Distributed impedance

From this physical model, an electrical model of the interface can be given. Free corrosion is the association of an anodic process (iron dissolution) and a cathodic process (electrolyte reduction). Ther ore, as discussed in Section 9.2.1, the total impedance of the system near the corrosion potential is equivalent to an anodic impedance Za in parallel with a cathodic impedance Zc with a solution resistance Re added in series as shoxvn in Figure 13.13(a). The anodic impedance Za is simply depicted by a double-layer capacitance in parallel with a charge-transfer resistance (Figure 13.13(b)). The cathodic branch is described, following the method of de Levie, by a distributed impedance in space as a transmission line in the conducting macropore (Figure 13.12). The interfacial impedance of the microporous... 

Impedance plethysmography is closely related to tomography because both are concerned with the recording of local tissue immittivity variations or distributions. Impedance plethysmography is the measurement of immittance changes due to respiration or perfusion and is described in more detail in Section 10.5. 

The disadvantages of IS are primarily associated with possible ambiguities in interpretation. An important comphcation of analyses based on an equivalent circuit (e.g. Bauerle [1969]) is that ordinary ideal circuit elements represent ideal lumped-constant properties. Inevitably, aU electrolytic cells are distributed in space, and their microscopic properties may be also independently distributed. Under these conditions, ideal circuit elements may be inadequate to describe the electrical response. Thus, it is often found that Z/to) cannot be well approximated by the impedance of an equivalent circuit involving only a finite number of ordinary lumped-constant elements. It has been observed by many in the field that the use of distributed impedance elements [e.g. constant-phase elements (CPEs) (see Section 2.2.2.2)] in the equivalent circuit greatly aids the process of fitting observed impedance data for a cell with distributed properties. 

Bisqueit J, Belmonte GG, Santiago FF et al (2000) Application of a distributed impedance model in the analysis of eonducting polymer films. Electrochem Commun 2 601-605. doi 10.1016/ S1388-2481(00)00089-8... 

The method of calculating system vent flow is illustrated in Figure 10. The fluid flow model chosen consisted of a transfer line having a distributed impedance due to valves, line friction, etc, with an orifice at the downstream end. During pressurized cooldown, the downstream orifice operates at, or near, choked flow, and compressible fluid flow theory was used to calculate vent flow. 

R. Sandenberg, J. M. A. Figueiredo, Relationship between spatial and spectral properties of ionic solutions the distributed impedance of an electrolytic cells, Electrochim. Acta, 2010,55, pp. A722-i727. 

For accurate measurements of media conductivity, it is necessary to realize that the measured resistance value of a sample at an arbitrarily chosen AC sampling frequency may not be a correct representation of the media bulk resistance. The measured total resistance may contain contributions from electrode polarization, Faradaic impedances, lead cables, and other artifacts. To make accurate measurements of the bulk resistive properties of a material, it is necessary to know the measurement frequency range where both capacitive interference from the double layer (and other electrode interfacial impedance effects such as adsorption/desorption) and the bulk capacitance are absent [5]. A sampling frequency has to be chosen that is within the frequency region where the impedance spectrum is dominated by the bulk-material resistance. This task essentially involves the development of a concept of spatially distributed impedance. 

An equivalent-circuit model describing the impedance response of a typical lubricant has to take into account processes divided spatially into bulk lubricant and interfacial electrochemical (adsorption, mass transport, and charge transfer) zones [6]. Separation between these two zones can be achieved following the distributed impedance analysis in Section 6-3. The bulk resistance BULK represents a lossy part of the overall bulk-media relaxation mechanism [3,4], always existing in parallel with a bulk-media capacitance as ... 

Figure 13.15 Typical layout of a typical transmission and distribution network and significance of circuit impedances at various points...

Series capacitor - connected in series at the far end of a long transmission or FTP distribution line to offset the reactive component of the line impedance, contain the voltage drop and enhance the receiving-end voltage. It can support a transmission or distribution system in the following ways ... 

It is pertinent to note that since a filter circuit will provide a low impedance path to a few harmonic currents in the circuit (in the vicinity of the harmonic, to which it has been tuned) it may also attract harmonic currents from neighbouring circuits which would otherwise circulate in those circuits. This may necessitate a slightly oversized filter circuit. This aspect must be borne in mind when designing a filter circuit for a larger distribution network having more than one load centre. 

For ease of calculation, let us consider the impedance of the transformer as its leakage reactance, ignoring resistance and draw an equivalent circuit diagram as in Figures 24.25 (b) and (c) Assuming the length of the primary distribution line to be 15 km, the total line parameters will become... 

In a d.c. system the current distribution through the cross-section of a current-canying conductor is uniform as it consists of only the resistance. In an a.c. system the inductive effect caused by the induced-electric field causes skin and proximity effects. These effects play a complex role in determining the current distribution through the cross-section of a conductor. In an a.c. system, the inductance of a conductor varies with the depth of the conductor due to the skin effect. This inductance is further affected by the presence of another current-carrying conductor in the vicinity (the proximity effect). Thus, the impedance and the current distribution (density) through the cross-section of the conductor vaiy. Both these factors on an a.c. system tend to increase the effective... 

Figure 28.25 Distribution of inductive reactance and impedance of each phase in a three-phase system...

The role of oxygen and hydrogen solutions in the metal catalyst does not appear to be that of impeding the major reactions, but merely to provide a source of these reactants which is uniformly distributed diroughout the catalyst particles, without decreasing die number of surface sites available to methane adsorption. It is drerefore quite possible that a significatit fraction of the reaction takes place by the formation of products between species adsorbed on the surface, and dissolved atoms just below the surface, but in adjacent sites to the active surface sites. 

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