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

^{*}

## Abstract

**:**

## 1. Introduction

^{3}is required [19]. A volume of about 0.016 mm

^{3}is sufficient when using class 2 capacitors [20]. Materials such as barium titanate, calcium titanate, strontium titanate, magnesium titanate, and calcium zirconate, to name but a few, can be used as dielectric for ferroelectric capacitors. The material composition and the grain size of the dielectric result in different dielectric constants and temperature dependencies [21,22]. However, the exact structure of the capacitors and its dielectric composition are not given by the manufacturer. A typical structure of such capacitors is shown in Figure 1. Further investigations (e.g., energy-dispersive X-ray spectroscopy, scanning electron microscopy) are required in this regard [23].

## 2. Materials and Methods

#### 2.1. Characterization of Ceramic Capacitors by Measurement

^{3}[29]. According to the manufacturer’s specifications [29], the dielectric consists of barium titanate and the inner electrodes are made of nickel. The size of the GRM022R60G473ME15L capacitor is typically 0.4 × 0.2 × 0.2 mm

^{3}[20]. An inner electrode thickness of approximately 0.4 µm and a ceramic layer thickness of about 0.5 µm are reported in the manufacturer’s specifications [30]. The inner electrodes are made of nickel [31].

#### 2.2. Characterization of the Circuit Topologies by Measurement

_{1}, loss resistor R

_{1}(760308100110, Würth Elektronik eiSos GmbH & Co. KG, Waldenburg, Germany, without ferrite) and parallel-connected capacitors C

_{1}(FKP1, WIMA GmbH & Co. KG, Mannheim, Germany) is driven through a half-bridge consisting of two N-MOSFETS (IRFB5615PbF, Infineon Technologies AG, Munich, Germany). The half-bridge is driven by a signal generator (DG5102, Rigol Technologies, Inc., Suzhou, China) and a gate driver (UCC27211, Texas Instruments Inc., Dallas, TX, USA). The gate driver is supplied with a constant voltage of 17 V and the half-bridge with a variable voltage between 0 V and 30 V using the Agilent U8031A power supply.

_{1}(LL4148, Vishay Intertechnology, Malvern, PA, USA) and the capacitor C

_{4}(4.7 µF, 50 V, 1206). Inductive power harvesting is achieved using a parallel resonant circuit consisting of an inductance L

_{2}, a loss resistor R

_{2}(760308101104, Würth Elektronik, without ferrite) and a circuit topology of ceramic capacitors. The electrode impedance is represented by the ohmic load R

_{L}.

_{L}, leading to the stimulation current Istim, were measured in a time span between 0.4 ms and 0.8 ms using the Tektronix MDO4104-6 (Tektronix, Inc., Beaverton, OR, USA) oscilloscope and two TESTEC TT-MF312-2-6 11020-2-6 (TESTEC Elektronik, GmbH, Frankfurt, Germany) probes. The measurements were recorded at a sample rate of 2.5 GS/s. Depending on the investigated circuit topology of capacitors, the frequency of the inductively coupled system was set between 183 kHz and 951 kHz. Accordingly, the pulse duration was set between 2 ms and 9 ms in order to consider the system in steady state. The distance between the extracorporeal and the implantable circuit was set to 5 cm, 3 cm and 1 cm, corresponding to a coupling factor of about 1%, 2% und 11%, respectively. The coupling factor was calculated by measuring the inductance of the extracorporeal transmitter for an open- and short-circuit inductance of the implantable circuit using the Agilent 4294A precision impedance analyzer.

#### 2.3. Modeling in Mathcad

- $k$: inductive coupling factor between the inductances L
_{1}and L_{2};

- ${A}_{mp}$: amplitude of the sinusoidal voltage ${u}_{1}\left(t,{A}_{mp},\omega \right)$;

- $\omega $: angular frequency of the sinusoidal voltage ${u}_{1}\left(t,{A}_{mp},\omega \right);$

- ${i}_{L1}\left(t\right)$: electrical current across the primary resonant circuit;

- ${u}_{C1}\left(t\right)$: electrical voltage across the capacitor C
_{1};

- ${i}_{L2}\left(t\right)$: electrical current across inductance L
_{2}and its loss resistance R_{2};

- ${i}_{C2}\left(t\right)$: electrical current across the capacitor C
_{2};

- ${u}_{C2}\left(t\right)$: electrical voltage across the capacitor C
_{2};

- ${u}_{D1}\left(t\right)$: electrical voltage across diode D
_{1};

- ${i}_{D1}\left({u}_{D1}\left(t\right)\right)$: electrical current flowing through the diode D
_{1}as a function of the voltage ${u}_{D1}\left(t\right)$;

- ${u}_{C4}\left(t\right)$: electrical voltage across the capacitor C
_{4};

- ${i}_{C4}\left(t\right)$: electrical current across the capacitor C
_{4};

- ${i}_{Stim}\left(t\right)$: electrical current across the resistive load R
_{L}.

^{−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 Section 2.2). The number of points for a given solution interval is obtained by dividing the pulse duration by 10 ns. Thus, the number of points ranges between 200 k and 900 k. The capacitors were measured at the frequency of inductive power transfer (see Section 2.1) and were interpolated in Mathcad with third-order B-spline functions.

_{c2}(t) and current i

_{c2}(t) in Equations (1)–(9) are expanded according to the circuit topologies of ceramic capacitors shown in Figure 4.

## 3. Results

_{L}to 300 Ω, 680 Ω and 1000 Ω. For the sake of illustration, only the results for a distance of 1 cm are shown in order to characterize Istim over a wide range of Uc2.

#### 3.1. Circuit Topology Consisting of One Capacitor

#### 3.2. Circuit Topology Consisting of Two and Four Series-Connected Capacitors

#### 3.3. Circuit Topology Consisting of Two and Four Parallel-Connected Capacitors

#### 3.4. Circuit Topology Consisting of One Capacitor Connected in Series to Two Parallel-Connected Capacitors

## 4. Discussion

_{L}(300 Ω, 680 Ω and 1000 Ω), frequencies (between 183 kHz and 951 kHz) and 20 circuit topologies consisting of linear and/or nonlinear capacitors connected in series and/or in parallel. The resulting nonlinearity of the investigated topologies can be divided into three sections: (1) an approximately linear increase in the stimulation current, (2) a stabilization of the stimulation current, and (3) an unstable state of the system.

_{L}leads to a higher stimulation current and vice versa for a circuit topology consisting of linear and nonlinear capacitors. It should be ensured that the stimulation current remains within a safe range for application-specific electrode impedances.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Typical structure of a multilayer ceramic chip capacitor (MLCC) with: (1) ceramic dielectric layers, (2) inner electrode layers and (3, 4, 5) termination electrodes. The termination electrodes consist of: (5) a substrate layer for connecting the termination to the inner electrodes, (4) a barrier layer as thermal protection of the dielectric from soldering and an external layer (3) for soldering the MLCC.

**Figure 2.**Inductively coupled system for power transfer consisting of an extracorporeal transmitter (

**left**) and an implantable electronic circuit (

**right**). The extracorporeal transmitter consists of a resonant half-bridge converter, a capacitor C

_{1}, an inductance L

_{1}and a loss resistor R

_{1}. The implantable electronic circuit consists of a parallel resonant circuit, which is composed of the inductance L

_{2}, loss resistor R

_{2}and a circuit topology of ceramic capacitors, a half-wave rectifier consisting of the diode D

_{1}and capacitor C

_{4}and an ohmic load R

_{L}representing the electrode impedance. The inductive coupling between the extracorporeal transmitter and the implantable electronic circuit is represented by the coupling factor k.

**Figure 3.**Exemplary representation of the pulsed inductive power supply of the implantable electronics. Induced voltage u

_{C2}(t) (

**left**) and rectified stimulation current i

_{Stim}(t) (

**right**) versus time t.

**Figure 4.**Circuit topologies of voltage-dependent ceramic capacitors with: (

**a**) one capacitor; (

**b**) two series-connected capacitors; (

**c**) four series-connected capacitors; (

**d**) two parallel-connected capacitors; (

**e**) four parallel-connected capacitors; (

**f**) one capacitor connected in series to two parallel-connected capacitors.

**Figure 5.**Measured capacitance C according to the bias voltage of the capacitor CGA5L1X7T2J473K160AC and GRM022R60G473ME15L at a frequency of 360 kHz and 400 kHz, respectively (N = 8).

**Figure 6.**Stimulation current Istim as a function of the induced voltage Uc2 for a circuit topology consisting of: (

**a**) linear capacitor; (

**b**) nonlinear capacitor. The measurements (black, red, green) and calculations (blue, cyan, magenta) were performed for R

_{L}= 300 Ω, 680 Ω and 1000 Ω, respectively.

**Figure 7.**Stimulation current Istim as a function of the induced voltage Uc2 for a circuit topology of two series-connected: (

**a**) linear capacitors; (

**b**) linear and nonlinear capacitors; (

**c**) nonlinear capacitors. The measurements (black, red, green) and calculations (blue, cyan, magenta) were performed for R

_{L}= 300 Ω, 680 Ω and 1000 Ω, respectively.

**Figure 8.**Stimulation current Istim as a function of the induced voltage Uc2 for a circuit topology of: (

**a**) four series-connected linear capacitors; (

**b**) two series-connected linear and two series-connected nonlinear capacitors; (

**c**) four series-connected nonlinear capacitors. The measurements (black, red, green) and calculations (blue, cyan, magenta) were performed for R

_{L}= 300 Ω, 680 Ω and 1000 Ω, respectively.

**Figure 9.**Stimulation current Istim as a function of the induced voltage Uc2 for a circuit topology of two parallel-connected capacitors consisting of: (

**a**) two linear capacitors; (

**b**) a linear and a nonlinear capacitor; (

**c**) two nonlinear capacitors. The measurements (black, red, green) and calculations (blue, cyan, magenta) were performed for R

_{L}= 300 Ω, 680 Ω and 1000 Ω, respectively.

**Figure 10.**Stimulation current Istim as a function of the induced voltage Uc2 for a circuit topology of four parallel-connected capacitors consisting of: (

**a**) four linear capacitors; (

**b**) two linear and two nonlinear capacitors; (

**c**) four nonlinear capacitors. The measurements (black, red, green) and calculations (blue, cyan, magenta) were performed for R

_{L}= 300 Ω, 680 Ω and 1000 Ω, respectively.

**Figure 11.**Stimulation current Istim as a function of the induced voltage Uc2 for a circuit topology of one linear capacitor series-connected to two parallel-connected: (

**a**) linear capacitors; (

**b**) linear and nonlinear capacitors; (

**c**) nonlinear capacitors. The measurements (black, red, green) and calculations (blue, cyan, magenta) were performed for R

_{L}= 300 Ω, 680 Ω and 1000 Ω, respectively.

**Figure 12.**Stimulation current Istim as a function of the induced voltage Uc2 for a circuit topology of one nonlinear capacitor series-connected to two parallel-connected: (

**a**) linear capacitors; (

**b**) linear and nonlinear capacitors; (

**c**) nonlinear capacitors. The measurements (black, red, green) and calculations (blue, cyan, magenta) were performed for R

_{L}= 300 Ω, 680 Ω and 1000 Ω, respectively.

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**MDPI and ACS Style**

Olsommer, Y.; Ihmig, F.R.
Experimental Characterization of Ferroelectric Capacitor Circuits for the Realization of Simply Designed Electroceuticals. *Electron. Mater.* **2021**, *2*, 299-311.
https://doi.org/10.3390/electronicmat2030021

**AMA Style**

Olsommer Y, Ihmig FR.
Experimental Characterization of Ferroelectric Capacitor Circuits for the Realization of Simply Designed Electroceuticals. *Electronic Materials*. 2021; 2(3):299-311.
https://doi.org/10.3390/electronicmat2030021

**Chicago/Turabian Style**

Olsommer, Yves, and Frank R. Ihmig.
2021. "Experimental Characterization of Ferroelectric Capacitor Circuits for the Realization of Simply Designed Electroceuticals" *Electronic Materials* 2, no. 3: 299-311.
https://doi.org/10.3390/electronicmat2030021