Consistent and Efficient Modeling of the Nonlinear Properties of Ferroelectric Materials in Ceramic Capacitors for Frugal Electronic Implants

Abstract

In recent years, the development of implantable electronics has been driven by the motivation to expand their field of application. The main intention is to implement advanced functionalities while increasing the degree of miniaturization and maintaining reliability. The intrinsic nonlinear properties of the electronic components, to be used anyway, could be utilized to resolve this issue. To master the implementation of functionalities in implantable electronics using the nonlinear properties of its electronic components, simulation models are of utmost importance. In this paper, we present a simulation model that is optimized in terms of consistency, computing time and memory consumption. Three circuit topologies of nonlinear capacitors, including hysteresis losses, are investigated. An inductively coupled measurement setup was realized to validate the calculations. The best results were obtained using the Trapezoid method in ANSYS with a constant step size and a resolution of 500 k points and using the Adams method in Mathcad with a resolution of 50 k points. An inductive coupling factor between 7% and 10% leads to a significant improvement in consistency compared to lower coupling factors. Finally, our results indicate that the nonlinear properties of the voltage rectifier capacitor can be neglected since these do not significantly affect the simulation results.

Experimental Characterization of Ferroelectric Capacitor Circuits for the Realization of Simply Designed Electroceuticals

“…In other words, we plan to use the ferroelectric material as smart material to realize closedloop control functionalities in simply designed implantable circuits. Compared to previous publications [27,28], the investigations were expanded to a total of 20 circuit topologies of series-and/or parallel-connected ferroelectric ceramic capacitors, a frequency range between 183 kHz to 951 kHz and loads of 300 Ω, 680 Ω and 1000 Ω. In addition, Since the 1940s, the increasing interest in ferroelectric ceramics has led to the development of numerous applications, such as high-dielectric-constant barium titanate capacitors, medical diagnostic ultrasonic transducers, non-volatile memories, tunable microwave circuits and the realization of sensor and actuator functionalities in microelectromechanical systems [24,25].…”

“…In our previous investigations [27,28], the main focus was on the optimization in terms of consistency, computing time and memory-consumption of the model introduced in Mathcad and ANSYS. Circuit topologies consisting of one linear and nonlinear capacitor, two series-connected and two parallel-connected nonlinear capacitors were investigated at a constant load of 1 kΩ and frequency of 375 kHz.…”

“…• 𝑘: inductive coupling factor between the inductances L1 and L2; Based on previous investigations and regarding computing time, memory consumption and consistency, the above differential equations are solved using the Adams method with a calculation tolerance of 10 −7 [27,28]. The frequency and pulse duration of the inductive power transfer as well as the time span for calculating Uc2 and Istim were set according to the settings in the measurement setup (see Chapter 2.2).…”

“…In other words, we plan to use the ferroelectric material as smart material to realize closed-loop control functionalities in simply designed implantable circuits. Compared to previous publications [27,28], the investigations were expanded to a total of 20 circuit topologies of series-and/or parallel-connected ferroelectric ceramic capacitors, a frequency range between 183 kHz to 951 kHz and loads of 300 Ω, 680 Ω and 1000 Ω. In addition, ferroelectric capacitors of different capacitance-voltage dependencies were used.…”

Investigation of an embedded closed-loop stimulation current control principle based on the use of nonlinear ceramic capacitors

“…The calculations are performed in Mathcad. A detailed description of the model can be found in [8,9].…”