Abstract: A method and device for frequency synthesizing, in which the digital frequency synthesizer includes a clock pair having two similar ring-oscillators to separately generate a search frequency and an output frequency, a frequency tracking unit, and a clock controlling unit. The frequency-search method includes two stages: one stage is the coarse search stage based on the "Prune-and-Search", and other stage is the fine search stage based on the "fixed-step" algorithm. In order to determine which search scheme is used to search the target frequency and to determine the lock status, two cost functions for search and lock-in are derived. These two cost functions define the search threshold and the lock threshold, and these thresholds define the cost window and the lock window. If the frequency error is higher than both the search and lock thresholds, a coarse search is activated to estimate the correct frequency.