Discharging equivalent circuit

The operative working condition of a battery can be represented by simple equivalent circuits, which are only valid for charging or discharging operations without considering the current transient phenomena. The discharging equivalent circuit of a battery is shown in Fig. 5.11. 

The difference with the discharging equivalent circuit is the resistance and the switch S. The resistance takes in account the charging losses, which start to... 

The distribution of potential in TC is practically the same as that near the flat surface if the electrolyte concentration is about 1 mol/1 [2], So the discharge of TC may be considered as that of a double electric layer formed at the flat electrode surface/electrolyte solution interface, and hence, an equivalent circuit for the TC discharge may be presented as an RC circuit, where C is the double layer capacitance and R is the electrolyte resistance. 

Fig. 5-60. Equivalent circuit for an interfacial electric double layer comprising a space charge layer, a surface state and a compact la3 er at semiconductor electrodes Csc = capacity of a space charge layer C = capacity of a surface state Ch = capacity of a compact layer An = resistance of charging and discharging the surface state.

In the treatment which follows, we assume that discharge of the doublelayer capacitance drives the reaction, and therefore use C = in Eq. (41). The effects of changes in coverage of the adsorbed intermediate are then taken into account by combining Eq. (41) with the kinetic equations for steps in the mechanism. In this method, no assumptions need then be made about the equivalent circuit or the nature of the pseudocapacitance, and the transient current during potential decay is not assumed to be equal to the steady-state current. The results then enable all three definitions of [Eqs. (46)-(48)] to be evaluated and compared, as illustrated in Fig. 10. 

Assuming in this equivalent circuit that the discharge occurs when the applied voltage... 

Figure 7. Proposed equivalent circuit for a single discharge...

The internal cell resistance is approximately the sum of / , Rc i, and Rah- The values of the resistance were determined by using the complex non-linear least squares (CNLS) fitting of the impedance spectra to the equivalent circuit of Figure 10(b). As a matter of fact, whatever models one selects for the impedance spectra in Figure 10(a), the values of total internal cell resistance and relaxation time necessary for charge/discharge of all the capacitive elements remain constant (see below). 

A problem with Debye theory and the use of ideal components in the equivalent circuits has been that most dielectrics actually do not follow an exponential discharge curve, but a fractional power discharge curve. This law is called the Curie — von Schweidler s law (Schweidler, 1907). We shall revert to this phenomenon later in Section 9.2.12. 

The anode of a Ni-Cd battery typically consists of a mix of Cd and CdO powders with the addition of a conductive additive (acetylene black). The impedance of the anode-particle surface is determined by the activated adsorption of OH anions first on the metal surface, with subsequent conversion into Cd(OH)2 and hydrated CdO layers (Duhirel et al. [1992])). Reaction products are also present in a partly dissolved Cd(OH)3" state. The activated adsorption mechanism of the anode reaction, as well as porous structure of the electrode, makes it appropriate to use for its analysis the equivalent circuit shown in Figure 4.5.14. It was shown by Xiong et al. [1996], by separate impedance measurements on the anode and cathode, that most of the impedance decrease during discharge is due to the anode, as the initial formation of a Cd(OH)Jrate limiting step of the reaction. The... 

Capacitors are not ideal drcuit elements. The equivalent circuit of a capadtor (valid from DC up to the low radio frequency range) is shown in Fig. 2.51(a). The shunt resistance Rp (which, in general, is the function of frequency) at DC and low frequendes is referred as the insulation resistance of the capacitor. It accounts for dielectric leakage current and dielectric power losses. When the capacitor is charged to V(0) volts and allowed to discharge through itself, the capacitor voltage is... 

FIGURE 10.254 The equivalent circuit of the facility shown in Fig. 10.253. Note the discharge current path through the electronic equipment. 

Model-based predictions of battery performance and longevity are required to provide depletion indicators for batteries such as RRT (recommended replacement time), typically based on discharge voltage or resistance, to allow patients to schedule a replacement surgery before batteries reach EOS (end of service). Electrical characteristics of primary batteries used in medical applications have been modeled in a variety of ways including empirically or thermodynamics-based voltage curve models [16,17], equivalent circuit models [18,19], resistance models [11,20], and more recently physics-based comprehensive models [17, 21-23] that can be used to predict pulse performance [24],... 

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