This reference work on phase-locked loops for wireless communications engineers includes summary chapters on the circuit theory needed to explain the theory and operation of phase-locked loops and the supporting mathematics necessary for analysis. These include concise discussions of Laplace transformations, Z-transformations, root locus, Bode analysis, partial fraction expansion, and others. The material develops systematically from analog through digital loops. Included is broad coverage of synchronization methods and techniques, modern digital interpolation techniques in modem design, modem acquisition and tracking, fading channel performances, as well as practical rules-of-thumb for modem designers to use in specifying loop bandwidths for good performances. The book provides numerous real world applications, and each chapter has problem sets that reinforce important concepts presented. The text features a collection of topics needed by both the wireless and traditional phase-locked loop specialist to design and analyze high performance circuits and software algorithms.