Phase jitter

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. 

Theoretical level populations. Sinee there are population variations on time seale shorter than some level lifetimes, a complete description of the excitation has been modeled solving optical Bloch equations Beacon model, Bellenger, 2002) at CEA. The model has been compared with a laboratory experiment set up at CEA/Saclay (Eig. 21). The reasonable discrepancy when both beams at 589 and 569 nm are phase modulated is very likely to spectral jitter, which is not modeled velocity classes of Na atoms excited at the intermediate level cannot be excited to the uppermost level because the spectral profile of the 569 nm beam does not match the peaks of that of the 589 nm beam. 

For example, consider Eq. (3.19) corresponding to control of photodissociation of) an initial two-level supeiposition state that is excited to the continuum. If there arer sufficiently strong external perturbations, or excessive jitter in the laser phase, thefij-this results in a complete average over 2, and Eq. (3.19) becomes f ... 

For cw lasers, laser decoherence appears via the jitter and drift of the laser phase in the field E(z,t) [e.g., Eq. (3.16)] with a concomitant reduction in control (see Section 5.3). However, suitable design of the control scenario can result in a method that is immune to the effects of laser jitter. In particular, to do so we rely upon the way in which the laser phase enters into control scenarios. 

This control scenario is not limited to the specific frequency scheme discusi above. Essentially all that is required is that two or more resonantly enhaw photodissociation routes interfere and that the cumulative laser phases of the routes be independent of laser jitter. As one sample extension, consider the ci... 

Figure 2-7. The mechanical chopper developed by Cole and coworkers [15]. The disc interior (a) and exterior (b) are shown togedier widi die wheel casing and mount (c) and holes for the X-ray and light-emitting diodes (LED) (d). Parts (e), (f) and (g) resemble X-ray pulse lengths that arise from the relative positioning of wheels in phase (e), one rotated 90° to the other (f), and completely out of phase to each other (g). Part (h) is a schematic diagram of the chopper jitter and timing control via LED lying in holes coloured black, and photodiodes lying behind die small hollow hole post-X-ray (photodiodes are behind each LED pre-X-ray)...

Figure 11. Spatio-temporal binary code obtained for stimulns 1. Each row corresponds to a given PN (from 1 to 6) and each column corresponds to a given peak of the LFP (from 1 to 10). The hit 1 or 0 within a given box corresponds to a synchronization or a desynchronization of a given PN at a given peak of the LFP. For example, the bit 1 foimd in the box (LFP 4, PN 3) means that PN 3 is synchronized at the 4 peak of the LFP. This has to be compared to figure 6 left where the phases of the spikes fired by PN 3 at the 4 peak 4 of the LFP present a very small jitter over the 20 trials.

A fiber laser may behave as a driven second-order system by introducing a time-dependent parameter into the laser cavity, such as loss modulation, gain (or pump) modulation, phase modulation, etc. For example, driving the mode locking element in a mode locked fiber laser at slightly below the cavity fundamental frequency has been observed to result in chaotic behavior, characterized by severe amplitude jitter on the optical pulses generated. 

For a laser with a fluctuating phase, the simulation procedure is similar to that of the collision. Several models may be assumed for the stochastic phase fluctuations. In this calculation we have assumed a random jump between 0 and 2ir with no memory of the previous phase. This is a model of Markovian "hard" phase jumps, which is different than the phase diffusion model assumed in our analytic work. This model may be applicable for actual lasers suffering from acoustic mirror jitter or other mundane laboratory noises. 

FIGURE 18.6 Ion ensembles in the fluid phase. MD simulation of ensembles with (a) one species (500 Be+ ions), (b) two species (500 Be+ ions (outer shells) and 100 HD" " ions (inner shells)), and (c) two species (500 Ba ions (outer shells) and 100 barium isotope ions (inner shells)) at different translational temperatures. Particle trajectories integrated over 1 msec are displayed. The view is in the (x-y)-plane. Only a short section along z is shown. The shell structure develops around 200 mK. With lowering of the temperature, the diffusion between and within shells decreases until at temperatures of a few mK and below (not shown) the ions are confined to the immediate neighborhood of particular sites, jittering around them. 

The system exciter, which to a large extent is integrated with the receiver down-converter subsystem, develops the required IF and RF reference signals for the transmitter and receiver. Many of the components of the system instabilities, which lead to a limit to the clutter suppression performance, are derived in the exciter subsystem timing jitter and oscillator phase noise being the two dominant contributors. 

There are several primary contributors to system instability. The most prevalent is oscillator phase noise. Others include timing jitter, amplifier additive noise, A/D quantization, and I/Q detector effects. 

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