Modelling the Nonlinear Properties of Ferroelectric Materials in Ceramic Capacitors for the Implementation of Sensor Functionalities in Implantable Electronics

For several years, the requirements on miniaturization of electronic implants with application in functional electrostimulation have been increasing, while functionality and reliability should not be impaired. One solution concept is to use neither active electronic components nor sensors or batteries. Instead, the functionalities are ensured by the use of intrinsic nonlinear properties of the already used components and energy is transferred by inductive coupling. In this paper, ceramic capacitors are investigated as a first step towards exploiting the nonlinear characteristics of ferroelectric materials. The ceramic capacitors are characterized by simulation and measurements. The modeling is carried out in Mathcad Prime 3.1 and ANSYS 2019 R2 Simplorer and different solvers are compared for exemplary calculations. Finally, a measurement setup is realized to validate the models. Calculations show that the trapezoid method with a number of 500 k points in the given solution interval is best suited for ANSYS. In Mathcad, the Adams, Bulirsch–Stoer, Backward Differentiation Formula, Radau5, and fourth order Runge–Kutta methods with an adaptive step width and a resolution of 50 k points are the most suitable. The nonlinear properties of ferroelectric materials in ceramic capacitors modeled with these methods using ANSYS and Mathcad show small and equal deviation from the measurements.