Circuit representations

While a good equivalent-circuit representation of the transport processes in a fuel cell can lead to an increased understanding, it is not as good as taking a 1-D sandwich model and taking it into the frequency domain. These models typically analyze the cathode side of the fuel cell. °2.3i3 3i4 pj g j ost comprehensive is probably that of Springer et al. °2 The use of impedance models allows for the calculation of parameters, like gas-phase tortuosity, which cannot be determined easily by other means, and can also allow for the separation of diffusion and migra-... 

C equivalent circuit representation of bulk sample capacitance... 

Figure 17. Equivalent circuit representation of the injection/recombination process. (Reproduced with permission from Ref. [81].)...

Figure 3.40 Equivalent circuit representation of an electrode incorporating an adsorbed redox active species (see text for notation). The components responsible for the ER (electroreflectance) response are shown within the dotted frame, where VF is the interfacial admittance, and the subscript F refer to the current and potential associated with the faradaic or interfacial modulation.

In the analysis of the relaxation data we often need to represent the dielectric as a combination of pure resistances and capacitances. The manner of their connection in the dielectric is also assumed. It is through the use of such circuit representation that the dielectric data are analysed. 

Fig. 5 When representing mechanical elements with equivalent circuits, elements which are placed in series to each other, physically, have to be drawn as parallel elements in the circuit representation because currents (speeds) are additive for parallel electrical elements. Conversely, mechanical elements which are physically placed in parallel have to be represented in series because the voltage (force) is additive for electrical elements placed in series. In the literature on polymer rheology, springs and dashpots are depicted as on the right-hand side, but connected to each other as on the left-hand side. This convention differs from the convention chosen here. It amounts to a different set of Kirchhoff rules...

Apart from these practicalities, there is an important new concept contained in the equivalent circuit representation, which is the load impedance, Zi. The load impedance in this context is the ratio of the stress, a, and the speed, ii, at the crystal surface. The load impedance is normaUzed to area (unlike the mechanical impedance). 

Fig. 1 Equivalent circuit representation of the quartz crystal including a load. Piezoelectric stiffening (described by the element 42 in Fig. 13, Chap. 2 in this volume) was neglected. The sample is represented by the load Zl...

In the simple-spring model, the crystal is in contact with an immobile object. The model can be extended to cover situations where the object takes part in the oscillation to some extent. A typical object of this kind would be a small (< 10 im) sphere [40]. Figure 2c depicts the physical situation and the equivalent circuit representation. Note that the motion occurs into the lateral direction even though the spring is drawn vertically. In the following, we assume a spring constant independent of frequency, labeled its. From Fig. 2c, we infer the load to be ... 

FIGURE 22.3 Circuit representation of membrane current. The conductance can be nonlinear as indicated by the powers p and q on the state variables m and hi, respectively. These state variables are typically time-varying functions of the transmembrane potential difference, V. The battery, , represents the electrochemical gradient of the ionic species responsible for the current. 

The portion of the electrical circuit representation of a system that delivers the oscillatory resonance behavior at one or more rescmance frequencies ( resonance and antiresonance frequencies). 

Blif-mv consists of symbolic hardware, where high level objects are modeled either by wires, if they are non-memorising, or latches, if they are memorising. These objects are very close to those found in Verilog. Blif-mv also contains so called multi-variables, which is a representation of enumerated variables. The next value of latches is the output wire of a circuit representation of the transition function. In Blif-mv, all objects are scalar, and all functions are either a subcircuit (a network of more elementary functions) or a function given in tabular form. No predefined function exists. 

Costa Branco, P. J. and Dente, J. A. (2006). Derivation of a continuum model and its electric equivalent-circuit representation for ionic polymer-metal composite (IPMC) electromechanics. Smart Materials and Structures 15, pp. 378-392. 

FIGURE 4.3.19. Equivalent circuit representation of an electrode-solution interface for a simple charge-transfer process. (A) Without adsorbed intermediates, and (B) with adsorbed intermediates. 

This paradox highlights the hidden bias of circuit representations with dipolar devices. They need to be accompanied by the convention chosen for stating which is the across variable and which one is the through variable. 

Fig. 6 Equivalent circuit representation of a typical impedance cell used in microbiology. The symbols R, and Q represent the interfacial resistances and capacitances, respectively, while Rm is the resistance of the medium separating the two electrodes. 

Of course, Eq. (6.27) might also have other equivalent circuit representations. 

FIGURE 18.13 (a) Equivalent circuit representation of an internal short, (b) Simulation of power generation as a function of variation in short and cell resistance during internal short. The maximum power generated in the short area is when the cell resistance equals the internal short resistance. (For color version of this figure, the reader is referred to the online version of this book.)... 

The circuit representation is easily converted into the bond graph in Fig. 4.27. It includes an effort detector representing the sensor of the output voltage Vo. 

The input impedance of an antenna is defined as the ratio between the voltage and the current at its terminals, when the antenna is in transmit mode. The equivalent circuit representation is displayed in Fig. 26.2. 

Q < 00. A circuit representation ofthe product of transfer functions is shown in Fig. 7.108 the individual blocks representing Tj, j = 1,2,3, are said to be connected in cascade. It is assumed that there is no loading between the blocks in the figure. From a purely mathematical point of view, the order of the blocks in the figure does not make a difference. But from a practical view, the order of placement may be important. If the input signal to the filter is of... 

Macroscopic Modeling of Porous Electrodes, Fig. 1 Simple equivalent-circuit representation of a porous electrode. The total current density, i, flows through the separator or membrane to the electrolyte phase (2) and then into the solid or electronic phase... 

FIGURE 1.82. Schematic representation of the equivalent circuit ladder network corresponding to Fletcher porous electrode model for electronically conducting polymers (see Refs. 68, 69). The specific equivalent circuit representation of the interfacial impedance element is also illustrated. 

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