Analysis of self-noise in a clock recovery system with a high-order nonlinearity

This paper presents a new technique to compute efficiently the spectra of the in-phase (I) and quadrature (Q) components as well as the cross-spectrum of the in-phase and quadrature (I-Q) components of self-noise appearing at the output of the zero-memory, high-order nonlinear (NL) device employed in a clock recovery system. It is known that these spectra play an important role in the phase jitter performance of the clock regenerator. The results are very general and applicable to many cases of practical interest. Numerical examples and computer simulations provided show that the new approach yields very accurate results and is much faster than the usual computer simulation method. In addition, we give a theorem to show that for the signal shapes having linear phase, the cross-power spectrum of self-noise is zero. We also provide a general expression for the jitter variance of the generated clock signal in terms of the power spectra of self-noise in-phase and quadrature components. It is shown that the cross-power spectrum also contributes to timing jitter if the selected signaling shape does not have any symmetry in time domain. The optimal periodic sampling instants are determined by the axis crossings of the clock signal in the positive direction. The axis is set at a level whereby the jitter variance takes on a minimum value. It is concluded that when the cross-power spectrum is zero for all frequencies then the optimal sampling instants occur at the positive zero crossings of the clock signal and only the Q noise contributes to the timing jitter performance.