Admittance parameters

The admittance time constant is uniquely defined by ty, independent of G, as if the circuit were voltage driven. The admittance parameter therefore has the advantage that the measured characteristic frequency determining xy is directly related to the capacitance (membrane effects) and series resistance in tissue. The same is not true for impedance the impedanee is defined by both ty and X2. 

The next step in designing an LP prototype filter network is to select inductors and capacitors so that the admittance parameters 21 and 722 are as specified in Table 4.10. The procedure is demonstrated for a representative fourth-order filter (Chebyshev with 3-dB ripple), and the results are given in Table 4.11 for... 

The unknown coefficients Vf and in the general solution expressed as Equation 1.110 are determined from boundary conditions. There are many approaches to obtain voltage and current solutions in a multiconductor system. The most well-known method is the four-terminal parameter (F-parameter) method of two-port circuit theory. The impedance parameter (Z-parameter) and the admittance parameter (Y-parameter) methods are also well known. It should be noted that the F-parameter method is not suitable for application in high-frequency regions, while the Z- and F-parameter methods are not suitable in low-frequency regions because of the nature of h5q)erbolic functions. 

The optical admittance parameter has been introduced into thin-film optics with one specific aim, namely to visualize optical phenomena occurring within such systems by means of a graphical representation of the optical events known as the admittance diagram. Although this is one of a class of diagrams known collectively as circle diagrams, it is particularly powerful and attractive and therefore it is used extensively in thin-film optics. 

Here, Y) (x, j=l, 2) are called admittance parameters (Y-parameters). Admittance parameters are more often used than impedance parameters since a voltage source is typically given as a boundary condition. 

The impedance and admittance parameter methods are stable for 0 since it is based on convergence functions, coth(0) and cosech(0). Thus, the method is suitable for the transient analysis. However, it should not be used for the analysis of low-frequency phenomena since cosech(0) becomes infinite for 0 -> 0, that is, CO 0. 

The most important parameter in the analysis of pressure-coupled combustion instability is the acoustic admittance Y, which is the ratio of the amplitude of the acoustic velocity V to the amplitude of the acoustic pressure amplitude of the acoustic velocity V to the amplitude of the acoustic pressure P ... 

When the propellant burning rate is espressed by Eq. (5b), the parameter p /e can be considered as the transient sensitivity of the burning rate to pressure. This parameter depends on the transient combustion characteristics, and its evaluation depends on the particular model of the combustion process. Thus, the acoustic admittance provides the link between experimental observation and theoretical prediction. 

These studies have indicated that the independent parameters controlling the postulated solid-phase reactions significantly affect the resulting acoustic admittance of the combustion zone, even though these reactions were assumed to be independent of the pressure in the combustion zone. In this combustion model, the pressure oscillations cause the flame zone to move with respect to the solid surface. This effect, in turn, causes oscillations in the rate of heat transfer from the gaseous-combustion zone back to the solid surface, and hence produces oscillations in the temperature of the solid surface. The solid-phase reactions respond to these temperature oscillations, producing significant contributions to the acoustical response of the combustion zone. 

It is quite easy to derive the faradaic admittance from eqns. (63) using eqn. (57). For the sake of simplicity, we introduce the parameter p defined by... 

Fig. 17. (a) The components of the faradaic impedance plotted against to. (b) The components of the faradaic admittance plotted against to1/2. System parameters fict = lficm1, p = 0.03. The solid parts of the plots indicate the frequency range that is normally accessible for meaningful analysis of data with the simple theory described in this section... 

Rct is better visualized in a complex admittance plane diagram (i.e. Yal plotted against V j) or a complex impedance plane diagram (i.e. Zal = Z" plotted against Z ei + Rn = Z )- The latter is known as the Sluyters plot and is widely used to determine the respective parameters. Some typical examples are represented in Fig. 18. 

The interfacial admittance applied to the study of adsorption parameters... 

In this section, the interpretation of interfacial admittance data in the case of an a.c. reversible reaction with adsorption of O is briefly described. The relationships expressing the frequency dependence were derived some time ago [15, 17], but the essential meaning of the parameters involved was fully explained only recently [143], The brief description here is derived from the latter reference. 

Two such circuits having different relaxation time constants and connected in series lead to two semicircles as shown in Fig. 2.55(b). As in the case of any other spectroscopic analysis the separate responses may overlap and the experimental curve must then be resolved into its separate constituent semicircles. Impedance spectroscopy makes use of other electrical parameters, including the admittance (Y = Z 1), to assist in quantifying the circuit parameters. 

AW device sensitivity to viscoelastic parameters and electrical pnqieities can be used to advantage in some film characterization techniques. In these situations, a comparison of the AW device response to a model of the AW/thin film interaction is often crucial to the effective evaluation of thin film parameters. These additional interaction mechanisms typically involve changes in both the wave velocity and the wave attenuation for SAW, APM and FPW devices, and changes in both resonant frequency and admittance magnitude in TSM devices. In contrast, mass loading does not contribute to wave attenuation or decreases in admittance since moving mass involves no power dissipation (see Chapter 3). 

Relaxations in such assumed circuits can proceed through two independent processes known as serial and parallel processes. Macedo et al. (1972) proposed on the basis that impedances (and not admittances) are additive in a series process, use of a dimensionless parameter, A/ = l/e, as appropriate for the analysis of conductivity relaxation. A/, therefore, is also resolved into real and imaginary parts as ... 

The faradaic admittance of reactions (116) and (117) is described by Eq. (135). Analysis of the complex plane plots in such a case was presented by Cao. Bai and Conway presented three-dimensional plots for such a reaction. Two general cases should be considered, depending on the sign of the parameter B ... 

The above analysis shows that in the simple case of one adsorbed intermediate (according to Langmuirian adsorption), various complex plane plots may be obtained, depending on the relative values of the system parameters. These plots are described by various equivalent circuits, which are only the electrical representations of the interfacial phenomena. In fact, there are no real capacitances, inductances, or resistances in the circuit (faradaic process). These parameters originate from the behavior of the kinetic equations and are functions of the rate constants, transfer coefficients, potential, diffusion coefficients, concentrations, etc. In addition, all these parameters are highly nonlinear, that is, they depend on the electrode potential. It seems that the electrical representation of the faradaic impedance, however useful it may sound, is not necessary in the description of the system. The systen may be described in a simpler way directly by the equations describing impedances or admittances (see also Section IV). In... 

It is also possible to measure the complex impedance or complex admittance of an overpotential network. Instead of measuring the whole complex impedance (or admittance) curve, it is usually sufficient to measure only one or two values at given frequencies. The frequencies used are in the range 50-10,000 Hz, most often 1000 Hz. The admittance of a gel VRLA battery during discharge at the 10-h rate is shown in Fig. 8.11 [8] note that, frequency and SoC are parameters. Instead of... 

The aim of network analysis is the investigation of the amplitude and phase response of a two- or four-port network. Impedance analysis determines the complex impedance or admittance of a device. This method is appropriate for quartz resonators in order to obtain more complete information than is conceivable by merely considering the shift of the resonance frequency. The method especially allows the determination of the equivalent circuit elements (BVD) presented in Fig. 8. Actually many commercial instriunents directly provide this information. Determination of the physical parameters, or their effective values, for accurate modeling of the sensor behavior based on Eq. 5 requires mathematical procedures which fit the calculated curves (e.g., with Eq. 2) to the experimentally measured values. It is recommended to include an external capacitance parallel to Co to accoimt for uncompensated para-... 

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