Equivalent electric circuit

Equivalent Electrical Circuit, In spite of the complex nature of the inhibition process, the inhibited systems actually display simple impedance responses. 

We found an equivalent electrical circuit that fits best the LixC6 electrode behavior at high frequency. The circuit consists of a resistor R in parallel with a constant phase element (CPE). The latter is defined with a pseudo-capacitance Q and a parameter a with 0< a <1 [6], The impedance of... 

The heat transfer path through the surface area, A, can be represented as an equivalent electric circuit as shown in Figure 11.8. The thermal resistances, or their inverses, the conductances, can be computed using standard heat transfer methods. Some will be illustrated here. 

The theoretical model that best describes regulation of transepithelial transport is derived from the Ussing-Zerahn equivalent electrical circuit model of ion transport theory [57] (Figure 15.1B). The model predicts that epithelia are organized as a layer(s) of confluent cells, where plasma membranes of neighboring cells come into close contact and functionally occlude the intercellular space. Accordingly, molecules can move across epithelia either through the cells... 

As mentioned in Section 2.4, in the ionic model the chemical bond is an electrical capacitor. It is therefore possible to replace the bond network by an equivalent electric circuit consisting of links which contain capacitors as shown in Fig. 2.6. The appropriate Kirchhoff equations for this electrical network are eqns (2.7) and (2.11). It is thus possible in principle to determine the bond fluxes for a bond network in exactly the same way as one solves for the charges on the capacitors of an electrical network. While solving these equations is simple in principle providing the capacitances are known, the calculation itself can be... 

For time t > % this current is zero because the carrier would have reached the substrate. The current I(t) can be detected via the voltage it induces in the external circuit. Shortly, the equivalent electrical circuit of the XTOF experiment under the small-signal condition contains the coupling capacitance Cl (the sum of the amplifier and the parasitic capacitances) and f L ( l is the load resistance). The total current is the sum of the conduction current due to the drift of photogenerated charge and the displacement current and is equal to zero (for further details, see Ref [15]),... 

Figure 7-2. a) Atomic processes during the oxidation reaction Me + y02 = MeO, thick film regime and b) its equivalent electrical circuit [W. Jost (1937)]. 

Modeling and optimization of chemical sensors can be assisted by creating equivalent electrical circuits in which an ordinary electrical element, such as a resistor, capacitor, diode, and so on, can represent an equivalent nonelectrical physical parameter. The analysis of the electrical circuit then greatly facilitates understanding of the complex behavior of the physical system that it represents. This is a particularly valuable approach in the analysis and interpretation of mass and electrochemical sensors, as shown in subsequent chapters. The basic rules of equivalent circuit analysis are summarized in Appendix D. Table 3.1 shows the equivalency of electrical and thermal parameters that can be used in such equivalent circuit modeling of chemical thermal sensors. 

Using the equivalency relationships in Table 3.1, propose an equivalent electrical circuit diagram for an enzyme thermistor operated (a) in direct detection mode and (b) in the feedback, push-pull mode. 

The output of the model is then compared with the output of the real device and the individual elements are iteratively adjusted. When a good fit is obtained, the model is tested. It is a very important step, because the robustness of this procedure must be characterized by establishing the range of validity of the model, for the frequency and amplitude of the excitation signal, as well as for the range of values of the individual circuit elements. The wider the validity range, the more accurate is the representation of the real device by its model. The flowchart for building the equivalent electrical circuit model is shown in Fig. 4.11, and the equivalent electrical circuit of a QCM harmonic oscillator is shown in Fig. 4.12. Close to its resonance,... 

Both Rct and Cdi are voltage-dependent, but Rs is not. Explanation of the location, and properties of Rct, Rs, and C,u is what electrochemistry is about. We explain these nonlinearity-causing resistors and capacitors by equivalent electrical circuit analysis as we go forward. 

Rational optimization of performance should be the main goal in development of any chemical sensor. In order to do that, we must have some quantitative tools of determination of key performance parameters. As we have seen already, for electrochemical sensors those parameters are the charge-transfer resistance and the double-layer capacitance. Particularly the former plays a critical role. Here we outline two approaches the Tafel plots, which are simple, inexpensive, but with limited applicability, and the Electrochemical Impedance Spectroscopy (EIS), based on the equivalent electrical circuit model, which is more universal, more accurate, and has a greater didactic value. 

The equivalent electrical circuit approach has already been introduced in connection with analysis of mass sensors (Chapter 4). Its application is older and somewhat... 

Fig. 5.6 Equivalent electrical circuit of electrochemical cell (top) and corresponding Nyquist plot containing Warburg impedance W (bottom)...

Fig. 6.17 Equivalent electrical circuit representing potentiometric sensor with asymmetrically placed membrane (as in Fig. 6.16b). The field-effect transistor input to the voltmeter is added...

As the potential is scanned from positive to negative, the reduction of Ox 1 takes place first. As the potential is made even more negative, Ox2 begins to be reduced, then Ox3, and so on. Thus, at the applied potential E, only Ox will be reduced, but at the more negative potential 2, simultaneous reduction of Ox and Ox2 will take place. In order to determine these two species separately, measurements at two potentials must be made. In order to do that, the two potentials have to be at least 180 mV apart. Given an electrochemical window of 2.5V, we can see that the maximum number of electroactive species that can be accommodated is not more than 13, provided that their standard potentials are equally spaced. In reality, the number of different species that can be selectively determined in a mixture by using the selection of the applied potential is 4-6 at most. Thus, the choice of applied potential offers only a very limited selectivity and is used only to complement other modes of selectivity. In the context of the equivalent electrical circuit (Fig. 7.8), this strategy would be represented by the same potential applied to all resistive channels... 

Frequency as an experimental variable offers additional design flexibility. This approach has several advantages. The most important one is the lack of polarization of the contacts. The second one is the fact that equivalent electrical circuit analysis can be used that aids in elucidation of the transduction mechanisms. Perhaps the most important distinguishing feature of this class of conductometric sensors is the fact that their impedance is measured in the direction normal to their surface. In fact, there may be no requirement on their DC conductivity and their response can be obtained from their capacitive behavior. In the following section, we examine so-called impedance sensors (or impedimetric sensors see Fig. 8.1b). 

Fig. 8.13 A capacitive impedance sensor. Schematic diagram (a) and equivalent electrical circuit (b) 1-vapor absorbing layer 2-Cr/Ni/Au plate of the capacitor (Cl) 3-Ta plate (C2) 4-top, porous metal plate 5 insulating substrate...

The simplest dielectrometer is a capacitor containing a layer of a material that can more or less reversibly take up chemical vapor of a given dielectric constant. The diagram of such a sensor and its equivalent electrical circuit is shown in Fig. 8.13 (Garverick and Senturia, 1982). 

Commercial impedance analyzers offer equivalent circuit interpretation software that greatly simplifies the interpretation of results. In this Appendix we show two simple steps that were encountered in Chapters 3 and 4 and that illustrate the approach to the solution of equivalent electrical circuits. First is the conversion of parallel to series resistor/capacitor combination (Fig. D.l). This is a very useful procedure that can be used to simplify complex RC networks. Second is the step for separation of real and imaginary parts of the complex equations. 

Equivalent electrical circuit for a two-electrode setup with planar electrodes. (WE working electrode CE/RE counter electrode and reference electrode, respectively, being fulfilled by one single electrode.)... 

The equivalent electrical circuit in the case of a three-electrode setup is given in Fig. 2.9. Working and counter electrode are identical as for a two-electrode setup, while the reference electrode, as a non-current conducting electrode, only has the role of potential reference and therefore does not contribute to the impedance. However, the position of the Haber-Luggin capillary determines the contribution of Re and Rcomp to Ra given by the following equation ... 

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