Optimal Discontinuous Frequency Modulation for Spread-Spectrum Clocking

Recent all-digital spread-spectrum clock generators allow the synthesis of clock signals with a discontinuous frequency behavior. Following the electromagnetic interference (EMI) test guidelines, this paper investigates for the first time the peak-level reduction of the spectrum (modulation gain) achievable by using discontinuous frequency modulated signals in spread-spectrum clocking applications. In this paper, the spectrum of discontinuous frequency clock signals, measured by a spectrum analyzer in a peak-hold mode, is computed analytically in closed form. This expression is used to formulate the problem of finding the optimal discontinuous frequency modulated waveform as the solution of a nonlinear differential equation. A suboptimal modulation waveform, which can be computed in closed form, is also derived in this paper. To verify the effectiveness of developed approach, the spectrum of frequency-modulated clock signals with different modulation waveforms and different modulation parameters (frequency deviation, modulation frequency) has been calculated for two different spectrum analyzer resolution bandwidths (100 kHz, 1 MHz). The obtained results show that discontinuous frequency modulations can result in an improvement of 1.5-2 dB in comparison to continuous frequency clock signals.