A digital synthesizer is described that comprises: a ramp generator configured to generate a signal of frequency control words, FCW, that describes a desired frequency modulated continuous wave; a digitally controlled oscillator, DCO configured to receive the FCW signal; a feedback loop; and a phase comparator coupled to the ramp generator and 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 at least one gain from a plurality of selectable gains to the N-bit oscillator control signal that set a selectable loop gain of the digital synthesizer and thereby set a selectable loop bandwidth; andcalculate and apply a gain offset dependent upon the selected gain that is adapted when the selected gain is changed.