourier transform of the pulse test results was the final method. 

Type of Instability Onset Frequency Response Caused by... 

Figure E-5 Frequency response of a second-order common-mode filter L = 1 mhl).

Characterized by high frequency response, accelerometers are compact and rugged, ideal for mounting on machinery cases, foundations, piping, etc. Applications to gear trains and rolling element bearings are typical. 

If the observed surface is moving, the modulator/demodulator output varies in direct proportion to the peak-to-peak movement of the observed surface. Having a flat frequency response from DC to 10,000 Hz, the transducer is able to accurately follow motion at frequencies in excess uf those typically encountered. 

Photomultipliers are used as detectors in the single-channel instruments. GaAs cathode tubes give a flat frequency response over the visible spectrum to 800 nm in the near IR. Contemporary Raman spectrometers use computers for instrument control, and data collection and storage, and permit versatile displays. 

Frequency response characteristics of first-order systems... 

Fig. 6.6 Frequency response diagrams for a second-order system.

In general, the complete system frequency response is obtained by summation of the log modulus of the system elements, and also summation of the phase of the system elements. 

An important difference between analysis of stability in the. v-plane and stability in the frequency domain is that, in the former, system models in the form of transfer functions need to be known. In the latter, however, either models or a set of input-output measured open-loop frequency response data from an unknown system may be employed. 

The closer the open-loop frequency response locus G(ja )//(ja ) is to the (—l,j0) point, the nearer the closed-loop system is to instability. In practice, all control... 

Relationship between open-loop and closed-loop frequency response... 

The M and N circles can be superimposed on a Nyquist diagram (called a Hall chart) to directly obtain closed-loop frequency response information. 

Alternatively, the closed-loop frequency response can be obtained from a Nyquist diagram using the direct construction method shown in Figure 6.25. From equation (6.73)... 

Fig. 6.25 Closed-loop frequency response from Nyquist diagram using the direct construction method.

The Nichols chart shown in Figure 6.26 is a rectangular plot of open-loop phase on the x-axis against open-loop modulus (dB) on the jr-axis. M and N contours are superimposed so that open-loop and closed-loop frequency response characteristics can be evaluated simultaneously. Like the Bode diagram, the effect of increasing the open-loop gain constant K is to move the open-loop frequency response locus in the y-direction. The Nichols chart is one of the most useful tools in frequency domain analysis. 

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