Optimal Design of Passive Resonating Wireless Sensors for Wearable and Implantable Devices

Passive resonating wireless sensors consist of a variable capacitive ( $C_{s}$ ) sensing element in resonance with a coil ( $L_{s}$ ) that is inductively coupled with a proximal readout circuit. They have been utilized in a number of medical and contactless industrial applications for their simple, small, battery-less, and wireless capabilities. An external readout coil ( $L_{r}$ ) detects the changes in the impedance phase spectrum, resulting from the changes in the parameter of interest ( $\Delta P$ ), such as pressure, humidity, or permittivity. A method of optimization for this class of sensors is presented based on a new figure of merit (FoM) to help designers find optimal geometries for both the sensing and inductive link components of the resonating sensor, leading to maximum signal-to-noise ratio (SNR) and sensitivity at a desired reading range. To verify the proposed FoM and optimization algorithm, we fabricated an all-soft resonating wireless sensor prototype for chemical detection with optimal geometry. The phase-dip ( $\Delta \varphi _{dip}$ ) of the sensor at 5-mm interrogation distance is 43°, a 1380% improvement after optimization, at 313.5-MHz operating frequency. The maximum sensitivity, $\partial (\Delta f_{\mathbf {0}}/f_{\mathbf {0}})/\partial (\Delta P$ ), is 9200 ppm, a 24% improvement after optimization, when $100~\mu \text{L}$ of methanol (MeOH) is applied on the interdigitated capacitive sensor. The design methodology was also applied to an intraocular pressure (IOP) sensor and an implantable humidity sensor from literature and led to 661% and 41% improvement in the proposed FoM in simulations, respectively.