Based on the theory of the passive hydrogen maser, along with the technology of frequency modulation and modulation transfer spectroscopy, the theoretical expression of the single frequency modulation for the passive hydrogen maser and the function of the cavity and H line error signals separation are derived, which are basically coincident with the experiment. The absorption and dispersion spectrum curves with different resonance widths show that the cavity and hydrogen transition serve as discriminators, and the two error signals can be separated. Through the calculations of the two error signals in the passive hydrogen maser, it analyzes the traditional method of the two error signals separation, and then describes a new improved method for the passive hydrogen servo loops consisting in the use of a single modulation frequency and frequency discrimination. A null interaction of the two error signals for the new selection of the phase setting is deduced theoretically and validated by the simulation. The preliminary experimental result confirms the feasibility of this new approach, which can reduce the influence from the cavity frequency variety on the crystal oscillator and contribute significantly to the long term performance of the passive hydrogen maser.