Dispersion input signals

Fig. 3 shows the number of the period in waveform of the amplitude of the cable s input impedance is proportional to the distance to the fault. The peaks in Fig. 4 are smaller for longer cables because of attenuation and dispersion. The measurement deviation for wire fault location depends on the step frequency of the input signals A/and the load impedances. 

FIGURE 20.42 (a) Ideal filter frequenq response, (b) waveform of input signal, (c) waveform of output signal from ideal filter, (d) nonideal filter frequenq response with ideal phase but nonideal amplitude response, (e) output waveform of nonideal filter showing its components as time shifted versions of the input signal, (f) output waveform of nonideal filter a dispersed version of the input signal. 

The extent of gas dispersion can usually be computed from experimentally measured gas residence time distribution. The dual probe detection method followed by least square regression of data in the time domain is effective in eliminating error introduced from the usual pulse technique which could not produce an ideal Delta function input (Wu, 1988). By this method, tracer is injected at a point in the fast bed, and tracer concentration is monitored downstream of the injection point by two sampling probes spaced a given distance apart, which are connected to two individual thermal conductivity cells. The response signal produced by the first probe is taken as the input to the second probe. The difference between the concentration-versus-time curves is used to describe gas mixing. 

As an example, the special phase matching condition for the stimulated Raman ej fect or the one for CARS (Eq. 3.6-5) is contained in Eq. 3.6-7 (ki =kT,=ki and ki = k ). The phase matching condition is a consequence of the coherent generation of the signal field and dispersion in the linear refractive index of the matter. When the latter is significant (as in condensed media), it is required that the input fields overlap at the specific angle which satisfies Eq. 3.6-7. This overlap condition is illustrated in Fig. 3.6-7 for the general case of coherent Raman processes. 

The values of the dispersion coefficients will be established for most actual cases by experiments, which pursue the registration and interpretation of the exit time distribution of a signal that passes through a physical reduced model of the real device. However, in some cases, the actual device can be used. The method for identifying the dispersion coefficient [3.27, 3.28] is, in fact, the classical method of flow identification based on the introduction in the device input of a signal (frequently as a 5 impulsion or a unitary impulsion) the exit response is then recorded from its start until it disappears. It is evident that this experimental part of the method has to be completed by calculation of the dispersion model flow and by identification of the value of the dispersion coefficient. For this last objective, the sum of the square differences between the measured and computed values of the exit signal, are minimized. 

For the mathematical solution of the dispersion model flow, we add the univo-city conditions that include the signal input description for the initial conditions to Eq. (3.97) or (3.98). A more complete description of this mathematical model... 

In the analysis of residence time distributions, it is conventional to normalize time using the mean residence time of a noneliminated bolus input. This makes the normalized mean residence time (f ) of the signal in the dispersion model fi=l. 

For a dispersion model with closed boundary conditions, the change in the normalized variance, Aa, where cr ut and (j are the output and input variances of the signal, upon passage through the transduction cascade is given by... 

The Faraday cup described in Figure 7.1 was the earliest mass spectral detector in which ion detection was accomplished by direct charge (current) measurement The Faraday cup is a fixed detector in which mass spectrometers must be scanned to focus ions into the cup. Because mass spectrometric ion beams can be as low as a few fA (1 fA = 6,242 ions/s), 10 to 10 electronic amplification is required. The high input impedance with large feedback resistance required for Faraday cup amplification produces a slow, stable signal but with high electronic noise. Limited by noise and speed, Faraday cup detectors are relatively insensitive and too slow for application to scanning or time-dispersive mass spectrometry. 

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