Impedance and Admittance

In this section, the principles outlined above will be applied to derive the expression for the interfacial admittance valid for a simple system as described before. In addition, this treatment will illustrate the use of impedances and admittances in the study of electrochemical kinetics. 

If the components of the impedance and admittance in phase are represented by Z and Yf respectively and the components with phase angle of jt/2 represented by Z" and Y", then... 

We can generalize the analogy by considering the viscoelastic materials as a continuum where the theory of transmission lines can be applied. In this way, a continuous distribution of passive elements such as springs and dash-pots can be used to model the viscoelastic behavior of materials. Thus the relevant equations for a mechanical transmission line can be written following the same patterns as those in electrical transmission lines. By representing the impedance and admittance per unit of length by g and j respectively, one has... 

The complex-capacitance-plane plot is presented in Figure 16.11. The data are presented as a locus of points, where each data point corresponds to a different measurement frequency. As discussed for the impedance- and admittance-plane representations (Figures 16.1 and 16.6, respectively), the complex-capacitance-plane... 

J. R. Macdonald and J. A. Garber, "Analysis of Impedance and Admittance Data for Solids and Liquids," Journal of The Electrochemical Society, 124 (1977) 1022-1030. 

This is a nonlinear least-squares fit of the real and imaginary parts, or the magnitude and phase angle of the experimental impedance and admittance to a given model. In general, the sum of squares ... 

However, as illustrated in Figure 10.2, living tissue has capacitive properties because of, for example, cell membranes. Therefore, the u and i signals are not in-phase, and impedance and admittance are complex quantities. They are written in bold characters and can be decomposed in their in-phase and quadrature components... 

Impedance is the ratio between voltage and current. It applies to both direct current (DC) and alternating current (AC). Admittance is the inverse of impedance—that is, not impede, but admit, current flow. Immittance is the combined term for impedance and admittance, so a better and more generic term than bioimpedance is bioimmittance. 

Impedance and admittance are basically AC parameters. It is easy to believe that AC values approach DC values when the AC frequency 0 Hz. However, this is not necessarily true because of electrolysis. At sufficiently low frequencies, one polarity lasts long enough to generate irreversible products that change the chemical environment permanently. 

Immittance is not a quantity it is the general term of both impedance and admittance, and in a specific case a quantity must be chosen either impedance [Q] or admittance [S]. Such quantities with names ending on —ance are dependent on sample and electrode geometries. Quantities with names ending on —ivity such as impedivity [Qm], admittivity [S/m], and permittivity 0 /m] are material constants. 

However, if we excite the same series RC-circuit with a controlled current step and record the voltage across the RC circuit, the voltage will increase linearly with time ad infinitum. The time constant is infinite. Clearly, the time constant is dependent not only on the network itself, but on how it is excited. The time constant of a network is not a parameter uniquely defined by the network itself. Just as immittance must be divided between impedance and admittance dependent on voltage or current driven excitation, there are two time constants dependent on how the circuit is driven. The network may also be a three-or four-terminal network. The time constant is then defined with a step excitation signal at the first port, and the possibly exponential response is recorded at the second port. 

The equivalent circuit is shown on Figure 9.21 for the impedance and admittance cases. 

Impedance variables such as Z, R, X, p, and Cs are preferably used when components are connected in series. Admittance variables such as Y, G, B, a, and Cp are preferably used when components are connected in parallel. Immittance is the combined term for both impedance and admittance. It is often used in order to force the reader to be sensitive to the choice there is no such thing as an immittance equation. 

Passive oscillator mode Impedance analysis of the forced oscillation of the quartz plate provides valuable information about the coating even if the active mode is not applicable anymore. For impedance analysis, a frequency generator is used to excite the crystal to a constraint vibration near resonance while monitoring the complex electrical impedance and admittance, respectively, dependent on the applied frequency (Figure 2B). For low load situations near resonance, an equivalent circuit with lumped elements - the so-called Butterworth—van-Dyke (BVD) circuit — can be applied to model the impedance data. The BVD circuit combines a parallel and series (motional branch) resonance circuit. The motional branch consists of an inductance Lq, a capacitance Cq, and a resistance Rq. An additional parallel capacitance Co arises primarily from the presence of the dielectric quartz material between the two surface electrodes (parallel plate capacitor) also containing parasitic contributions of the wiring and the crystal holder (Figure 2B). 

Both impedance and admittance are called immittances. Between other related functions, complex dielectric constant should also be mentioned [78]. It is used in the analysis of dielectric relaxation and is obtained from the measured admittance (impedance) of a cell with a given dielectric (liquid or solid) ... 

Fig. 13.1 Complex plane impedance and admittance plots for circuit in Fig. 2.34 with = 10 O,...

Fig. 13.5 Complex plane impedance and admittance plots fin hydrogen-doped LisN monocrystals (a) impedance plot and fit to model indicated in inset, (b) admittance plot and fit to Eq. (13.12) points experimental, line fits (From Ref. [575] Reproduced with pramission of Electrochemical Society)...

It is good to realize that we have normalized the irradiation intensity and the photocurrent to particles per second per unit area. In this way the IMPS impedance and admittance are dimensionless. 

The Applicability and Power of Complex Nonlinear Least Squares for the Analyses of Impedance and Admittance Data, J. Electroanal. Chem. 131, 77-95. 

Y.-T. Tsai and D. W. Whitmore [1982] Nonlinear Least-Squares Analysis of Complex Impedance and Admittance Data, Solid State Ionics 1, 129-139. 

The measurements (Fig. 3) show two areas of dispersion a, /5 in the frequency range 40 Hz-10 MHz. Measured impedance is analyzed by evaluating characteristic points in the impedance and admittance representation and by fitting several impedance models. Characteristic points (Fig. 3) allow analyzing the impedance evolution over time. The characteristic... 

In Table 5.24, the impedances and admittances of the three passive elements are given. The admittance is the inverse of the impedance. 

Figure 11.17 The common experimental arrangement for electrochemical impedance experiments relies on the use of a frequency response analyser to derive the Cartesian or polar coordinates of the impedance and admittance.

First, this book will illustrate a transient on a single-phase line from a physical viewpoint, and how it can be solved analytically by an electric circuit theory. The impedance and admittance formulas of an overhead line will also be described. Approximate formulas that can be computed using a pocket calculator will be explained to show that a transient can be analytically evaluated via hand calculation. Since a real power line contains three phases, a theory to deal with a multiphase line will be developed. Finally, the book describes how to tackle a real transient in a power system. A computer simulation tool is necessary for this— specifically the well-known simulation tool Electro Magnetic Transients Program (EMTP), originally developed by the U.S. Department of Energy, Bonneville Power Administration— which is briefly explained in Chapter 1. 

In this chapter, a theory of distributed-parameter circuits is explained starting from the approximate impedance and admittance formulas of an overhead conductor. The derivation of the approximate formulas is described from the viewpoint of the physical behavior of current and voltage on a conductor. 

To analyze a transient in a distributed-parameter line, a traveling-wave theory is explained for both single- and multiconductor systems. A method to introduce velocity difference and attenuation in the multiconductor system is described together with field test results. Impedance and admittance formulas of unusual conductors, such as finite-length and vertical conductors, are also explained. 

In general, the impedance and admittance of a conductor are composed of the conductor s internal impedance Z,- and the outer-media impedance Z. The same is applied to the... 

It should be noted that the impedance and admittance in this equation become a matrix when a conductor system is composed of multiconductors. Remember that a single-phase cable is, in general, a multiconductor system because the cable consists of a core and a metallic sheath or a screen. In an overhead conductor, no conductor internal admittance y exists, except a... 

Impedance and Admittance Formulation of an Overhead Conductor System... 

Considering the impedance and admittance explained in Section 1.2, the single distributed-parameter line in Figure 1.5a is represented by a lumped-parameter equivalence, as in Figure 1.5b. 

Surge impedance Zq and surge admittance Yq in these equations are extreme values of the characteristic impedance and admittance in Equation 1.49 for frequency f oo. 

From this equation, the characteristic impedance and admittance matrices are... 

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