Settling time specifications: phase or frequency?

The tuning speed of frequency synthesizers is usually specified by either phase or frequency setting. This paper shows that in frequency hopping systems (with FSK type of modulation) phase settling characteristics correspond to system performance better than frequency settling characteristics. This paradoxical condition is discussed in three ways: (1) a simulation compares frequency and phase settling to system performance, (2) intuitive explanations are developed, (because one cannot accept mathematical proof unless it makes sense), and (3) confirmation by mathematical analysis is presented. Finally, phase settling specifications are discussed.<>