Modeling and Analysis of a PLL-Based Resonant Frequency Tracking System Using a Resonant Cavity Sensor

Resonant sensors are widely employed in several applications, and resonant cavity sensors have advantages when noninvasive and non-destructive measurements are required. In this technology, the resonant frequency of the sensor is used to estimate different measurement parameters, since it varies according to the permittivity of the material under test. In this paper, a resonant frequency tracking system, combining a resonant cavity sensor and a phase-locked loop circuit, is investigated. The system has a quadrature phase detector being able to estimate both, phase and magnitude information, and is well suited for applications involving water as a material under test. A complete description of the measurement system combining experimental results with theoretical models, previously reported in the literature, is accomplished. Such theoretical models are based on the amplitude-phase dynamics and assume that the sensor is modeled as a linear resonator. Hence, a semi-empirical modeling is elaborated and the validation results precisely demonstrate the reliability of the modeling, proving to be very useful for further analysis.