A frequency synthesizer is disclosed. The frequency synthesizer includes a period control word generator, a delta-sigma modulator, and a delay line unit. The period control word generator generates a period control word. The delta-sigma modulator receives the period control word and generates a phase selection signal. The delay line unit generates an output clock based on the phase selection signal. The delta-sigma modulator performs a carry-in operation based on a base number and the base number is adjustable and determined by a calibration process of the delay line unit.