Frequency domain analysis of double sampling phase-locked loop

Double sampling phase-locked loop (2-SPLL) is used in frequency synthesis. The unique feature of single sampling PLL is that its phase detector (PD) has a very low unwanted periodic output in steady state. In 2-SPLL, a second sample and hold circuit (S&H) is connected in cascade to suppress further the unwanted periodic PD output. However, the absence of a proper baseband model and design equations prevent the exploitation of all benefits of 2-SPLL. This paper develops a nonlinear baseband model for the 2-SPLL. Then based on the linearized baseband model, analysis is performed in the frequency domain and the frequency responses required to determine the spectrum of the output signal as a function of reference and VCO noise and modulation inputs are developed. Finally, the theoretical results are verified by measurements