A clock circuit includes an oscillator (15) for generating a reference frequency signal, and a spread spectrum clock generator (14) cooperating with the oscillator for generating a spread spectrum clock output signal having a fundamental frequency and reduced amplitude EMI spectral components at harmonics of the fundamental frequency. The spread spectrum clock generator preferably includes a clock pulse generator for generating a series of clock pulses, and a spread spectrum modulator for frequency modulating the clock pulse generator to broaden and flatten amplitudes of EMI spectral components which would otherwise be produced by the clock pulse generator. The spread spectrum modulator frequency modulates the clock pulses with specific profiles of frequency deviation versus the period of the profile. Electronic devices including the spread spectrum clock circuit and associated method are also disclosed.