z-domain model for discrete-time PLL´s

The well-known s-domain model for continuous-time phase-locked loops (PLLs) is a fundamental tool for the linearized analysis of these systems. For PLLs with digital inputs and outputs, however, a discrete-time z-domain model more accurately describes loop behavior. In this study, a methodology is described for obtaining an accurate z-domain description of a discrete-time PLL. The modeling technique transforms portions of the s-domain PLL model directly into the z-domain, requiring only straightforward algebraic manipulations even for complex loop filters. This methodology is demonstrated for a simple loop filter, and measurements from the digital signaling interface integrated circuit are used to compare s-domain, z-domain, and time-step analysis results for a more complicated loop filter. The z-domain model, although only incrementally more complicated than the s-domain model, is shown to be more accurate, especially at higher jitter frequencies