Quantitative Modeling of Phase Detection in Passive Inductively Coupled Resonant Sensors

We develop a model to quantify the signal strength in passive inductively coupled resonant sensor (PICRS) systems. We also explore the relationship between detectability and signal strength, which is critical for signal strength-sensitive applications. Either the phase or magnitude of the input impedance of a coupled reader can be used as a measurand; here, we focus on phase, but the model can be easily adapted to other measurands. The model employs dimensionless parameters, i.e., the quality factor (Q) of the PICRS and coupling factor (k) between the reader and PICRS. We experimentally verify the model using readers and sensors of different Q and k factors. The model incorporates the effect of the reader coil, which is essential for co-selection of readers and sensors. This model can find broader application as a tool for the design and detection of nonisochronous weakly coupled resonant sensors.