Frequency measurement is one of the most important tasks in modern electrical metrology. In particular, for highly sensitive sensors with a frequency output, the resolution and sensitivity depends of the frequency measurement method used. The principle of rational approximations is a technique for frequency measurement, and its use has been proposed for application in sensors. In this work, a device which implements the principle of rational approximations is presented, and its characteristics are analyzed. Particularly, the system is used to measure the signal generated by a quartz crystal microbalance, and the relationship between the measured frequency, temperature and measurement time are evaluated.