TABLE OF CONTENTS Control-systems theory and analysis of PLLs is covered in this chapter. This chapter could have been combined with the Chapter 3 on system requirements; however, this chapter was separated to emphasize the importance of system analysis. In addition, system analysis gives a deeper understanding of how a PLL works, building upon the material covered in Chapter 1. A general system concept of how PLLs work will help in understanding the following chapters.
First, VCO and phase detector mathematical relationships are discussed. Then, Bode plot analysis of PLLs is studied so that stability requirements can be designed. The relationship between step response and stability is studied in order to recognize the stability of a loop and its measured step response. Error tracking of a PLL to various stimuli is studied so that the correct loop architecture can be selected to meet tracking requirements. Finally, a simple charge pump synthesis example of a loop filter is studied to begin to understand the relationship between system analysis and component-value synthesis to meet the system requirements. Understanding control systems helps an engineer build stable and robust loops.
We begin with a mathematical description of a VCO so that it can be used in the analysis of the loop. Understanding this relationship will help with the linear analysis of the loop. We will study the mathematical description of a phase-modulated signal because that is what occurs in a VCO. Consequently, (2.1) gives a mathematical description of a phase-modulated signal, from [1,...
