Impedance measurement linearity

Although EIS offers many advantages for diagnosing fuel cell properties, clear difficulties exist for applying impedance methods and fitting the data to the model to extract the relevant electrochemical parameters. The limitations of the EIS technique derive from the several requirements required to obtain a valid impedance spectrum, because the accuracy of EIS measurement depends not only on the technical precision of the instrumentation but also on the operating procedures. Theoretically, there are three basic requirements for AC impedance measurements linearity, stability, and causality. 

There are important figures of merit (5) that describe the performance of a photodetector. These are responsivity, noise, noise equivalent power, detectivity, and response time (2,6). However, there are several related parameters of measurement, eg, temperature of operation, bias power, spectral response, background photon flux, noise spectra, impedance, and linearity. Operational concerns include detector-element size, uniformity of response, array density, reflabiUty, cooling time, radiation tolerance, vibration and shock resistance, shelf life, availabiUty of arrays, and cost. 

Additional information with respect to the mechanism of the grain boundary resistance can be obtained from temperature- and voltage-dependent impedance measurements. The grain boundary semicircle varies, for example, considerably with the applied dc bias (Fig. 39a). The current-voltage relations calculated from such bias-dependent impedance measurements are thus non-linear. In the logarithmic plot (Fig. 39b) it can be seen that the low bias regime exhibits a non-linearity factor a (= d og(I/A)/d og(U/ V)) of almost one (ohmic behavior), while at a bias value of about 0.35 V this factor changes to a x 2. 

Electrochemical systems can be studied with methods based on impedance measurements. These methods involve the application of a small perturbation, whereas in the methods based on linear sweep or potential step the system is perturbed far from equilibrium. This small imposed perturbation can be of applied potential, of applied current or, with hydrodynamic electrodes, of convection rate. The fact that the perturbation is small brings advantages in terms of the solution of the relevant mathematical equations, since it is possible to use limiting forms of these equations, which are normally linear (e.g. the first term in the expansion of exponentials). 

It is useful to calibrate the EQCM, i.e., to determine Cf, e.g., by electrodeposition and electrodissolution of silver. The rigidity layer behavior can be tested by depositing films of different thicknesses. Usually relatively thin films (10 nm-some hundreds nm) show rigid layer behavior. The deviation from linearity regarding the Am vs. Q function is related to the appearance of the viscoelastic effect. By the help of impedance measurements... 

FFT techniques can measure multiple-frequency AC impedance at the same time as a stimulus waveform containing multiple frequencies. FFT performs very fast AC impedance measurements and can function as a complement to the single sine wave technique. The stimulus waveform, which is constructed by multiple sine waves, should also have as low an amplitude as possible to avoid or decrease the harmonic distortion effects at the non-linear regime. However, if the amplitude of the stimulus wave is too low, each single sine wave will be much lower and may be distorted by noises. Fortunately, some commercially available analyzers have the option of selecting the frequencies for AC impedance measurements. Usually, stimulus frequencies are selected in such a way that each is not coincident with the main harmonics of the lower frequencies. As a result, the main components of the harmonic distortion from each frequency in the stimulus waveform do not interfere with the other stimulus frequencies. 

Ac impedance measurements of the compound sintered at 700 °C were performed in air in the temperature range of 200-600 °C. The Arrhenius plots of the ionic conductivity are shown in Figure 4. The relationship between conductivity and the reciprocal of the absolute temperature is linear over the temperature range measured. 

Electrochemical impedance measurements are often performed imder potentio-static regulation. In these measurements the potential is a fixed value with a superimposed (often sinusoidal) perturbation of fixed amplitude. This approach is attractive because, as discussed in Section 8.2.2, linearity in electrochemical systems is controlled by potential. 

J. Diard, B. LeGorrec, and C. Montella, "Deviation from the Polarization Resistance Due to Non-Linearity 3. Polarization Resistance Determination from Non-Linear Impedance Measurements," Journal of Electroanalytical Chemistry, 432 (1997)53-62. 

There are two main sources of error in this type of measurement. The first arises from the failure of the approximation Y jcoCsd if the sample has a poor ohmic contact or the frequency is too high. If this is the case, the out-of-phase component is no longer a linear function of Csd. The error, which usually manifests itself as an unexpected frequency dependence of Csd, can be avoided by making frequency-dependent impedance measurements with a frequency response analyser (as discussed in Section 12.2.2). The other source of errors arises from the frequency response of... 

Recently, Diard et al. studied the effects of electrochemical non-linearities on impedance measurements using an FRA. They derived theoretical expressions for the error in impedance measurements using the odd harmonic test criterion.Measurements of the fundamental and third... 

It is useful to calibrate the EXJCM, i.e., to determine Cf, e.g., by electrodeposition and electrodissolution of silver. The rigidity layer behavior can be tested by depositing films of different thicknesses. Usually relatively thin films (10 nm - some hundreds nm) show rigid layer behavior. The deviation from the linearity regarding the Am vs. Q function is related to the appearance of the viscoelastic effect. By the help of impedance measurements the viscoelastic characteristics of the surface film can also be tested [4, 5, 6, 7, 10]. In the absence of any deposition the change of the density and viscosity in the double layer or in the diffusion layer may cause 0.1-10 Hz frequency change. It may interfere with the effect caused by the deposition of monolayers or submonolayers. In some cases other effects, e.g., stress, porosity, pressure, and temperature, should also be considered. 

Depending on the technique used for data acquisition, different methods for data validation can be applied. If a sinusoidal signal were applied to a nonlinear system, the response function would contain multiples (harmonics) of the excitation signal. Popkirov and Schindler utilized this effect to develop a technique for assessing the linearity of an impedance measurement obtained using a time-domain technique (see Sect. 2.G.7.2) [8]. They compared the frequencies contained in the perturbation and the response... 

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