Editing Humidity Detector Based on Quartz Crystal Oscillator (section)

=== Background and Theoretical Inspiration ===
Accurate humidity monitoring is a fundamental requirement in numerous industrial, meteorological, and scientific applications. While traditional humidity sensors largely rely on capacitive or resistive mechanisms, they often exhibit limitations regarding response time, hysteresis, and long-term stability. To address the demand for high-precision, real-time sensing, mass-sensitive acoustic wave devices have garnered significant attention.<ref>  X. Ding, X. Chen, N. Li, et al., “A QCM humidity sensor based on fullerene/graphene oxide nanocomposites with high quality factor,” Sensors and Actuators B: Chemical, vol. 266, pp.534–542, 2018.</ref>

The theoretical foundation of our project is inspired by the Quartz Crystal Microbalance (QCM) principle. At its core, this principle relies on the mass-loading effect described by the Sauerbrey equation <ref> G. Sauerbrey, “Verwendung von Schwingquarzen zur W¨agung d¨unner Schichten und zur Mikrow¨agung,” Zeitschrift f¨ur Physik, vol. 155, no. 2, pp. 206–222, 1959.</ref>

<math> 
\Delta f = - \frac{2 f_0^2}{A \sqrt{\rho_q \mu_q}} \Delta m
</math>

Where a change in the mass (<math>\Delta m</math>) attached to the surface of a piezoelectric quartz crystal results in a directly proportional, negative shift in its resonant frequency (<math>\Delta f</math>). While commercial QCM systems utilize highly specialized and often expensive internal circuitry, the fundamental physical phenomenon—that a crystal's oscillation frequency drops as it gets heavier—serves as the conceptual basis for our humidity detector.