Frequency-dependent parameters characteristic impedance

Using Eq. 1-2 for resistance R and Eq. 1-3 for capacitance C, which are frequency-dependent parameters when analyzed over a broad frequency range, a general impedance equation (Eq. 1-10) can be developed as a function of the frequency-dependent characteristic electrical properties of the analyzed material or system. This expression takes into account the frequency-dependent values of relative permittivity e((o) and resistivity p(co) or its inverse, electrical conductivity a(co), combined with the geometry factors of the electrode surface area (/4) and the sample s thickness between the bounding electrodes (d) ... 

Here, the impedance response is independent of the working point, and the frequency dependence is determined solely by the material parameters of the composite. For / <linear branch appears only at frequencies co > a/Cfr). Doublelayer charging and proton transport dominate the overall electrode response in this regime, whereas Faradaic processes are insignificant due to the high frequencies. An equivalent representation of this system is an RC-transmission line [130], Since no fractality or branching of the network is assumed, the response resembles that of a Warburg impedance with a characteristic proportionality Z a where... 

In Equation 1.263, Zq is the characteristic impedance that is frequency dependent. When the frequency dependence of a distributed-parameter line explained in Section 1.5 is to be considered, a frequency-dependent line such as Semiyen s and Marti s line models is prepared as a subroutine in the EMTP. 

From the separate lines of Eqs. 13-12 and 13-13 real and imaginary components of impedance at first (fundamental), second, third, and fourth harmonics can be calculated from the known voltage signal parameters and measured frequency-dependent current. The values for the Aaracteristic total capacitance C V ) and conductance G(f,j.) of the circuit can be computed. Comparison of the experimental and calculated frequency-dependent data for each harmonic serves as a diagnostic criterion that the system can indeed be represented by a simple parallel G C combination. Poor fit between the experimental and the calculated frequency-dependent impedance or current functions implies that a more complicated kinetic mechanism is responsible for the measured impedance characteristics. 

On a RDE, in the absence of a surface layer, the EHD impedance is a function of a single dimensionless frequency, pSc1/3. This means that if the viscosity of the medium directly above the surface of the electrode and the diffusion coefficient of the species of interest are independent of position away from the electrode, then the EHD impedance measured at different rotation frequencies reduces to a common curve when plotted as a function of p. In other words, there is a characteristic dimensionless diffusional relaxation time for the system, pD, strictly (pSc1/3)D, which is independent of the disc rotation frequency. However, if v or D vary with position (for example, as a consequence of the formation of a viscous boundary layer or the presence of a surface film), then, except under particular circumstances described below, reduction of the measured parameters to a common curve is not possible. Under these conditions pD is dependent upon the disc rotation frequency. The variation of the EHD impedance with as a function of p is therefore the diagnostic for... 

Impedance is the preferred parameter characterizing the two resistors, one capacitor series circuit, because it is defined by one unique time constant Xz (Eq. (12.8)). This time constant is independent of R, as if the circuit was current driven. The impedance parameter therefore has the advantage that measured characteristic frequency determining Xz is directly related to the capacitance and parallel conductance (e.g., membrane effects in tissue), undisturbed by an access resistance. The same is not true for the admittance the admittance is dependent both on xz and X2, and therefore on both R and G. 

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