A custom mixed-signal CMOS integrated circuit has been developed for high performance positron emission tomography (PET) front-end applications. The application specific integrated circuit (ASIC) contains four differential variable-gain constant bandwidth amplifiers, which receive buffered photomultiplier tube (PMT) voltage pulses. All four amplified PMT signals are summed by adding their outputs and feeding this sum to the timing channel of the ASIC. The timing channel, which consists of a constant fraction discriminator and subnanosecond time to digital converter, offers excellent PET count rate performance and randoms noise reduction through low deadtime (100 ns) and excellent timing resolution (312.5 ps LSB). Amplified PMT signals are also distributed to energy processing channels for lowpass filtering and buffering for subsequent digitization by external ADCs. The ASIC offers substantial size, power, and cost reductions over existing PET front-end discrete designs. Fabricated in a 5 V, 0.5 m, triple metal, double poly, n-well CMOS process, the new ASIC has a die size of 20 mm 2 and dynamic power dissipation under 425 mW.Index Terms-CMOS integrated circuits, constant fraction discriminator (CFD), front-end electronics, nuclear pulse processing, positron emission tomography (PET), time to digital converter (TDC), variable gain amplifier (VGA).
The conventional definition of group speed U = dω/dk is the speed of a wave group composed of collinear wave components. When there is dispersion and refraction, the wave components cannot remain parallel. Then U is found to be the apparent speed of the group in the direction of movement of the wavelets within the group. The velocity of a group composed of nonparallel wave components is found to depend upon the directional distribution of the wave components, and it is here termed the geometric group velocity. The geometric group speed G = U cos ϕ, where the angle ϕ is the difference between the direction of the wave group and the direction of the wavelets. For a wave group in which the bandwidth and the directional spread of the wave components are both small the wavelet velocity is nearly equal to the phase velocity of a wave component. The path of a wave packet is found to be given by Snell's law with the geometric group velocity, while at each point along the path the wavelets have a direction defined by Snell's law with the wavelet velocity. The findings are illustrated by using examples of gravity water waves and are confirmed by field observations.
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