Phase shift oscillator

For sufficiently long times (index n ), the exponential can be neglected, leaving an oscillation of the turnover variable phase shifted with respect to the sound wave and with its amplitude reduced by the finite relaxation... 

The Ziegler and Nichols closed-loop method requires forcing the loop to cycle uniformly under proportional control. The natural period of the cycle—the proportional controller contributes no phase shift to alter it—is used to set the optimum integral and derivative time constants. The optimum proportional band is set relative to the undamped proportional band P , which produced the uniform oscillation. Table 8-4 lists the tuning rules for a lag-dominant process. A uniform cycle can also be forced using on/off control to cycle the manipulated variable between two limits. The period of the cycle will be close to if the cycle is symmetrical the peak-to-peak amphtude of the controlled variable divided by the difference between the output limits A, is a measure of process gain at that period and is therefore related to for the proportional cycle ... 

As expected, it satisfies condition (3.22). In other words, the shift in oscillation phase caused by collisions is very small. 

Koshelov et al. (1970) also reported tests results on a bank of three heated tubes in parallel. The phase shifts of flow oscillations were quite different for various tubes. Sometimes the flow oscillations in two tubes were in phase, while the flow oscillation in the third tube was in a phase shift of 120° or 180°. The amplitudes of the in-phase oscillations were different, that is, high in one tube and negligible in the other. Sometimes phase shift between individual tubes took place without apparent reason, but there were always tube in which the flow oscillations were 120° or 180° out of phase. 

Phase-shifting by melatonin is attributed to its action at MT2 receptors present in the SCN (Liu et al. 1997). The chronobiological effect of melatonin is due to its direct influence on the electrical and metabolic activity of the SCN, a finding that has been confirmed both in vivo and in vitro. The application of melatonin directly to the SCN significantly increases the amplitude of the melatonin peak, thereby suggesting that in addition to its phase-shifting effect melatonin directly acts on the amplitude of the oscillations (Pevet et al. 2002). However, this amplitude modulation seems to be unrelated to clock gene expression in the SCN (Poirel et al. 2003). 

By Fourier transforming the EXAFS oscillations, a radial structure function is obtained (2U). The peaks in the Fourier transform correspond to the different coordination shells and the position of these peaks gives the absorber-scatterer distances, but shifted to lower values due to the effect of the phase shift. The height of the peaks is related to the coordination number and to thermal (Debye-Waller smearing), as well as static disorder, and for systems, which contain only one kind of atoms at a given distance, the Fourier transform method may give reliable information on the local environment. However, for more accurate determinations of the coordination number N and the bond distance R, a more sophisticated curve-fitting analysis is required. 

One should note that the phase shift becomes time-independent and maximal for a = 1, i.e., at the resonance condition v = vG. The frequency spectrum 4>(a) bears a sine shape with a bandwidth inversely proportional to the number of oscillations of the gradient field (Fig. 4). Such a behaviour was also predicted in Ref. 15. Recording in a systematic way the phase shift as a function of vG without space encoding would be a very fast and efficient method to scan in a whole object the possible frequencies of spin motions. 

Figure 21.15 shows the transient response of the measured pressure shortly before and after the onset of the control. In Fig. 21.15, the apparent frequency of the oscillations was deduced as a function of time by measuring the zero crossing. Two sets of data are plotted since every other zero crossing corresponds roughly to one period of oscillation. The curve fit coincides with the average of the two. Figure 21.15c shows the resulting phase shift associated with the frequency change in Fig. 21.15. At about 40 ms after the control was turned...

Because the initial emphasis of this study was on extending ACC to liquid-fueled combustors, a simple closed-loop controller, which had been well tested in the previous studies involving gaseous fuel, was utilized. Such a controller, however, may not be effective in a combustor where the oscillation frequencies drift significantly with the control. The main problem was the frequency-dependent phase shift associated with the frequency filter. For such a case, it would be more useful to employ an adaptive controller that can rapidly modify the phase setting depending on the shift in the dominant oscillation frequencies. 

Figure 3.7. TMAFM images of a (001) surface of an as-received EDT-TTF-(CONHMe)2 single crystal measured under ambient conditions (2.5 im x 2.5 j.m) (a) topography and (b) phase. The phase angle is defined as the phase shift observed between the cantilever oscillation and the signal sent to the piezo-scanner driving the cantilever.

All unite developed up to now are based on use of an active oscillator, as shown schematically in Fig, 6.5. This circuit keeps the crystal actively in resonance so that any type of oscillation duration or frequency measurement can be carried out. In this type of circuit the oscillation is maintained as long as sufficient energy is provided by the amplifier to compensate for losses in the crystal oscillation circuit and the crystal can effect the necessary phase shift. The basic stability of the crystal oscillator is created through the sudden phase change that takes place near the series resonance point even with a small change in crystal frequency, see Fig. 6.6. 

Normally an oscillator circuit Is designed such that the crystal requires a phase shift of 0 degrees to permit work at the series resonance point. Long-and short-term frequency stability are properties of crystal oscillators because very small frequency differences are needed to maintain the phase shift necessary for the oscillation. The frequency stability Is ensured through the quartz crystal, even If there are long-term shifts In the electrical values that are caused by phase jitter due to temperature, ageing or short-term noise. If mass Is added to the crystal. Its electrical properties change. 

Fig. 6.7 shows the same graph as Fig 6.6, but for a thickly coated crystal. It has lost the steep slope displayed In Fig. 6.6. Because the phase rise Is less steep, any noise In the oscillator circuit leads to a larger frequency shift than would be the case with a new crystal. In extreme cases, the original phase/frequency curve shape Is not retained the crystal Is not able to carry out a full 90 ° phase shift.

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