A frequency-providing circuit is disclosed for providing an output signal at a frequency fout. The circuit comprises a frequency-generating unit, a frequency-changing circuit, and a synchronizing circuit. The frequency-generating unit receives a frequency-selecting control signal and provides a frequency output at a frequency fosc, whereby the frequency-generating unit is switchable between different frequencies substantially without a settling time. The frequency-changing circuit receives the frequency output and a frequency-changing control signal and derives the output signal therefrom, whereby the frequency fout of the output signal can be changed, with respect to the frequency fosc, in accordance with the setting of the frequency-changing control signal. The synchronizing circuit synchronizes the frequency-selecting control signal and the frequency-changing control signal.