Impedance modulus

Equivalent Circuit Analysis. IS measurements yield values of V and Z the real and imaginary components of the impedance, as a function of f, the AC frequency. The data are usually displayed as Nvauist plots (Z, vs. Z ) or Bode plots (impedance modulus,... 

Figure 28.25 The impedance modulus at low frequency (IZIo.ihz) dependence on the scribe types and depths and the exposure time in the Prohesion corrosion test chamber.

Figure 9 compares the frequency spectra of the impedance modulus jZj and phase shift for resonators with or without a confluent layer of cells on the surface. In either case, the measuring chamber is filled with cell culture medium so that the resonator is always at least under liquid loading. 

This method falls short only when the capacitance values of the metal-solution interphase are so small [70] (of the order of some picofarads) that the limit of the impedance modulus as l/u> —y 0 does not provide a reliable evaluation when the maximum frequency value is about 60 kHz. This situation can be observed especially in the case of organic coatings where, for practical purposes, the presence of microscopic defects is negligible. 

Figure 6 Impedance modulus profile in the absence of diffusivity gradients around the surface. Arrows indicate increasing values of the relative change of the impedance (measured with respect to the bulk value). Level lines range from -10 to -L with a value step of 1,...

The measurement were performed as a comparative one using Gamry Reference 600 [8] as a reference instinunent. The results of the measurement were presented in Fig. 5. Due to high impedance of the object (especially for frequencies below 1 kHz, impedance modulus goes above 1 MQ), the measurement were performed inside the Faraday cage. 

Figure 6. Relative error of impedance modulus of test circuit for the presented impedance analyzer (AMIA) and the Reference 600 (Gamry). 

The results of the coating measurement were presented in Fig. 9. The obtained results are very similar especially in case of impedance modulus. The differences between both instruments in case of impedance argument (in 0.2 100 Flz frequency range) require further... 

Figure 11. Impedance modulus and argument of anticorrosion coating on PGE Arena Stadium steel construction obtained using the presented analyzer (AMIA) and the Atlas 0441 High Impedance Analyzer (Atlas).

Figure 7.29 Transfer impedance frequency spectrum from forearm impedance modulus...

Nordbotten, B.J., Tronstad, C., Martinsen, 0.G., Grimnes, S., 2011. Evaluation of algorithms for calculating bioimpedance phase angle values from measured whole-body impedance modulus. Physiol. Meas. 32, 755-765. 

It can be seen from Fig. 3.10 that noise is always larger at low frequencies. This means that in order to obtain good data one should use larger amplitudes at low frequencies, while they could be lower at higher frequencies. Such a method was suggested by Popkirov and Schindler [105, 106]. They used the first impedance measurement as a test and adjusted amplitudes of all the sine waves, a, as proportional to the impedance modulus ... 

Fig. 3.14 Impedance modulus for Aluzinc in 0.1 M Na2S04 after 14 days of immersion measured with two total amplitudes (a) 8 mV and (b) 48 mV continuous line - IZI, - noise estimated from...

If impedance measurements are carried out at the same sensitivity scale for the real and imaginary components, the stochastic errors of the real and imaginary impedances will be similar, and one can use modulus weighting. Modulus weighting assumes the same statistical weights for real and imaginary parts, and they are proportional to the impedance modulus. This means that small and large impedances contribute in a similar way to the sum of squares and are equally important. 

These relations offer the possibility to examine measured transfer functions (impedance spectra) on errors caused by time instability or time drift. However, KK-checking techniques have fundamental problems in their application to practical measurements. Therefore many attempts have been made to overcome these limitations by means of different interpolation procedures. An attempt is the Z-HIT approximation, applied by Schiller et al. [2001], Agarwal et al. [1995], and Ehm et al. [2000], an approximation formula for the calculation of the impedance modulus course from the phase angle by integration. 

The relationships are integral equations which can be written in various forms [26]. Choosing a logarithmic form for phase shifty and impedance modulus IZI ... 

Equation (8.41) gives the phase shift 0 at one particular frequency cOc as an integral of the impedance modulus over all frequencies. Equations (8.42) and (8.43) similarly give the impedance modulus compared with the impedance at infinitely high frequency or zero frequency as an integral of the phase shift over all frequencies. 

It is important to realise that the complementarity between phase and impedance modulus implied in Equations (8.41)-(8.43) is a property of any passive network composed of resistors, capacitors and inductors. Such a network is said to be K-K transformable. Therefore if an electrochemical system is to be represented by an equivalent passive network, which is one of the objectives in impedance analysis, the measured impedance must be K-K transformable. Note that this is a necessary but not a sufficient condition, i.e. the fact that a measured response satisfies the K-K integral equations is not a guarantee that it is a true response from the electrochemical system under investigation ... 

Figure 7. Measurement results of the comparison experiment top line Deviation of impedance modulus and phase for each measurement device with respect to the simulation middle line Relative deviation for modulus and phase bottom line left Bode plot of the simulation and the average of the 5 measurements right Standard deviation for modulus and phase for the 5 different measurement devices.

Various applications of impedance spectroscopy have been described in food engineering, such as monitorization of yogurt processing [39], salt and moisture measurement in salmon fillets [40], and testing of meat quality [41], A relevant example is the construction of a low-cost and nondestructive system to evaluate the salt levels in food based on a punctual measurement of the impedance in the samples. A coaxial electrode, consisted of an isolated wire inserted into a hollow needle, facilitating the placement inside the food sample, was used (Figure 1.5). Furthermore, the impedance modulus and phase values obtained for each frequency were processed using PLS in order to estimate and predict the salt content in minced pork meat [42],... 

All these examples show the interest of IS measurements, particularly when the membranes are in contact with electrolyte solutions, since qualitative information on membranes structure can be obtained. Other impedance representations (impedance modulus Z and/or tan 4) = (Zimg/Zreai) versus frequency) as well as different complex magnitudes such as dielectric constant and modulus or dielectric loss can also be determined from IS measurements and they are also commonly used in the literature [47, 48]. 

An opposite case would be a cell where the anode is undergoing pitting, while the cathodic reaction is the reduction of dissolved oxygen or an imposed galvanic situation. Since the anodic noise is preponderant, Eq. (5.27) shows that Z is equal to the impedance modulus of the cathode, Z. The anodic noise is the internal signal source utilized for the measurement of the impedance of the cathode. 

In order to obtain the impedance modulus of the EEI, (4) can be written as follows... 

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