A phase or frequency locked-loop circuit includes an oscillator configured to generate an output clock signal having a frequency set by an oscillator control signal. A modulator circuit receives a first signal and a second signal and is configured to generate a control signal having a value modulated in response to the first and second signals. A filter circuit generates the oscillator control signal by filtering the control signal. A delta-sigma modulator circuit operates to modulate the second signal in response to a modulation profile. As a result, the output clock signal is a spread spectrum clock signal.