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A frequency control loop which locks the frequency of a 5-MHz quartz crystal oscillator to a value defined by the hyperfine transition of 199Hg+ ions is described. The properties of the closed loop are studied using the z-transform technique. The loop parameters are calculated in order to optimize the response time to some usual deterministic perturbations of the VCXO frequency. The results of this analysis can be applied to other digital control loops, such as the hydrogen-maser auto-tuning system.