This paper presents a new method to improve the long-term frequency stability of an oven-controlled crystal oscillator (OCXO) without an external reference source. The frequency drift of the crystal oscillator can be obtained in real time by measuring the phase shift between the pins of the crystal resonator. In this paper, according to an equivalent circuit of a crystal oscillator, a linear equivalent mathematical model based on the phase shift of the crystal resonator and the output frequency is established. The experiments were conducted to observe the relation between the phase shift and frequency drift of the OCXO. At the same time, a crystal oscillator self-calibration frequency control system is established to improve the frequency drift of the OCXO. The results show that this method can effectively improve the drift of OCXOs. The OCXO drift rate was significantly improved from 1.53 10⁻¹⁰/day to 9.8 10⁻¹²/day, and after three days, it settled at 5.24 10⁻¹¹. The long-term frequency stability also underwent remarkable improvement, from 1.16 10⁻¹¹/1000 and 3.24 10⁻¹¹/10,000 to 3.47 10⁻¹²/1000 and 1.05 10⁻¹¹/10,000.

We analyze the phenomena of phase group synchronization between the different nominal frequency signals and propose a new theory of the equivalent comparison between them. The exact expression of the equivalent comparison is deduced. High resolution frequency measurement and phase comparison can be realized using this theory with the divider. For avoiding the frequency mixing, multiplication and synthesis, the system phase noise is improved and the higher resolution comparison and measurement are achieved between the different nominal frequencies by theory.

The cesium fountain clock is used as the primary frequency standard to improve the accuracy of the excitation source (active hydrogen maser) through cesium atomic transition frequency. The authors find that the frequency stability of cesium fountain clock is poorer than the active hydrogen maser according to the laws of the frequency stability evaluated by the Allan variance. The cesium fountain frequency stability can only reach 2 × 10⁻¹⁵ after 10 000 s. The traditional stability improvement methods are based on the Ramsey line-width optimization. The correction signal of fountain clock contains error, which can be removed partly by data correction. A new method to improve the frequency stability by modified error factor with statistical theory is presented in this paper. The results of frequency stability can reach 1.03 × 10⁻¹⁴/2 s and 2.78 × 10⁻¹⁶/16 400 s.