# Capacitive-Coupling Impedance Spectroscopy Using a Non-Sinusoidal Oscillator and Discrete-Time Fourier Transform: An Introductory Study

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- By coupling electrodes capacitively to the measured object and by incorporating the resulting couplings into an oscillation circuit, an alternating current is applicable inside the object covered with a thin insulating layer.
- (2)
- By measuring the amplitude and phase of the object’s current and those of the object’s potential difference resulting from oscillation, even with unknown coupling capacitance, the impedance of the object is measurable.
- (3)
- By estimating the impedance of the measured object from the amplitude and phase spectrum obtained from the waveform of a few oscillation cycles, the temporal resolution of IS is improved.
- (4)
- By making the oscillation waveform a non-sinusoidal wave, the fundamental frequency of oscillation and its higher harmonic waves are usable for the analysis. In this manner, the operation to switch frequency of a sinusoidal wave becomes unnecessary.

## 2. Approach of Capacitive-Coupling IS

#### 2.1. Non-Sinusoidal Oscillator Circuit with Capacitive Couplings

#### 2.2. Determination of Unknown Capacitance and Resistance in Series Connection

#### 2.3. Experimental Method

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Brear, A.R.C.; Chown, A.L.; Burton, A.R.; Farnum, B.H. Electrochemical impedance spectroscopy of metal oxide electrodes for energy applications. ACS Appl. Energy Mater.
**2020**, 3, 66–98. [Google Scholar] [CrossRef][Green Version] - Encinas-Sánchez, V.; de Miguel, M.T.; Lasanta, M.I.; García-Martín, G.; Pérez, F.J. Electrochemical impedance spectroscopy (EIS): An efficient technique for monitoring corrosion processes in molten salt environments in CSP applications. Sol. Energy Mater. Sol. Cells
**2019**, 191, 157–163. [Google Scholar] [CrossRef] - Itagaki, M.; Suzuki, S.; Shitanda, I.; Watanabe, K. Electrochemical impedance and complex capacitance to interpret electrochemical capacitor. Electrochemistry
**2007**, 75, 649–655. [Google Scholar] [CrossRef][Green Version] - Bonomo, M.; Naponiello, G.; Dini, D. Oxidative dissolution of NiO in aqueous electrolyte: An impedance study. J. Electroanal. Chem.
**2018**, 816, 205–214. [Google Scholar] [CrossRef] - Fabregat-Santiago, F.; Garcia-Belmonte, G.; Mora-Seró, I.; Bisquert, J. Characterization of nanostructured hybrid and organic solar cells by impedance spectroscopy. Phys. Chem. Chem. Phys.
**2011**, 13, 9083–9118. [Google Scholar] [CrossRef] [PubMed] - Balasubramani, V.; Chandraleka, S.; Subba Rao, T.; Sasikumar, R.; Kuppusamy, M.R.; Sridhar, T.M. Review—Recent advances in electrochemical impedance spectroscopy based toxic gas sensors using semiconducting metal oxides. J. Electrochem. Soc.
**2020**, 167, 037572. [Google Scholar] [CrossRef] - Valiūnienė, A.; Rekertaitė, A.I.; Ramanavičienė, A.; Mikoliūnait, L.; Ramanavičius, A. Fast Fourier transformation electrochemical impedance spectroscopy for the investigation of inactivation of glucose biosensor based on graphite electrode modified by Prussian blue, polypyrrole and glucose oxidase. Colloids Surf. A Physicochem. Eng. Asp.
**2017**, 532, 165–171. [Google Scholar] [CrossRef] - Yamaguchi, T.; Takisawa, M.; Kiwa, T.; Yamada, H.; Tsukada, K. Analysis of response mechanism of a proton-pumping gate FET hydrogen gas sensor in air. Sens. Actuators B Chem.
**2008**, 133, 538–542. [Google Scholar] [CrossRef][Green Version] - Sekine, I. Recent evaluation of corrosion protective paint films by electrochemical methods. Prog. Org. Coat.
**1997**, 31, 73–80. [Google Scholar] [CrossRef] - Bonora, P.L.; Deflorian, F.; Fedrizzi, L. Electrochemical impedance spectroscopy as a tool for investigating underpaint corrosion. Electrochim. Acta
**1995**, 41, 1073–1082. [Google Scholar] [CrossRef] - Deflorian, F.; Fedrizzi, L.; Rossi, S.; Bonora, P.L. Organic coating capacitance measurement by EIS: Ideal and actual trends. Electrochim. Acta
**1999**, 44, 4243–4249. [Google Scholar] [CrossRef] - Amirudin, A.; Thieny, D. Application of electrochemical impedance spectroscopy to study the degradation of polymer-coated metals. Prog. Org. Coat.
**1995**, 26, 1–28. [Google Scholar] [CrossRef] - Mansfeld, F.; Tsai, C.H. Determination of coating deterioration with EIS: I. basic relationships. Corrosion
**1991**, 47, 958–963. [Google Scholar] [CrossRef] - Mansfeld, F.; Tsai, C.H. Determination of coating deterioration with EIS: Part II. development of a method for field testing of protective coatings. Corrosion
**1993**, 49, 726–737. [Google Scholar] - Rammelt, U.; Reinhard, G. Application of electrochemical impedance spectroscopy (EIS) for characterizing the corrosion-protective performance of organic coatings on metals. Prog. Org. Coat.
**1992**, 21, 205–226. [Google Scholar] [CrossRef] - Kendig, M.; Scully, J. Basic aspects of electrochemical impedance application for the life prediction of organic coatings on metals. Corrosion
**1990**, 46, 22–29. [Google Scholar] [CrossRef] - Walter, G.W. A review of impedance plot methods used for corrosion performance analysis of painted metals. Corros. Sci.
**1986**, 26, 681–703. [Google Scholar] [CrossRef] - Lindqvist, S.A. Theory of dielectric properties of heterogeneous substances applied to water in a paint film. Corrosion
**1985**, 41, 69–75. [Google Scholar] [CrossRef] - Grossi, M.; Riccò, B. Electrical impedance spectroscopy (EIS) for biological analysis and food characterization: A review. J. Sens. Sens. Syst.
**2017**, 6, 303–325. [Google Scholar] [CrossRef][Green Version] - Davies, S.J.; Davenport, A. The role of bioimpedance and biomarkers in helping to aid clinical decision-making of volume assessments in dialysis patients. Kidney Int.
**2014**, 86, 489–496. [Google Scholar] [CrossRef][Green Version] - Kyle, U.G.; Bosaeus, I.; De Lorenzo, A.D.; Deurenberg, P.; Elia, M.; Gómez, J.M.; Heitmann, B.L.; Kent-Smith, L.; Melchior, J.-C.; Pirlich, M.; et al. Bioelectrical impedance analysis—Part I: Review of principles and methods. Clin. Nutr.
**2004**, 23, 1226–1243. [Google Scholar] [CrossRef] - Kyle, U.G.; Bosaeus, I.; De Lorenzo, A.D.; Deurenberg, P.; Elia, M.; Gómez, J.M.; Heitmann, B.L.; Kent-Smith, L.; Melchior, J.-C.; Pirlich, M.; et al. Bioelectrical impedance analysis—Part II: Utilization in clinical practice. Clin. Nutr.
**2004**, 23, 1430–1453. [Google Scholar] [CrossRef] [PubMed] - Jaffrin, M.Y.; Morel, H. Body fluid volumes measurements by impedance: A review of bioimpedance spectroscopy (BIS) and bioimpedance analysis (BIA) methods. Med. Eng. Phys.
**2008**, 30, 1257–1269. [Google Scholar] [CrossRef] [PubMed] - Szuster, B.; Roj, Z.S.D.; Kowalski, P.; Sobotnicki, A.; Woloszyn, J. Idea and measurement methods used in bioimpedance spectroscopy. Adv. Intell. Syst. Comput.
**2017**, 623, 70–78. [Google Scholar] - Demura, S.; Sato, S.; Kitabayashi, T. Percentage of total body fat as estimated by three automatic bioelectrical impedance analyzers. J. Physiol. Anthropol. Appl. Hum. Sci.
**2004**, 23, 93–99. [Google Scholar] [CrossRef][Green Version] - Cha, K.; Chertow, G.M.; Gonzalez, J.; Lazarus, J.M.; Wilmore, D.W. Multifrequency bioelectrical impedance estimates the distribution of body water. J. Appl. Physiol.
**1995**, 79, 1316–1319. [Google Scholar] [CrossRef] - Piccoli, A. Bioelectric impedance measurement for fluid status assessment. Contrib. Nephrol.
**2010**, 164, 143–152. [Google Scholar] - Piccoli, A.; Rossi, B.; Pillon, L.; Bucciante, G. A new method for monitoring body fluid variation by bioimpedance analysis: The RXc graph. Kidney Int.
**1994**, 46, 534–539. [Google Scholar] [CrossRef][Green Version] - Nwosu, A.C.; Mayland, C.R.; Mason, S.; Cox, T.F.; Varro, A.; Ellershaw, J. The association of hydration status with physical signs, symptoms and survival in advanced cancer—The use of bioelectrical impedance vector analysis (BIVA) technology to evaluate fluid volume in palliative care: An observational study. PLoS ONE
**2016**, 11, e0163114. [Google Scholar] [CrossRef][Green Version] - Toso, S.; Piccoli, A.; Gusella, M.; Menon, D.; Crepaldi, G.; Bononi, A.; Ferrazzi, E. Bioimpedance vector pattern in cancer patients without disease versus locally advanced or disseminated disease. Nutrition
**2003**, 19, 510–514. [Google Scholar] [CrossRef] - Nescolarde, L.; Piccoli, A.; Román, A.; Núñez, A.; Morales, R.; Tamayo, J.; Doñate, T.; Rosell, J. Bioelectrical impedance vector analysis in haemodialysis patients: Relation between oedema and mortality. Physiol. Meas.
**2004**, 25, 1271–1280. [Google Scholar] [CrossRef] - Piccoli, A.; Italian CAPD-BIA Study Group. Bioelectric impedance vector distribution in peritoneal dialysis patients with different hydration status. Kidney Int.
**2004**, 65, 1050–1063. [Google Scholar] [CrossRef][Green Version] - Pillon, L.; Piccoli, A.; Lowrie, E.G.; Lazarus, J.M.; Chertow, G.M. Vector length as a proxy for the adequacy of ultrafiltration in hemodialysis. Kidney Int.
**2004**, 66, 1266–1271. [Google Scholar] [CrossRef][Green Version] - Bozzetto, S.; Piccoli, A.; Montini, G. Bioelectrical impedance vector analysis to evaluate relative hydration status. Pediatr. Nephrol.
**2010**, 25, 329–334. [Google Scholar] [CrossRef] - Codognotto, M.; Piazza, M.; Frigatti, P.; Piccoli, A. Influence of localized edema on whole-body and segmental bioelectrical impedance. Nutrition
**2008**, 24, 569–574. [Google Scholar] [CrossRef] - Nwosu, A.C.; Morris, L.; Mayland, C.; Mason, S.; Pettitt, A.; Ellershaw, J. Longitudinal bioimpedance assessments to evaluate hydration in POEMS syndrome. BMJ Support. Palliat. Care
**2016**, 6, 369–372. [Google Scholar] [CrossRef][Green Version] - Stewart, G.N. The changes produced by the growth of bacteria in the molecular concentration and electrical conductivity of culture media. J. Exp. Med.
**1899**, 4, 235–243. [Google Scholar] [CrossRef] [PubMed][Green Version] - Grossi, M.; Lazzarini, R.; Lanzoni, M.; Riccò, B. A novel technique to control ice-cream freezing by electrical characteristics analysis. J. Food Eng.
**2011**, 106, 347–354. [Google Scholar] [CrossRef] - Pompei, A.; Grossi, M.; Lanzoni, M.; Perretti, G.; Lazzarini, R.; Riccò, B.; Matteuzzi, D. Feasibility of lactobacilli concentration detection in beer by automated impedance technique. MBAA Tech. Q.
**2012**, 49, 11–18. [Google Scholar] [CrossRef] - Chuang, C.H.; Du, Y.C.; Wu, T.F.; Chen, C.H.; Lee, D.H.; Chen, S.M.; Huang, T.C.; Wu, H.P.; Shaikh, M.O. Immunosensor for the ultrasensitive and quantitative detection of bladder cancer in point of care testing. Biosens. Bioelectron.
**2016**, 84, 126–132. [Google Scholar] [CrossRef] - Ma, H.; Wallbank, R.W.R.; Chaji, R.; Li, J.; Suzuki, Y.; Jiggins, C.; Nathan, A. An impedance-based integrated biosensor for suspended DNA characterization. Sci. Rep.
**2013**, 3, 2730. [Google Scholar] [CrossRef][Green Version] - van Grinsven, B.; Vandenryt, T.; Duchateau, S.; Gaulke, A.; Grieten, L.; Thoelen, R.; Ingebrandt, S.; De Ceuninck, W.; Wagner, P. Customized impedance spectroscopy device as possible sensor platform for biosensor applications. Phys. Status Solidi A
**2010**, 4, 919–923. [Google Scholar] [CrossRef] - Wang, Y.; Ye, Z.; Ying, Y. New trends in impedimetric biosensors for the detection of foodborne pathogenic bacteria. Sensors
**2012**, 12, 3449–3471. [Google Scholar] [CrossRef][Green Version] - Ibba, P.; Falco, A.; Abera, B.D.; Cantarella, G.; Petti, L.; Lugli, P. Bio-impedance and circuit parameters: An analysis for tracking fruit ripening. Postharvest Biol. Technol.
**2020**, 159, 110978. [Google Scholar] [CrossRef] - Chowdhury, A.; Singh, P.; Bera, T.K.; Ghoshal, D.; Chakraborty, B. Electrical impedance spectroscopic study of mandarin orange during ripening. J. Food Meas. Charact.
**2017**, 11, 1654–1664. [Google Scholar] [CrossRef] - Niu, J.; Lee, J.Y. A new approach for the determination of fish freshness by electrochemical impedance spectroscopy. J. Food Sci.
**2000**, 65, 780–785. [Google Scholar] [CrossRef] - Breugelmans, T.; Tourwé, E.; Van Ingelgem, Y.; Wielant, J.; Hauffman, T.; Haubrand, R.; Pintelon, R.; Hubin, A. Odd random phase multisine EIS as a detection method for the onset of corrosion of coated steel. Electrochem. Commun.
**2010**, 12, 2–5. [Google Scholar] [CrossRef] - Min, M.; Pliquett, U.; Nacke, T.; Barthel, A.; Annus, P.; Land, R. Broadband excitation for short-time impedance spectroscopy. Physiol. Meas.
**2008**, 29, 185–192. [Google Scholar] [CrossRef] - Min, M.; Parve, T.; Ronk, A.; Annus, P.; Paavle, T. Synchronous sampling and demodulation in an instrument for multifrequency bioimpedance measurement. IEEE Trans. Instrum. Meas.
**2007**, 56, 1365–1372. [Google Scholar] [CrossRef] - Darowicki, K.; Ślepski, P. Dynamic electrochemical impedance spectroscopy of the first order electrode reaction. J. Electroanal. Chem.
**2003**, 547, 1–8. [Google Scholar] [CrossRef] - Lyu, C.; Liu, H.; Luo, W.; Zhang, T.; Zhao, W. A Fast Time Domain Measuring Technique of Electrochemical Impedance Spectroscopy Based on FFT. In Proceedings of the 2018 Prognostics and System Health Management Conference, Chongqing, China, 26–28 October 2018; pp. 450–455. [Google Scholar]
- Zappen, H.; Ringbeck, F.; Sauer, D.U. Application of time-resolved multi-sine impedance spectroscopy for lithium-ion battery characterization. Batteries
**2018**, 4, 64. [Google Scholar] [CrossRef][Green Version] - Orlikowski, J.; Ryl, J.; Jarzynka, M.; Krakowiak, S.; Darowicki, K. Instantaneous impedance monitoring of aluminum alloy 7075 corrosion in borate buffer with admixed chloride ions. Corrosion
**2015**, 71, 828–838. [Google Scholar] [CrossRef] - Valiūnienė, A.; Baltrūnas, G.; Valiūnas, R.; Popkirov, G. Investigation of the electroreduction of silver sulfite complexes by means of electrochemical FFT impedance spectroscopy. J. Hazard. Mater.
**2010**, 180, 259–263. [Google Scholar] [CrossRef] - Carstensen, J.; Foca, E.; Keipert, S.; Föll, H.; Leisner, M.; Cojocaru, A. New modes of FFT impedance spectroscopy applied to semiconductor pore etching and materials characterization. Phys. Status Solidi (a)
**2008**, 205, 2485–2503. [Google Scholar] [CrossRef] - Toyoda, K.; Tsenkova, R. Measurement of freezing process of agricultural products by impedance spectroscopy. IFAC Proc. Vol.
**1998**, 31, 89–94. [Google Scholar] [CrossRef] - Niedzialkowski, P.; Slepski, P.; Wysocka, J.; Chamier-Cieminska, J.; Burczyk, L.; Sobaszek, M.; Wcislo, A.; Ossowski, T.; Bogdanowicz, R.; Ryl, J. Multisine impedimetric probing of biocatalytic reactions for label-free detection of DEFB1 gene: How to verify that your dog is not human? Sens. Actuators B Chem.
**2020**, 323, 128664. [Google Scholar] [CrossRef] - Macdonald, J.R. Impedance spectroscopy and its use in analyzing the steady-state AC response of solid and liquid electrolytes. J. Electroanal. Chem. Interfacial Electrochem.
**1987**, 223, 25–50. [Google Scholar] [CrossRef] - Kobayashi, K.; Suzuki, T.S. Development of impedance analysis software implementing a support function to find good initial guess using an interactive graphical user interface. Electrochemistry
**2020**, 88, 39–44. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Schematic model of electrodes capacitively coupled to a conductive material via a thin insulator: (

**a**) cross-sectional diagram; (

**b**) equivalent circuit.

**Figure 2.**Circuit diagrams illustrating the measurement of impedance shown in Figure 1: (

**a**) with a sinusoidal voltage source; and (

**b**) in a non-sinusoidal oscillator.

**Figure 3.**Example of the oscillation waveforms of ${v}_{12}\left(t\right)$ and $v1\left(t\right)$ measured in the circuit of Figure 2b. The ${R}_{\mathrm{X}}$ and ${C}_{\mathrm{X}}$ were set to 4.0 kΩ and 10 nF, respectively. The segment of time with a colored background corresponds to two cycles of the oscillation and was used for the subsequent discrete Fourier transform (DFT) analysis.

**Figure 4.**Frequency spectra of: (

**a**) amplitude $\left|{\dot{V}}_{12}\right|$; (

**b**) phase ${\theta}_{\mathrm{V}12}$; (

**c**) amplitude $\left|{\dot{V}}_{1}\right|$; and (

**d**) phase ${\theta}_{\mathrm{V}1}$ at $\left(2m-1\right){f}_{0}$ ($m=1,2,3,\cdots ,20$ ) Hz. The spectra were obtained using DFT from the two-cycle segment of ${v}_{12}\left(t\right)$ and ${v}_{1}\left(t\right)$ in Figure 3. The ${R}_{\mathrm{X}}$ and ${C}_{\mathrm{X}}$ were set to 4.0 kΩ and 10 nF, respectively.

**Figure 5.**Frequency spectra of: (

**a**) absolute impedance $\left|{\dot{Z}}_{\mathrm{A}}\right|$; (

**b**) phase ${\theta}_{\mathrm{ZA}}$; (

**c**) absolute impedance $\left|{\dot{Z}}_{\mathrm{X}}\right|$; and (

**d**) phase ${\theta}_{\mathrm{ZX}}$ at $\left(2m-1\right){f}_{0}$ ($m=1,2,3,\cdots ,20$ ) Hz.

**Figure 6.**Three-dimensional perspective plots of: (

**a**) impedance ${\dot{Z}}_{\mathrm{X}}$; and (

**b**) admittance ${\dot{Y}}_{\mathrm{X}}$. Three-dimensional DFT data is projected onto each plane. The solid and dashed lines are theoretical curves of ${\dot{Z}}_{\mathrm{X}}$ and ${\dot{Y}}_{\mathrm{X}}$.

**Figure 7.**Frequency spectra of: (

**a**) real part $\mathrm{Re}({\dot{Z}}_{\mathrm{X}})$; and (

**b**) imaginary part $\mathrm{Im}({\dot{Z}}_{\mathrm{X}})$ of impedance ${\dot{Z}}_{\mathrm{X}}$. The DFT data were fitted to Equations (22) and (23) for determining ${R}_{\mathrm{X}}$ and ${C}_{\mathrm{X}}$ (dashed lines).

**Figure 8.**${R}_{\mathrm{X}}$ and ${C}_{\mathrm{X}}$ estimated using oscillation waveforms and DFT: (

**a**) estimated ${R}_{\mathrm{X}}$; (

**b**) absolute error of estimated ${R}_{\mathrm{X}}$; (

**c**) estimated ${C}_{\mathrm{X}}$; (

**d**) relative error of estimated ${C}_{\mathrm{X}}$.

**Figure 9.**Equivalent circuit modeling of ${\dot{Z}}_{\mathrm{A}}$: (

**a**) Cole–Cole plot for ${C}_{\mathrm{X}}=$ 0.10 nF and ${R}_{\mathrm{X}}=$ 0 Ω; (

**b**) equivalent circuit with a stray resistance ${R}_{\mathrm{AS}}$ and stray inductance ${L}_{\mathrm{A}}$. The symbol $n$ represents the harmonic number of ${\dot{Z}}_{\mathrm{A}}\left(n{f}_{0}\right)$. We used pyZwx software to fit the DFT data to the equivalent circuit model [59].

**Figure 10.**${R}_{\mathrm{X}}$ and ${C}_{\mathrm{X}}$ estimated using optimized ${\dot{Z}}_{\mathrm{A}}$: (

**a**) estimated ${R}_{\mathrm{X}}$; (

**b**) absolute error of estimated ${R}_{\mathrm{X}}$; (

**c**) relative error of estimated ${C}_{\mathrm{X}}$.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yamaguchi, T.; Ueno, A. Capacitive-Coupling Impedance Spectroscopy Using a Non-Sinusoidal Oscillator and Discrete-Time Fourier Transform: An Introductory Study. *Sensors* **2020**, *20*, 6392.
https://doi.org/10.3390/s20216392

**AMA Style**

Yamaguchi T, Ueno A. Capacitive-Coupling Impedance Spectroscopy Using a Non-Sinusoidal Oscillator and Discrete-Time Fourier Transform: An Introductory Study. *Sensors*. 2020; 20(21):6392.
https://doi.org/10.3390/s20216392

**Chicago/Turabian Style**

Yamaguchi, Tomiharu, and Akinori Ueno. 2020. "Capacitive-Coupling Impedance Spectroscopy Using a Non-Sinusoidal Oscillator and Discrete-Time Fourier Transform: An Introductory Study" *Sensors* 20, no. 21: 6392.
https://doi.org/10.3390/s20216392