Dependency of jitter variance on PLL normalized noise bandwidth

The present paper describes the dependency of jitter variance on the PLL normalized noise bandwidth, b_L, applying a linearized model of a PLL. The timing circuit consists of a square-law device, a pre-filter, and a PLL arranged in tandem. The transmission systems are PAM, ASK, and QAM for a root roll-off bandlimiting scheme. An additive white Gaussian noise exists at the receive filter input The pre-filter and PLL are referred to as the extractor. The SN and NN components of jitter variance are proportional to b_L, whereas the SS component is proportional to the square of b_L. The mechanism of this discrepancy is clarified through a detailed discussion of the relationships among the jitter source PSD, the extractor transfer function characteristics, and the jitter PSD. This proportional relation holds for any transmission system, any SNR, and any roll-off factor considered herein.