Equivalent network

T.J. Cui and C.H. Liang, Reconstruction of the permittivity profile of an inhomogeneous medium using an equivalent network method, 1993, IEEE Trans. Antennas Propagat., 41, pp. 1719-1726. 

The mesh size was determined from an equivalent network, prepared from a mixture of protonated and deuterated precursors. The radius of gyration of the mesh strands was found to be 25 A, which is identical to the radius of gyration of the uncross-linked precursors. 

Figure 8.4 Equivalent network circuit of a partial discharge in a solid dielectric.

Related Calculations. If the six surfaces are not black but gray (in the radiation sense), it is nominally necessary to set up and solve six simultaneous equations in six unknowns. In practice, however, the network can be simplified by combining two or more surfaces (the two smaller end walls, for instance) into one node. Once this is done and the configuration factors are calculated, the next step is to construct a radiosity network (since each surface is assumed diffuse, all energy leaving it is equally distributed directionally and can therefore be taken as the radiosity of the surface rather than its emissive power). Then, using standard mathematical network-solution techniques, create and solve an equivalent network with direct connections between nodes representing the surfaces. For details, see Oppenheim [8],... 

The hypothetical single p-hydroquinone structure is inherently unstable, as it has a large unoccupied cavity at the center of the unit cell. In fact a second, translation-equivalent network (displaced by one-half of the vertical body diagonal of the supercube) can be introduced such that the spacious voids of each network are filled by [OH], rings of the other. This system of two mutually interpenetrating, but unconnected, networks constitutes the basis of the P-hydroquinone host lattice, which can accommodate small guest species such as Xe, ... 

As a result the region between the grains can be represented by an electrical equivalent network consisting of three RC branches as it has been noticed in introduction. 

Section 2.1.3 shows how the process of diffusion in one dimension can be represented by a chain of resistors and capacitors, and Section 2.1.6 shows how porous electrodes can be represented by a similar network. While this approach is valid even for a distributed process with no boundary (like diffusion into infinite space), discretization is even more important for the case where a distributed process is limited in space. In this case, a finite number of discrete elements can describe the system to arbitrary precision, and can be used for numerical calculations, as treated in next chapter, even if no analytical solution is possible. Another convenience of discretizing a distributed process is the resulting ability to add additional subprocesses directly to the equivalent circuit rather than starting the derivation by formulating a new differential equation. For example the equivalent network representing electric response of a pore is given in Figure 4.5.3. 

Butterworth, and others, and is shown in Fig. 3.5. FIGURE 3.5 In the equivalent network, the circuit parameters nator. 

Bourouina T, Grandchamp JP (1996) Modeling micropumps with electrical equivalent networks. J Micromech Microeng 6(4) 398-404... 

Equivalent network for vapor flow and pressures in column... 

S. Fletcher, The two-terminal equivalent network of a three-terminal electrochemical cell, Elec-trochem. Comm., 2001,3, pp. 692-6%. 

A. Sadkowski, J.-P. Diard, On thefletcher s two-termimd equivalent network cfa three-terminal electrochemical cell, Electrochim. Acta, 2010,55, pp. 1907-1911. 

Past work on electrical measurements of columns consisting of spheres of ion-exchange resins and electrolyte solutions, and on the interpretation of the results by the simple equivalent-network model described above is then reviewed. The experimental results covered are conductivity measurements at low frequencies (60 and 1000 Hz), electrical potential differences between two different NaCl solutions separated by such columns, and the variation of the dielectric constant and conductivity of the columns above 20 MHz, all over a range of sulution concentrations. It will be shown that not only does the proposed network describe the variation of the measured parameters with solution concentration and/or frequency, but that the geometrical parameters of the model are roughly the same for all these measurements. 

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