Equivalent circuits 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.

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 ... 

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. 

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 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. 

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. 

FIGURE 1.84. Equivalent circuit representation of the elements X and Z in the Fletcher model. 

FIGURE 3-1 Equivalent circuit representation of an operational amplifier. 

Figure 3-1 is an equivalent circuit representation of an operational amplifier. In this figure, the input voltages are represented by and V-. The input difference voltage IV is the difference between these two voltages that is, IV = - v. The power supply connections arc... 

Physieal models and equivalent circuit representations for conducting polymer actuators and sensors are presented, including mechanical, electrical, and electromechanical descriptions. The underlying concept of most models is that strain is proportional to charge density, and sense voltage is proportional to stress. Dynamics are determined by the rate of charge transfer, as well as the mechanical properties of... 

Fig. 2 Schematic cross section of the ferroelectret foil shown in Fig. 1 left). Ferroelectrets are cellular polymers, with oppositely charged voids. Equivalent circuit representation of the cellular ferroelectret foil (right). The ferroelectret is represented by a current source and by a capacitor. Current is generated when electrical forces are apphed to the ferroelectret. The capacitance of a ferroelectret foil is small, typically around 20 pF for a c acitor with an area of 1 cm ...

More details on impedance analysis of practical electrochemical systems composed of these processes and their interrelationships can be found in Chapters 6 and 7. In these chapters an emphasis will be put on developing a complete equivalent circuit representation of an analyzed system and establishing relationships among various components of the circuit. 

---