A digital synthesizer is described that comprises: a digitally controlled oscillator, DCO; a feedback loop; a ramp generator configured to generate a signal of frequency control words, FCW, that describes a desired frequency modulated continuous wave; and a phase comparator configured to compare a phase of the FCW output from the ramp generator and a signal fed back from the DCO via the feedback loop and output a N-bit oscillator control signal. The digital synthesizer comprises a gain circuit coupled to a multiplier located between the ramp generator and the DCO and configured to apply a frequency-dependent gain signal to the N-bit oscillator control signal to maintain an open loop gain of the all-digital phase locked loop, ADPLL, and a PLL loop bandwidth that is substantially constant across a frequency modulation bandwidth.