Inductor, electrical model component

The problem when trying to make an electrical model of the physical or chemical processes in tissue is often that it is not possible to mimic the electrical behavior with ordinary lumped, physically realisable components such as resistors (R), capacitors (C), inductors, semiconductor components, and batteries. Let us mention three examples 1) The constant phase element (CPE), not realizable with a finite number of ideal resistors and capacitors. 2) The double layer in the electrolyte in contact with a metal surface. Such a layer has capacitive properties, but perhaps with a capacitance that is voltage or frequency dependent. 3) Diffusion-controlled processes (see Section 2.4). Distributed components such as a CPE can be considered composed of an infinite number of lumped components, even if the mathematical expression for a CPE is simple. 

A third passive two-terminal electrical component can also be seen in the LAB electrical models the inductor. This component is connected in series to represent the battery behavior in high frequencies in order to fit EIS measurements. One has to keep in mind that such a component does not really describe the battery, but only the cables used to connect it to the load (or the charger). For EIS, the rule of thumb is approximately 10 nH per centimeter of cable. Otherwise, the self-inductance L (in nH) of a straight wire of length I, small diameter d, made of a metal having a relative permeability equal to 1 (like Cu or Al, but not Fe) can be calculated as follows [30] ... 

The electric analogy is one of the most extensively used methods for flow and species transport modeling in channel-based microfluidic systems. A microfluidic network is equivalent to an electric circuit, of which each component can be individually described by resistors, ccmductors, and inductors. Equations 1 and 2 show the RLC circuit models in electric and fluidic domain ... 

The waveguide discontinuities shown in Fig. 4.23(a) to Fig. 4.23(f) illustrate most clearly the use of E and H field disturbances to realize capacitive and inductive components. An E-plane discontinuity (Fig. 4.23(a)) can be modeled approximately by a frequency-dependent capacitor. H-plane discontinuities (Fig. 4.23(b) and Fig. 4.23(c)) resemble inductors as does the circular his of Fig. 4.23(d). The resonant waveguide iris of Fig. 4.23(e) disturbs both the E and H fields and can be modeled by a parallel LC resonant circuit near the frequency of resonance. Posts in waveguide are used both as reactive elements (Fig. 4.23(f)) and to mount active devices (Fig. 4.23(g)). The equivalent chcuits of microstrip discontinuities (Fig. 4.23(k) to Fig. 4.23(o)) are again modeled by capacitive elements if the E field is interrupted and by inductive elements if the H field (or current) is interrupted. The stub shown in Fig. 4.23(j) presents a short chcuit to the through transmission line when the length of the stub is A. /4. When the stubs are electrically short (shunt capacitances in the through transmission Hne. 

From the expression in Eq. (19) most forms of equivalent circuit models of piezoelectric elements may be found. The Van Dyke circuit [14] is the simplest, using discrete electrical components combined to approximate the piezoelectric element s behavior. I tis used to represent the electrical irrqtedance about one resonance of a freely suspended piezoelectric element, using a shunt capacitor in parallel with an inductor, resistor, and capacitor placed in series to represent the motional or resonance behavior of the element. A multivibrator Van Dyke model may be formed by adding additional motional legs, each representing another resonance. Since it lacks any explicit treatment of the output force and velocity, it is not especially useful beyond electrical characterization (see... 

The circuit model includes, among others, a resistor, capacitor and inductor. Such component models are available from standard libraries. The model equations are v = R i, i = C der(v) and V =L-der(i), respectively, where der() denotes the time derivative. Each component has two electric pin interfaces (filled and non-filled blue squares in Figure la) that include the voltage v as a potential and current i as a flow variable. Model equations are introduced for connected component (object) interfaces as follows The potential is the same, whereas the sum of flow equals zero according to Kirchhoff s node rule. For example, in case of the circuit model shown by Figure la) v =v = V7 and... 

EIS data are commonly analyzed by fitting them to an equivalent electrical circuit model corresponding to a fuel cell component or components. Most of the circuit elements in the model are common electrical elements such as resistors, capacitors, and inductors. As an example, the electrolyte ohmic resistance can be represented with a resistor. Very few electrochemical cells... 

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