Complex admittance

For a periodic perturbation, 5 (AB(t)) is also periodic. The complex admittance [30] is given by... 

G Yu, Y Cao, C Zhang, Y Li, J Gao, and AJ Heeger, Complex admittance measurements of polymer light-emitting electrochemical cells ionic and electronic contributions, Appl. Phys. Lett., 73 111-113, 1998. 

Figure 8. Complex admittance (reciprocal of impedance) or porous Pt on YSZ in air at 700 °C. The largest portion of the impedance (appearing at lowest admittance) exhibits a response frequency of 20 Hz (response time of 0.01 s). (Reprinted with permission from ref 54. Copyright 1973 Laboratoire d Electrochimie et de Physicochimie des Materiaux et des Interfaces (INPG and CNRS), Saint Martin d Heres, France.)...

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. 

In bulk heterojunction solar cells, the metal/semiconductor interface is even more complex. Now the metal comes into contact with two semiconductors, one p-type (typically the polymer) and one n-type (typically the fullerene) semiconductor. A classical electrical characterization technique for studying the occurrence of charged states in the bulk or at the interface of a solar cell is admittance spectroscopy. If a solar cell is considered as a capacitor with capacitance C, the complex admittance Y is given by... 

For the equivalent circuit in Figure 3.10, the total complex admittance Y and complex impedance Z in Cartesian coordinates can be expressed as... 

Figure 3.12. Polar presentation of the total complex admittance Y...

It will be noticed that these equations imply that the real and ima nary coordinates of the complex admittance... 

It has been known for some time that for efficiently reducing the reflectance of highly reflective substrate with a complex admittance (i.e. metals, or coated metals, such as an OLED), it is convenient to use simple metal-dielectric AR coatings similar to those used in black absorbers (Dobrowolski, 1981 Lemarquis Marchand, 1999) or heat-reflector in solar-cells applications (Macleod, 1978). This type of coatings has been demonstrated for the contrast-enhancement of electroluminescent (EL) displays (Dobrowolski et al., 1992) and on the cathode side of bottom-emitting OLED (see above) (Krasnov, 2002). 

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... 

A word of caution is appropriate with regard to an over-interpretation of the Mason circuit in principle, one might attempt to calculate the complete admittance spectrum of a crystal directly from the Mason circuit. However, this possibility is of little practical use, because the electrical admittance cannot be measured accurately enough in experiment. In order to allow for a comparison with the prediction from the Mason circuit, the admittance would have to be measured as precisely as the resonance frequency (relative error of 10 ), which is impossible. The strength of the QCM lies in its tremendous accuracy with regard to frequency measurements. Unfortunately, this extreme accuracy is hmited to the frequency of the peak conductance it does not extend to the conductance (or, more generally, the complex admittance) itself. 

Nonequilibrium noise generated by carrier-mediated ion transport was studied in lipid bilayers modified by tetranactin (41). As expected, deviations of measured spectral density from the values calculated from the Nyquist formula 1 were found. The instantaneous membrane current was described as the superposition of a steady-state current and a fluctuating current, and for the complex admittance in the Nyquist formula only a small-signal part of the total admittance was taken. The justification of this procedure is occasionally discussed in the literature (see, for example, Tyagai (42) and references cited therein), but is unclear. 

An expression for the complex admittance, Y(jf), of an axon membrane is obtained by linearizing the Hodgkin-Huxley (HH) equations (I) and by applying a Laplace transformation (13, 14). The membrane admittance is then given by the general expression... 

Data Analysis. Complex admittance determinations were fitted by an admittance function (13, 14, 16) based on the linearized HH equations (I). Admittance measurements were made under steady-state conditions (see Figures 2 and 4). Series resistance (Rs), the access resistance between the two voltage electrodes and up to the inner and outer surfaces of the axon membrane was not removed from measurements. Instead Rs was included and determined in the fit of the steady-state admittance model to the data. The measured complex admittance, therefore, is... 

Rapid Complex Admittance Measurements. The voltage clamp system, chamber, and axial electrode techniques were described previously (10, 12). By superposing a repetitive small-amplitude (1-mV root mean square) Fourier-synthesized signal (8, 16, 19) onto large step clamps, a current response was acquired during voltage clamp pulses. Immediately... 

Figure 3. Admittance data from a K +-conducting membrane and curve fits (solid curves) of eqs 2, 3, and 4 with Y /jf,) = 0 plotted in the complex plane [X(f) vs. R(f)] as impedance [Z(jf) = R(f) + jX(f) = Y 1(jf/)] loci (400 frequency points) over the 12.5 5000-Hz frequency range. These data were acquired rapidly as complex admittance data, as illustrated in Figure 1, at premeasurement intervals of 0.1 and 0.5 s after step voltage clamps to each of the indicated membrane potentials from a holding of —65 mV. The near superposition and similarity in shape of the two loci at 0.1 and 0.5 s, at each voltage, indicates that the admittance data reflect a steady state in this interval after step clamps. Axon 86-41 internally perfused with buffered KF and externally perfused in ASW + TTX at 12 °C. The membrane area is 0.045 cm2.

The complex admittance method described here allows data to be analyzed without reference to any particular model. This condition is particularly important at this time, when new data and new concepts are challenging previously accepted concepts. The elucidation of the primary structure of channel proteins (2, 3) has stimulated the development of a number of structurally oriented models (e.g., references 21 and 22). In addition, new physical and mathematical concepts have been brought to bear on the problem of channel gating in excitable membranes. These concepts include... 

By using Eqs. (24) and (25), it is possible to compute, say, the complex admittance versus temperature curves for a nearly arbitrary given density of states g E), which may be compared to experimental data on a-Si H. An illustrative example is provided by the density of states shown in Fig. 16 for a series of nearly discrete (narrow Gaussian) levels of concentration fVj with a dominant 50-me V-deep shallow (dopant) level of concentration Ay. 

Reactance and. series resistance (real and imaginary parts of complex impedance) Susceptance and parallel conductance (real and imaginary parts of complex admittance)... 

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