TABLE OF CONTENTS The manner that a PLL changes to an input frequency or phase shows an important aspect of PLL performance. A step change of the input is one of the most important measures of its response. Does the output reach its final value quickly or slowly? Does it overshoot? If so, how long does it take to come finally within a specified offset from the final value? How great is the phase error during a frequency step? Does it surpass the range of the phase detector? To help answer such questions, we will generate a set of curves showing time responses under various conditions.
The challenge is to find a reasonably small set of curves that covers a large number of cases of practical importance. First, we will restrict our attention to linear performance. Consequently, the response to any size input step will be proportional to that step. So, a curve of unit step response will give us the response to all step sizes. Next, we will restrict our study to type 2 loops as another device for limiting the number of curves. Let's restrict our curves to damping factors less than 1 because of the difficulty of getting phase margins greater than 80 to have damping factors greater than 1. Finally, type 2 curves will be plotted against normalized time, ? nt, for various damping factors ?.
Studying the time-domain response of a loop gives us...
