Z-Domain Model for Square Wave PLL's.

The well-known s-domain model for sinusoidal phase-locked loops is a fundamental tool for the linearized analysis of these systems. For PLL's with digital inputs and outputs, however, a discrete time z-domain model more accurately describes loop behavior. In this paper, a methodology is described for obtaining an accurate z-domain description of a square wave PLL. This modelling 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 DSI (Digital Signalling 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 far more accurate, especially for jitter frequencies higher than 1/20th of the input transition rate.