Absolute impedance

AC bridge measurements provide only an absolute impedance and phase shift, so there is no way to distinguish between either a series or parallel R-C combination by use of a pure sinusoidal waveform. Thus the series R-C combination of the cell may be matched by the series combination shown in Figure 6.24b or the parallel combination of the Wien bridge shown in Figure 6.24c. Either an oscilloscope or phase-angle voltmeter100 are recommended as null indicators because they allow both the phase shift and the imbalance potential to be nulled. 

A sufficiently precise positioning of the electrodes is difficult and it is easier to work with dynamic images, which do not depend so much on absolute impedance values. If the tissue shows sufficient dispersion, a multifrequency approach has been found useful. Also, time series from changes in the tissue during recording, for instance, respiration, has proven useful. 

The finite element method is already estabhshed in modelling for eddy current sensors the same as analytical methods. For example, reference [1] solves for the absolute impedance of core-less coils, and [2], [3] solve for the induced voltage in the coil. The problem with these analytical models is the dependency on the crack size, shape and location, and the equations needs to be modified all the time. Consequently, the results may not necessarily be comparable. When the FEA is used instead, the results remain comparable for changed model parameters. Hence, the aim of this study is to build a 3D model to calculate the complex coil impedance for encircling coils that measure rods with any kind of cracks. In doing so, two main simplifications are applied as follows. 

Difference measurement using identical electrodes with an additional electrode set cmitacting a reference system is a reasonable solution, if the absolute impedance value is not important. This is veiy sensitive, but because the actual impedance of the reference system is not known (can be measured with certain effort), it is not always applicable. Simple arrangements are shown in Fig. 33. 

Figure 8.2 A representative Bode plot, showing (a) absolute impedance (IZI) versus frequency and (b) phase shift versus frequency. C, Cj, and Ohmic represent three major processes contributing to the overall impedance.

Conductometry, Fig. 5 Absolute impedance value and phase angle as a function of frequency of a conductance cell in... 

Additionally for further evaluations we calculate the relative deviation of absolute impedance mean value for each sample V [1, 300] at each parameter combination ... 

Figure 3. Frequency depended absolute impedance mean value of test resistors Dotted curves Ideal... 

Figure 5. Histograms from the relative deviation of absolute impedance mean value over frequencies fj transliterated into pixel for different test resistors and rotational speed cOj. The pixels to the right of each vertical cutoff frequency bar represent measurements over the individual cutoff frequencyThe histogram bar values are transliterated into pixel corresponding to the bottom color bar, whereby bar values over 50 are combined with the 50 color value. Each vertical pixel line has 50 pixels and represents one histogram from a measurement sweep with 100 values and three histograms are mapped next to each other for each frequency fj (see Tab. 1).

In the high-frequency region, the absolute impedance curve is almost independent of the frequency, with the phase angle value approaching zero degree. This is a typical response for a resistive behavior and corresponds to a resistance of the phosphate solution between the working and the reference electrode. 

Fig. 5.14 Under an excitation sine voltage amplitude of 200 mV, the absolute impedance versus frequency is relatively independent from the excitation voltage amplitude. Thus, under this boundary, the excitation voltage to measured current relationship is linear. The frequency axis is labeled as in the measurements, from higher down to the lower frequencies...

Impedance is usually expressed as a complex number, where the ohmic resistance is the real component and the capacitive reactance is the imaginary one. The most popular formats for evaluating electrochemical impedance data are the Nyquist and Bode plots. In the former format, the imaginary impedance component Z", out of phase) is plotted against the real impedance component Z in phase) at each excitation frequency, whereas in the latter format, both the logarithm of the absolute impedance, Z, and the phase shift, 0, are plotted against the logarithm of the excitation frequency. 

The "modulus weighting" proposed hy Boukamp, where error y or standard deviation of impedance measurement is proportional to the absolute impedance IZI, is accepted as an initial strategy in regression of impedance data obtained by FRA and PSD algorithms. An equation correcting for these small departures is proposed as [38] ... 

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