Effect of a pre-filter on timing jitter

The jitter variance in a digital transmission system has three components: SS, SN, and NN. The timing circuit is assumed to consist of a square-law device, a pre-filter, a PLL, and a ZCD. When the pre-filter is assumed to be a second-order Butterworth BPF, the SS component of jitter variance, which is often referred to as self-noise, decreases by more than 10 dB with a roll-off factor of 0.3 for 16QAM and SS becomes proportional to the cube of the PLL bandwidth. The Q value of the pre-filter is determined based on the PLL bandwidth. In addition, the SN and NN are proportional to the PLL bandwidth. The mechanism of these phenomena is clarified in terms of the jitter spectral characteristics and the extractor (a pre-filter and a PLL) transfer function characteristics.