Phase shift resonance

Confirmation analysis In most cases, the occurrence of dynamic resonance can be quickly confirmed. When monitoring phase and amplitude, resonance is indicated by a 180° phase shift as the rotor passes through the resonant zone. Figure 44.44 illustrates a dynamic resonance at 500 rpm, which shows a dramatic amplitude increase in the frequency-domain display. This is confirmed by the 180° phase shift in the time-domain plot. Note that the peak at 1200 rpm is not resonance. The absence of a phase shift, coupled with the apparent modulations in the FFT, discount the possibility that this peak is resonance-related. 

Blair, S. Heebner, J. E. Boyd, R. W., Beyond the absorption limited nonlinear phase shift with microring resonators, Opt. Lett. 2002, 27, 357 359... 

Bloch-Siegert phase shift is usually introduced in homonuclear nuclear decoupling with an inversion pulse that is far off-resonance to the spins in precession. To minimize the disturbance, the strength of the inversion pulse... 

The 13CO inversion pulse can be achieved by a PIP with the carrier placed at the centre of the 13C . This inversion PIP causes an additional procession of the 13C spins. The amount of the phase shift in the rotating frame of the 13CO, where the centre of the 13CO spins is on-resonance to the inversion PIP, can be calculated... 

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. 

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. 

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