Strategies for the Accurate Measurement of the Resonance Frequency in QCM-D Systems via Low-Cost Digital Techniques

In this paper, an FPGA (Field Programmable Gate Array)-based digital architecture for the measurement of quartz crystal microbalance (QCM) oscillating frequency of transient responses, i.e., in QCM-D (QCM and Dissipation) applications, is presented. The measurement system is conceived for operations in liquid, with short QCM transient responses due to the large mechanical load. The proposed solution allows for avoiding the complex processing systems typically required by the QCM-D techniques and grants frequency resolutions better than 1 ppm. The core of the architecture is a reciprocal digital frequency meter, combined with the preprocessing of the QCM signal through mixing operations, such as a step-down of the input frequency and reducing the measurement error. The measurement error is further reduced through averaging. Different strategies are proposed to implement the proposed measurement solution, comprising an all-digital circuit and mixed analog/digital ones. The performance of the proposed architectures is theoretically derived, compared, and analyzed by means of experimental data obtained considering 10 MHz QCMs and 200 μs long transient responses. A frequency resolution of about 240 ppb, which corresponds to a Sauerbrey mass resolution of 8 ng/cm², is obtained for the all-digital solution, whereas for the mixed solution the resolution halves to 120 ppb, with a measurement time of about one second over 100 repetitions.