Nonlinear impedances

McAdams, E.T., Jossinet, J., 1994. The detection of the onset of electrode-electrolyte interphase impedance nonlinearity a theoretical study. IEEE Trans. Biomed. Eng. 41 (5), 498—500. 

The form of the Hamiltonian impedes efficient symplectic discretization. While symplectic discretization of the general constrained Hamiltonian system is possible using, e.g., the methods of Jay [19], these methods will require the solution of a nontrivial nonlinear system of equations at each step which can be quite costly. An alternative approach is described in [10] ( impetus-striction ) which essentially converts the Lagrange multiplier for the constraint to a differential equation before solving the entire system with implicit midpoint this method also appears to be quite costly on a per-step basis. 

Generally the material response stress versus particle velocity curves in Fig. 8.6 are nonlinear and either a graphical or more complicated analytic method is needed to extract a spall strength, Oj, from the velocity or stress profile. When behavior is nominally linear in the region of interest a characteristic impedance (Z for the window and for the sample) specify material... 

Mishuk et a/.675,676 have applied the modified amplitude demodulation method to electrochemically polished pc-Bi in aqueous NaF solution. The curves of the real component of the nonlinear impedance Z" as a function of the electrode potential, unlike pc-Cd and pc-Pb, intersect for various cNaF at E - -0.62 V (SCE),674 i.e., at Ea=0 for pc-Bi, as obtained by impedance.666-672 The different behavior of pc-Bi from pc-Cd and pc-Pb at a > 0 has been explained by the semimetallic nature of pc-Bi electrodes. A comparison of inner-layer nonlinear parameter values for Hg, Cd, and Bi electrodes at a < 0 shows that the electrical double-layer structure at negative charges is independent of the metal.675,676... 

In (photo)electrochemistry, the expected photocurrent change, Ai, is typically dependent in a nonlinear way on the changes in the potential applied. The reciprocal complex impedance, 1/AZ, is the variable. The real part (flAconductivity change across the elec-... 

If the nonlinear character of the kinetic law is more pronounced, and/or if more data points than merely the peak are to be used, the following approach, illustrated in Figure 1.18, may be used. The current-time curves are first integrated so as to obtain the surface concentrations of the two reactants. The current and the surface concentrations are then combined to derive the forward and backward rate constants as functions of the electrode potential. Following this strategy, the form of the dependence of the rate constants on the potential need not be known a priori. It is rather an outcome of the cyclic voltammetric experiments and of their treatment. There is therefore no compulsory need, as often believed, to use for this purpose electrochemical techniques in which the electrode potential is independent of time, or nearly independent of time, as in potential step chronoamperometry and impedance measurements. This is another illustration of the equivalence of the various electrochemical techniques, provided that they are used in comparable time windows. 

Figure 26. Predictions of the Adler model shown in Figure 25 assuming interfacial electrochemical kinetics are fast, (a) Predicted steady-state profile of the oxygen vacancy concentration ( ) in the mixed conductor as a function of distance from the electrode/electrolyte interface, (b) Predicted impedance, (c) Measured impedance of Lao.6Cao.4Feo.8-Coo.203-(5 electrodes on SDC at 700 °C in air, fit to the model shown in b using nonlinear complex least squares. Data are from ref 171.

However, as we saw in section 3.3 for platinum on YSZ, the fact that i—rj data fits a Butler—Volmer expression does not necessarily indicate that the electrode is limited by interfacial electrochemical kinetics. Supporting this point is a series of papers published by Svensson et al., who modeled the current—overpotential i—rj) characteristics of porous mixed-conducting electrodes. As shown in Figure 28a, these models take a similar mechanistic approach as the Adler model but consider additional physics (surface adsorption and transport) and forego time dependence (required to predict impedance) in order to solve for the full nonlinear i—rj characteristics at steady state. 

Figure 3.67 IsSpice nonlinear core results of output impedance.

Other important characteristics of the converter are the reflected ripple attenuation and the turn-on characteristics. It is expected that the turn-on characteristics will be difficult to simulate because of the nonlinear characteristics of a saturating core. A nonsaturating core is simply described by Faraday s law, and it can be easily modeled by any of the SPICE simulators. The model used for the EMI filter is shown in Fig. 3.66, and the results of each of the simulators output and the measured impedance plots are shown in Figs. 3.67 to 3.70. 

Let us return to the reduction of shear stress at the crack tip due to the emission of dislocations. Figure 14-9 illustrates a possible stress reduction mechanism. It can be seen that the tip of a crack is no longer atomically sharp after a dislocation has been emitted. It is the interaction of the external stress field with that of the newly formed dislocations which creates the local stress responsible for further crack growth. Thus, the plastic deformation normally impedes embrittlement because the dislocations screen the crack from the external stress. Theoretical calculations are difficult because the lattice distortions of both tension and shear near the crack tip are large so that nonlinear behavior is expected. In addition, surface effects have to be included. 

Nonlinear load — Electrical load that draws currents discontinuously or whose impedance varies during each cycle of the input AC voltage waveform. Figure 1.6 shows the waveform of a nonlinear current drawn by fluorescent lighting loads. 

Non resonant techniques are only of limited use to determine microwave losses with high precision, in particular when the losses are very small. Flowever, for the investigation of nonlinear absorption phenomena (i.e. rf power dependent on surface impedance or loss tangent) by intermodulation distortion measurements broad-band test devices are more common. Typically, a planar transmission line with an impedance of 50 Ohms can be employed for intermodulation... 

Nonlinear Impedance and Low-Frequency Dispersion Effects of a Polyelectrolyte Under High Sinusoidal Fields... 

Since the two major results we obtained in our experiments are a nonlinear impedance and a low frequency dispersion effect of polyelectrolytes under high fields, it is logical for us to provide the readers with some background review in the field of nonlinear effects and high-field dispersion effects of electrolytic solutions. Most of the studies in these fields were devoted to Wien effects and DFW dispersion theory which are briefly discussed here. A detailed discussion of these two groups of studies with their recent developments is reported in a separate review chapter in Nonlinear Electromagnetics. 

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