In the GSM (Global System for Mobile Communications) standard of digital cellular telephony a large number of mobile stations can communicate with a network of base stations.  The mobile stations decode data from the base station network in digital form and, among many other functions, use this data to periodically adjust the master reference oscillator frequency of the mobile station. 
Classically this adjustment of the master reference oscillator frequency has been performed by using a digital to analog converter to change the digital frequency correction data into analog form and then applying the resulting analog signal to a varactor diode to warp a crystal reference oscillator. 
This method has several shortcomings.  First of all the frequency correction data is already in digital form in the GSM system.  It would be desirable to use the data in digital form and thus eliminate the digital to analog converter. 
Secondly, using a varactor diode to warp a crystal results in a non-linear tuning characteristic.  This requires a complex phasing algorithm to linearize the characteristic. 
Finally, the practical limitations of the digital to analog converter resolution and the crystal oscillator component tolerances require a fairly large step size in the frequency tuning characteristic.  In the GSM system this results in a step size of about 50 Hz.  Since the frequency accuracy of GSM is required to be &lt;100 Hz this can be a major problem. 
A digital automatic frequency control system can be realized by the use of fractional N synthesis.  Such a system is shown in U.S. Pat.  No.  5,111,162, entitled "Digital Frequency Synthesizer having AFC and Modulation Applied to Frequency Divider" authored by Hietala et al.  In this patent a secondary divider is used from the main oscillator output to derive a low frequency reference for offset synthesizers and logic circuitry.  This secondary divider operates at the output frequency, thus, draws excessive current. 
Therefore it would be advantageous to devise a digital automatic frequency control system which allows the digital automatic frequency control data to be used without conversion to analog form while providing a linear tuning characteristic with very fine minimum frequency step size and without drawing excessive current.