On the Error Structure of Impedance Measurements Simulation of FRA Instrumentation

A new paradigm is introduced for the investigation of errors in frequency-domain measurements. The propagation of errors from time-domain measurements to the desired complex variables in the frequency domain was analyzed for the frequency response analysis (FRA) algorithm, one of two techniques commonly used for spectroscopy measurements. Errors in the frequency domain were found to be normally distributed, even when the errors in the time-domain were not normally distributed and when the measurement technique introduced bias errors. For additive errors in time-domain signals, the errors in the real and imaginary impedance were found to be uncorrelated, and the variances of the real and imaginary parts of the complex impedance were equal. The equality of variances was realized except for cases where the time-domain signals contained proportional errors. The statistical characteristics of the results were in good agreement with experimental observations.

[1]  Mark E. Orazem,et al.  Development of physico-chemical models for electrochemical impedance spectroscopy , 1993 .

[2]  J. Ross Macdonald,et al.  A flexible procedure for analyzing impedance spectroscopy results: Description and illustrations , 1987 .

[3]  William J. Thompson,et al.  The collected works of john w. tukey , 1991 .

[4]  M. Orazem,et al.  Influence of surface phenomena on the impedance response of a rotating disk electrode , 1999 .

[5]  H. Takenouti,et al.  ac Response of a rotating ring—disk electrode: application to 2-D and 3-D film formation in anodic processes , 1989 .

[6]  D. Macdonald,et al.  Characterizing electrochemical systems in the frequency domain , 1998 .

[7]  M. Orazem,et al.  Modeling of the cast iron/drinking water system by electrochemical impedance spectroscopy , 1999 .

[8]  B. Tribollet,et al.  Relationship between the electrochemical impedance and the electrohydrodynamical impedances measured using a rotating disc electrode , 1980 .

[9]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[10]  B. Tribollet,et al.  Flow Modulation Techniques in Electrochemistry , 1991 .

[11]  U. Bertocci,et al.  Noise Resistance Applied to Corrosion Measurements III. Influence of the Instrumental Noise on the Measurements , 1997 .

[12]  Oliver C. Moghissi,et al.  Application of Measurement Models for Analysis of Impedance Spectra , 1993 .

[13]  James Ross Macdonald,et al.  IMPEDANCE SPECTROSCOPY: OLD PROBLEMS AND NEW DEVELOPMENTS , 1990 .

[14]  J. Macdonald.  Some new directions in impedance spectroscopy data analysis , 1993 .

[15]  F. Huet,et al.  Fluctuations in electrochemical systems. I. General theory on diffusion limited electrochemical reactions , 1993 .

[16]  Siegmund Brandt,et al.  Statistical and Computational Methods in Data Analysis , 1971 .

[17]  M. Orazem,et al.  Application of Measurement Models to Electrohydrodynamic Impedance Spectroscopy , 1996 .

[18]  B. Tribollet,et al.  A Transfer Function Approach for a Generalized Electrochemical Impedance Spectroscopy , 1994 .

[19]  F. Huet,et al.  Investigation of electrochemical processes by an electrochemical noise analysis. Theoretical and experimental aspects in potentiostatic regime , 1986 .

[20]  L. García-Rubio,et al.  Application of Measurement Models to Impedance Spectroscopy II . Determination of the Stochastic Contribution to the Error Structure , 1995 .

[21]  H. Takenouti,et al.  Copper dissolution in acidic sulphate media studied by QCM and rrde under ac signal , 1992 .

[22]  L. García-Rubio,et al.  Spectroscopy Applications of the Kramers‐Kronig Transforms: Implications for Error Structure Identification , 1997 .

[23]  J. S. Hunter,et al.  Statistics for experimenters : an introduction to design, data analysis, and model building , 1979 .

[24]  W. Kenan,et al.  Impedance Spectroscopy: Emphasizing Solid Materials and Systems , 1987 .

[25]  Mark E. Orazem,et al.  Application of Measurement Models to Impedance Spectroscopy III . Evaluation of Consistency with the Kramers‐Kronig Relations , 1995 .

[26]  H. Takenouti,et al.  A new experimental approach to the time-constants of electrochemical impedance: frequency response of the double layer capacitance , 2001 .

[27]  B. Boukamp.  A Nonlinear Least Squares Fit procedure for analysis of immittance data of electrochemical systems , 1986 .

[28]  F. Huet,et al.  Noise Resistance Applied to Corrosion Measurements I. Theoretical Analysis , 1997 .

[29]  M. Orazem,et al.  The Error Structure of Impedance Spectra for Systems with a Large Ohmic Resistance with Respect to the Polarization Impedance , 1996 .

[30]  G. Turin,et al.  Principles and applications of random noise theory , 1959 .

[31]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[32]  D. Fermín,et al.  A kinetic study of CdS photocorrosion by intensity modulated photocurrent and photoelectrochemical impedance spectroscopy , 1999 .

[33]  On the transformation of colored random noise by the Kronig-Kramers integral transforms , 1997 .

[34]  G. W. Snedecor.  STATISTICAL METHODS , 1967 .

[35]  J. J. García-Jareño,et al.  Charge compensation process in polypyrrole studied by ac electrogravimetry , 2001 .

[36]  Thermally Stimulated Deep‐Level Impedance Spectroscopy Application to an n‐GaAs Schottky Diode , 1996 .

[37]  Mark E. Orazem,et al.  Measurement Models for Electrochemical Impedance Spectroscopy I . Demonstration of Applicability , 1992 .

[38]  B. Tribollet,et al.  Thermoelectrochemical Transfer Function under Thermal Laminar Free Convection at a Vertical Electrode , 2000 .

[39]  Oscar D. Crisalle,et al.  On the Error Structure of Impedance Measurements Series Expansions , 2003 .

[40]  P. Żółtowski.  The error function for fitting of models to immittance data , 1984 .

[41]  Bernard A. Boukamp,et al.  A package for impedance/admittance data analysis , 1986 .

[42]  Brian E. Conway,et al.  Modern Aspects of Electrochemistry , 1974 .

[43]  J. Dygas,et al.  Variance of errors and elimination of outliers in the least squares analysis of impedance spectra , 1999 .

[44]  A. Lasia,et al.  Experimental study and modeling of impedance of the her on porous Ni electrodes , 2001 .

[45]  Claude Gabrielli,et al.  Fluctuations in electrochemical systems. II. Application to a diffusion limited redox process , 1993 .