Optimal Discontinuous Frequency Modulation for Spread-Spectrum Clocking

Recent all-digital spread-spectrum clock generators allow the synthesis of clock signals with frequency-discontinuous 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 frequency-discontinuous modulated signals in spread-spectrum clocking applications. In the paper, the spectrum of frequency-discontinuous clock signals, measured by a spectrum analyzer in peak-hold mode, is computed analytically in closed-form. This expression is used to formulate the problem of finding the optimal frequency-discontinuous modulated waveform as the solution of a non-linear differential equation. A suboptimal modulation waveform, that 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 (100kHz, 1MHz). The obtained results show that frequency-discontinous modulations can result in an improvement of 1.5-2dB in comparison to frequency-continuous clock signals.