Can Analog PLLs Hold Lock? A Paradox Explored [Open Column]

This article has extended the methods of earlier workers to devise formulas that predict the variance of phase-error accumulation in type-1 PLLs in response to h₃/f³ phase noise. The formulas are in terms of engineering specifications of the PLLs and of measurable specifications of phase noise spectra. Numerous approximations have been made so that the formulas cannot be expected to be highly accurate. More significantly, the analysis does not prove that the phase error accumulation actually occurs; the theory that implicitly underlies the formulas may not be valid under the conditions postulated. An experiment to test the predictions would be a worthy project.