In the Ramsey scheme, if one modulates two microwave pulses at the same frequency but with ±π/2 phase differences, the Ramsey fringes with zero amplitude at the central frequency can be obtained. By monitoring the variance of probe light absorption by atoms at the central frequency, one can get the error signals which feedbacks to the local oscillator. Theoretically, this method doubles the absorption signal intensity, compared with the case of Ramsey fringes with the same phase. Experimentally, the phase modulated Ramsey pattern in the integrating sphere cold atom clock system is the same with that from theoretical calculation. Moreover, the Ramsey fringe oscillation amplitude here is 1.6 times of that of Ramsey fringes with the same phase.