Design equations and baseband model for double-sampling phase-locked loop

As in the case of many other important mixed-signal circuits, the mathematical model of the double-sampling phase-locked loop (PLL) results in an integro-difference equation which cannot be solved easily. Nonuniform and nonideal sampling makes the design problem even more complicated. In this paper, a baseband model and design equations are derived for the double-sampling PLL. The new model proposed here takes into account the effect of nonideal sampling and generates all signals both in the discrete- and continuous-time domains. The theoretical results are verified by measurements. The advantage of the proposed model is that it improves the accuracy and reliability of the circuit design process