Analytical study of amplitude risetime compensated timing with germanium planar detectors

A method is developed for calculating the time dispersion of amplitude and risetime compensated (ARC) timing with germanium planar detectors. Universal curves for pulse shape dependent timing error and for time jitter indicate that there is an optimum ratio between the inverted and delayed pulses which leads to the best realization of a given experimental objective. Curves for the corresponding system parameters are given. It is shown that ARC timing with Ge planar detectors is always capable of giving superior performance than constant fraction timing. The work includes quantitative comparison with experimental results published elsewhere.