Admittance, real part

Effective cathode gas diffusivity Effective anode gas diffusivity Volume fraction porosity Surface exchange coefficient Impedance at angular frequency Imaginary part of admittance Real part of admittance Anode thickness Cathode thickness Electrolyte thickness Exchange current density Anode limiting current density Cathode limiting current density Three phase boundary length Transfer coefficient of symmetry factor... 

The real part 7 is called the -+ conductance and the imaginary part 7" is called the -+ susceptance. The term admittance was coined by Oliver Heaviside in 1887. 

FIGURE 9.1. The real part of the nondimensional nozzle admittance yyJMi as a function of the nondimensional frequency k for various values of the nozzle-entrance Mach number M, with y = 1.2 for longitudinal modes in a nozzle having a velocity linear with distance [20]. 

Basically, Impedance spectra and admittance spectra contain the same Information It is a matter of experimental and Interpretational convenience to decide which one to use. Moreover, the Imaginmy and real parts of Z and y are pairwise coupled by Kramers-Kron equations (variants of (1.4.4.31 and 321) so that in principle one can be obtained when the other Is known Such a transformation requires very accurate data over a large rringe of frequencies, which for Inorganic solids are not always available, so that for practical purposes these equations have only limited impact. However, mathematical expressions for Z and y should always agree with the Kramers-Kronlg relations, a fact that can be used to validate electrospectroscopic data ). 

Figure 3.30. Relation between the imaginary and real parts of the impedance (left) and admittance (right). The arrows indicate the direction of the increase of for V = R". Figure (b) is circular. Starting from the origin (where oj = 0) the frequency Increases. Solid lines for a resistance and ideal capacitance in series dashed for resistance and a constant phase element in series.

As angular frequency a tends toward zero, the real part of the admittance tends toward l/(jRe + R), and the imaginary part of the admittance tends toward zero according to co such that... 

Figure 16.7 Real and imaginary parts of the admittance as a function of frequency for Re — 10 Qcm, R = 100 Qcm, and C = 20 piF/cm. The blocking system of Table 16.1(a) is represented by dashed lines, and the reactive system of Table 16.1(b) is represented by solid lines, Characteristic frequencies are noted as /rc == (2n J C) and fc = 2nReC) a) real part of admittance and b) imaginary part of admittance.

The characteristic angular frequency for the blocking circuit is o c = 1/ReC, the same as is found for the admittance of the blocking circuit. At the characteristic angular frequency, the real part of the capacitance is equal to half the double-layer capacitance, and the imaginary part is equal to minus one-half of the double-layer capacitance. The complex-capacitance plot for tire blocking circuit traces a semicircle. 

The additive contributions to Iq and Rq are similar due to similar real and imaginary parts of Zi. Because Iq L q and Rq J uq holds, Q changes approximately inversely with This behavior is reflected in the plot of the real part of electrical admittance, G, of a quartz crystal with single side contact to water. Fig. 7. Both maximum and slope continuously decrease with... 

Fig. 7 Plot of real part admittance, G (Y = G +jX), against reduced frequency for AT-and BT-cut quartz crystals for different fundamental frequencies,/o...

This approach is dedicated to the measurement of hquid viscosity by determining the real part of the sensor admittance at series resonance frequency. According to this concept, one terminal of the sensor is fed with the (constant-level) output of a VCO. The resonator current I is measured by connecting a transimpedance amphfier at the second terminal. Due to the low input impedance of the transimpedance amphfier, the entire VCO output voltage is apphed to the sensor. Parasitic capacitances from the sensor terminals to ground (e.g., due the shielding of the connection cables) are on one side... 

Conductance (G) - For direct current, the reciprocal of resistance. More generally, the real part of admittance. [1]... 

Usually, the properties of a quartz crystal resonator with respect to frequency can be discerned from admittance plots, where the abscissa represents the real part of the admittance (conductance, G) and the ordinate the imaginary component (susceptance, B). Resonance occurs at two frequencies where the admittance locus crosses the real axis, fs and fp, which are the series and parallel resonance frequencies, respectively. If Rt is negligible, the series and parallel frequencies at which resonance occurs are given by eqn.(5) [2],... 

Fig. 18. Imaginary (solid) and real (dashed) part of 10 kHz admittance obtained for density of states in Fig. 16 under 5 V reverse bias (Ob = 0.55 eV). Note that the real part G/co is also expressed in picofarads (right-hand scale) and is multiplied by a factor of 10 compared to the capacitive part (which is offset). The junction area A is taken to be 2 X 10 cm .

Figure 4.17 Shift and change of the resonance frequency of a quartz crystal microbalance, real part of the admittance versus frequency, /q, Wq, resonance frequency and full width at half maximum (FWHM) of the initial gold electrode,/j, w, resonance frequency and FWHM of a gold electrode after formation of a rigid and smooth surface film (no damping), resonance frequency and FWHM of a gold electrode after formation of a viscoelestic and/or rough surface film (strong damping).

A transfer function, the admittance function, can be defined as y ((o) = iy((o)l6 , where iy(co)l represents the amplitude and c ) is the phase angle. The impedance function, Z(co), is the inverse of the admittance function, Z(a))=[y ((o)]" and since both the amplitude and the phase angle of the output may change with respect to the input values, the impedance is expressed as a complex number, Z = Z i -i- where Zjeji is the real part and Z is the imaginary part. 

Rs and Cm can be obtained from the measurement in the presence of the supporting electrolyte only if the distance between the Luggin capDlaiy and the working electrode is the same. One can also determine these parameters in the presence of the electroactive species R at high frequencies and Cm by interpolation of the Fj plot versus the potential before and after the faradaic peak. An example of such an interpolation is shown in Fig. 4.6, where the in-phase (real part) ac current propor-tirnial to the real part of the total admittance is displayed for Cd " reduction in dimethylsulfoxide (DMSO) [150]. Similar measurements of the out-of-phase (imaginary) part make it possible to determine the double layer capacitance in the presence of the redox reaction. 

Fig. 4.6 Dependence of in-phase current, proportional to real part of total electrode admittance for Cd reduction at Hg dropping electrode in dimethyl-sulfoxide (From Ref. [150] with permission of author)...

Although these relations will be written below for impedances they also hold for admittances and other complex transfer functions. Assuming that all the aforementioned conditions are met, the Kramers-KrcMiig relations are obtained allowing the calculation of the imaginary impedance from the real part... 

In the previous sections the expressions for the admittance of materials were developed on the assumption that they had no dc conductivity. The real part of the admittance arose from the dissipative process of dipole reorientation. Energy was absorbed by the system when the orientation of dipoles was changed with respect to the electric field vector. 

FIG. 1. (a) The real part of the admittance versus frequency during deposition... 

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