Equivalent circuit Subject

Fig. 23-4 Equivalent circuit diagram for a pipeline subjected to interference.

Many applications of this strategy are based on extensions of the concepts of impedance developed earlier in this chapter (41-43). However, the excitation waveform is usually an impulse in potential (rather than a periodic perturbation), and a transient current is measured. One records both E t) and i t) as observed functions. Then both are subjected to transformations, and comparisons are made in the frequency domain between E s) and i s). Ratios of the form i s)IE s) are transient impedances, which can be interpreted in terms of equivalent circuits in exactly the fashion we have come to understand. The advantages of this approach are (a) that the analysis of data is often simpler in the frequency domain, (b) that the multiplex advantage applies, and (c) the waveform E(f) does not have to be ideal or even precisely predictable. The last point is especially useful in high-frequency regions, where potentiostat response is far from perfect. Laplace domain analyses have been carried out for frequency components above 10 MHz. 

Many of the electrical engineering textbooks that include the subject of motors in their contents describe the eqnivalent circnit of an indnction motor as a series and parallel combination of resistances and reactances, see References 1 to 8. The eqnivalent circnit nsnaUy defines the situation for one of the three phases and so care needs to be taken to ensure that the final resnlts obtained apply to the complete motor. Care is also necessary in nsing the ohmic data from mannfacturers, they may have either star winding valnes or delta winding valnes and the choice may not be obvious. The equivalent circuit of most practical use is shown in Figure 5.1 for one star connected winding, where -... 

Linear resistance can be simply measured by an ohmmeter (Fig. 28.11, top), a so-called two-points measurement method. The equivalent circuit of this measurement setup is shown in Fig. 28.12. The ohmmeter is actually giving the total resistance of the subject and the measurement wires. This method is applicable when the resistance of the measured subject is much greater than the wires. However, conductive yams are usually expected to be highly conductive, and the measurement error introduced by the wire resistance will then be substantial. 

Many treatments of this subject have used an electrical equivalent circuit model to simulate the corroding metal/ electrolyte interface [1,38,39]. The simplest form of such a model is shown in Fig. 4. The three parameters discussed above... 

It cannot be proposed in a book such as the present to discuss common techniques such as EIS in detail reference is made to excellent monognq>hs on the subject [399]. To summarize briefly, however, in a typical AC technique, a constant-amplitude (sine wave) current of a given frequency is applied across two electrodes connected via the CP alone, or the CP in an electrochemical cell or device. The voltage that results is monitored via a lock-in amplifier which detects the in-phase and 90 -out-of-phase impedance components, which correspond respectively to the resistance and capacitance of the CP sample. If an ElS-type equivalent circuit analysis is not required, this information, as a function of several frequencies, is usually all that is sought for AC conductivity. Microwave and IR measurements are discussed separately within this chapter or elsewhere in this book. 

At this point it should be cautioned that the equivalent circuit approach can yield detailed information of the physicochemical processes of ohmic, mass transfer, and kinetic resistances for a given system, but it is subject to the assumptions of the equivalent circuit used. That is, the use of equivalent circuit analysis offers infinite possibilities and combinations of electrical circuits which all can be rearranged in different ways. The EIS... 

Figure 11.13. a) Equivalent circuit for a piezoelectric material subjected to an alternating electrical field and b) variations of the admittance with frequency... 

In contrast, in the above-described equivalent circuit analysis, we first separated the individual components by physical means, using various reconstitution methods. Contrary to common impressions, our data of isolated components was subjected to multiexponential analysis to obtain the time constants, such as X3 and X[. These deconvoluted data are then tested with the equivalent circuit. The equivalent circuit imposes a constraint that the investigator cannot manipulate or overcome by "massaging the data. Equation 128.3 can be simplified by using a brief light pulse so that p(t) = 8(t), where 8(t) is... 

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