An FMCW radar has a variable frequency microwave signal source for outputting a microwave signal, a frequency divider, a phase-locked loop, a loop filter and a reference signal source. The frequency divider is connected between the output of the variable frequency microwave signal source and an input of the phase-locked loop. The loop filter is connected between the output of the phase-locked loop and the input of the variable frequency microwave signal source. The reference signal source is connected to an additional input of the phase-locked loop. The frequency divider is adjustable, in particular digitally adjustable. A method for operating an FMWC radar includes adjusting a variable frequency microwave signal source by way of a closed-loop control circuit which uses a reference signal of a reference signal source, especially of a quartz oscillator, as the reference value, and a frequency-divided output signal of the microwave signal source as the feedback value.