Systems, methods, and circuits provide a digital frequency synthesizer where the output of the frequency synthesizer is a fractional factor of an input signal frequency. The digital frequency synthesizer may comprise a time to digital converter. A ramp offset signal may be added to the output of the time to digital converter. The ramp offset signal may be added to the output of a TDC until a reference dock signal reaches a value of pi. At such a point, the reference clock signal may be switched and the ramp offset signal may be restarted. As such, a frequency offset may be introduced at the input of the time to digital converter where the frequency offset may be modified by changing the slope of the ramp offset signal.