Hardwicke, K. R.; Applied Research Labs (International Foundation for Telemetering, 1992-10)
      The uncertainty in the gain of voltage controlled crystal oscillators (VCXOs) used in the implementation of certain analog phase-locked loops (PLLs) suggests some form of automatic tuning algorithm, both for pretuning and during operation. This paper proposes an adaptive PLL (APLL) algorithm to fill this need for PLLs used in the recovery of tones in noise. This algorithm makes use of a resonant error algorithm to remove the effects of VCXO noise, measurement noise, and parasitic poles. Both classical convergence theorems and robustness theorems that indicate the functionality of the proposed algorithm are given. Finally, the implementation of this algorithm is considered.