Discrete z-domain analysis of high order phase locked loops

Jitter transfer analysis using discrete z-domain transfer functions of a high order giga-bit rate phase locked loop (PLL) is presented. An impulse invariance method that produces the same z-domain equations as that of the differential analysis is first shown for a second order loop. The condition is obtained. Then a closed form third order loop equation in discrete zdomain is derived. Stability and frequency step response of a 3 order 1.25GHz phase lock loop is examined using the discrete z-domain transfer function. Random jitter performance is predicted, based on noise simulations of individual blocks, and the discrete z-domain transfer functions from each of the PLL sub-blocks to the PLL output. The predicted random jitter is compared against silicon measurements, and shown.