Physically Inspired Circuit Model for Systematic Analysis of Resonant Ion Sensor

Ions play a significant role in biological, industrial, and agricultural processes. Noninvasive, real-time detection of their presence and concentration has become of vital importance in a multitude of processes. In this paper, we present a lumped-element circuit model for an Archimedean spiral inductor based resonant sensor which accurately detects and quantifies ionic concentration of aqueous solutions. The development of the model is guided by observed physical phenomena caused by changing a solution's ionic concentration. The system's response to different concentrations of aqueous potassium chloride is measured, and the model parameters are extracted from measured data. The model parameters are extrapolated to obtain expressions that model the system's response over a wide range of concentrations. There is good agreement between the model and measured data, making it valid for concentrations ranging from 1.66 mmol/L to 1 mol/L. The model helps generate insight into the behavior of the physical system, could be used to systematically optimize the sensor design, and could be extended to other analytes.