Determination of short-term error caused by the reference clock in precision time-interval measurement and generation

A simple analysis based on the randomized clock cycle T ₀ yields a useful formula on its variance in terms of the Allan variance. The short-term uncertainty of the measured or generated time interval t is expressed by the standard deviation in an approximate form as a function of the Allan variance. The estimates obtained are useful for determining the measurement uncertainty of time intervals within the approximate range of 10 ms-100 s