Frequency-temperature considerations for digital temperature compensation

A fundamental requirement for compensation of the frequency-temperature (F-T) characteristics of a resonator is that the scheme used to estimate the frequency of the resonator from the temperature measurement be able to provide the necessary precision. A description is given of the anomalous behavior of the (F-T) characteristics of quartz resonators at the pp 10⁸ level, which necessitates a sophisticated estimation scheme. Estimation schemes, including least squares regression, minmax, segmented polynomials, and interpolation algorithms such as spline and Akima, are reviewed. There are many choices for (F-T) compensation algorithms which are superior to the usual least squares fit. These algorithms can be used with any digital compensation technique. The multisegment Lawson algorithm is the most efficient choice, but any of the interpolation schemes will give optimum results at the cost of requiring more memory