the present invention provides a frequency synthesizer comprising a noise - shaped quantizer and a divider . the noise - shaped quantizer is utilized for quantizing a period control word to a time - varying value . the divider is used for generating an output signal by of dividing a reference signal by the time - varying value . the output signal is fed back to the noise - shaped quantizer so that the noise - shaped quantizer generates the time - varying value in response to the feedback output signal . accordingly , the frequency synthesizer of the present invention can provide a very precise frequency synthesizer featuring very accurate long - term phase , frequency , and jitter stability .