An apparatus for generating an output signal having a particular frequency includes an oscillator, a first tuning module, and a second tuning module. The oscillator generates an output signal associated with an output frequency. When coupled to the oscillator, the first tuning module is capable of inducing, within a first amount of time, a change in the output frequency of a particular magnitude. When coupled to the oscillator, the second tuning module is capable of inducing, within a second amount of time, a change in the output frequency of the same magnitude. The second amount of time is greater than the first amount of time. The selector couples a selected one of the first tuning module and the second tuning module to the oscillator based on a difference between a frequency-divided version of the output signal and a reference signal.