Reliable and integrated technique for determining resonant frequency in radio frequency resonators. Application to a high-precision resonant cavity-based displacement sensor.

This paper presents a reliable and integrated technique for determining the resonant frequency of radio frequency resonators, which can be of interest for different purposes. The approach uses a heterodyne scheme as phase detector coupled to a voltage-controlled oscillator. The system seeks the oscillator frequency that produces a phase null in the resonator, which corresponds to the resonant frequency. A complete explanation of the technique to determine the resonant frequency is presented and experimentally tested. The method has been applied to a high-precision displacement sensor based on resonant cavity, obtaining a theoretical nanometric precision.