Approximating Frequency Synthesizers

The process of frequency synthesis is the step-by-step approximation to the normalized output frequency. In this paper, three different approximation algorithms are briefly discussed, namely continued fractions, Cantor products, and Engel series. Their common disadvantage is their uniqueness; it is shown that this difficulty may be overcome by application of the new general approximation theorem, but the solution can be provided only by computer. Approximation errors are generally small, sometimes smaller than 1 × 10-12. The advantage of modified Cantor products or Engel series algorithms is the possibility of standardizing the hard ware of frequency synthesizers, particularly if the IC technology and the use of off-the-shelf circuits is emphasized.