A paper clock model based on limited numbers of atomic clocks and a typical time interval counter was developed. The aim of this work is to use a small ensemble of cesium clocks and a traditional measurement system to generate a time scale keeping both short-term and long-term accuracy. We removed each clock’s drift, then weighted the residual fluctuations. The weight function is set to be proportional to the inverse exponential of the index of each clock’s frequency deviation. We find the resultant paper clock to be much more stable and accurate than any contributing clock. The paper clock can keep a ± 50 ns phase difference (compared with UTC) without any calibration, and the Allan deviation of this paper clock is about 1.0×10-13 ( τ = 10 minutes, compared with hydrogen maser). Here, a typical Allan deviation of the contributing cesium clock is 2.0~3.0×10-13 in our measurement system. Finally, we use this paper clock to synchronize a hydrogen maser via a phase-lock mechanism. A virtual test showed the phase difference between an adjusted hydrogen maser and the paper clock could be kept within 1 nanosecond without any prediction algorithm.
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