A frequency synthesizer directly generates phase modulated radio-frequency (RF) signals. The frequency synthesizer includes a voltage controlled oscillator (VCO) producing a synthesized frequency signal having a frequency controlled based on a signal received at an input of the VCO. A digitally adjustable frequency divider produces a reduced frequency signal from the synthesized frequency signal. A phase digital-to-analog converter (DAC) produces a delayed version of a timing signal (e.g., the reduced frequency signal, or a reference clock signal) that is delayed according to a digital control signal. A phase detector (PD) produces a phase control signal from the reduced frequency signal and/or the delayed timing signal. A digital signal converter controls the digitally adjustable frequency divider and the phase DAC so as to cause a phase or frequency of the synthesized frequency signal output by the VCO to track a desired phase or frequency trajectory encoded in a digital signal.