Time response characteristic impedance

Table 1.8 shows the time response of the frequency-dependent characteristic impedance given in Table 1.3. The time-dependent characteristic impedance increases as time increases. This is quite reasonable because of the inverse relation of time and frequency.

Figure 1.30 shows the time response of the characteristic impedance of a vertical twin-circuit line illustrated in Figure 1.25. The relation of magnitudes corresponds to that in the frequency domain explained for Figure 1.27 considering the inverse relation of time and frequency. It is observed from comparing Figure 1.25 with the frequency response of Figure 1.27 that the time dependence is greater than the frequency dependence of the characteristic impedance. For example, the variation of is 8.5%, 26.8%, and Z 31.3% for 2 ps < t <...

FIGURE 1.30 Time response of the characteristic impedance corresponding to Figure 1.27. TABLE 1.8 Time Responses of the Characteristic Impedances in Table 1.3... 

An EG G PARC 273 Potentiostat/Galvanostat was used in both the electrolysis and the CV experiments, coupled with an HP 7044B X/Y recorder. A Solartron 1255 HF Frequency Response Analyzer and a Solartron 1286 Electrochemical Interface were employed for the a.c. impedance measurements, using frequencies from 0.1 to 65 kHz and a 10 mV a.c. amplitude (effective) at either the open circuit potential (OCP) or at various applied potentials. As the RE can introduce a time delay at high frequencies, observed as a phase shift owing to its resistance and capacitance characteristics, an additional Pt wire electrode was placed in the cell and was connected via a 6.8 pF capacitor to the RE lead [32-34]. 

The third block in Fig. 2.1 shows the various possible sensing modes. The basic operation mode of a micromachined metal-oxide sensor is the measurement of the resistance or impedance [69] of the sensitive layer at constant temperature. A well-known problem of metal-oxide-based sensors is their lack of selectivity. Additional information on the interaction of analyte and sensitive layer may lead to better gas discrimination. Micromachined sensors exhibit a low thermal time constant, which can be used to advantage by applying temperature-modulation techniques. The gas/oxide interaction characteristics and dynamics are observable in the measured sensor resistance. Various temperature modulation methods have been explored. The first method relies on a train of rectangular temperature pulses at variable temperature step heights [70-72]. This method was further developed to find optimized modulation curves [73]. Sinusoidal temperature modulation also has been applied, and the data were evaluated by Fourier transformation [75]. Another idea included the simultaneous measurement of the resistive and calorimetric microhotplate response by additionally monitoring the change in the heater resistance upon gas exposure [74-76]. 

At the present time, the theory of electrochemical impedance of electrodes with distributed potentials is not yet completed, and algorithms of parametrical and structural identification procedures are not available. In addition, the interpretation of the results is very complicated. For this reason, in this work we analyzed only the frequency characteristics of impedance s components in the modified electrode system. As a result, we obtained a set of response peculiarities in the frequency range under investigation. Rather low frequency dispersion was observed in a solution containing a ferri-ferrocyanide system for both active (Fig.3, curve 2) and reactive (Fig.4, curve 3) components. In our opinion, this fact confirms that the independent on frequency resistance of charge transfer determines the main contribution to the impedance. 

Electrode geometry in controlled-potential electrolysis. When fast response and accuracy of potential control are desired, considerable attention must be paid to the design of the cell-potentiostat system, and several papers have discussed the critical parameters and made recommendations for optimum cell design.8"11 In general, to achieve stability and an optimum potentiostat rise time for a fast potential change, the total cell impedance should be as small as possible, and the uncompensated resistance should be adjusted to an optimum (nonzero) value that depends on the characteristics of the cell and potentiostat.9,12 The electrode geometry also should provide for a low-resistance reference electrode and a uniform current distribution over the surface of the... 

The impedance response of the R-RC circuit in Figure 4a is illustrated on a complex plane plot in Figure 4b. At low frequencies, the data approach the real axis at R + Rp (pathway 2), and the capacitive response is illustrated by the arc in the data. The frequency at the apex of the arc (to ) corresponds to the characteristic relaxation time (f ) of the circuit ... 

Since hydration of the skin has been shown to be the primary variable influencing the skin s impedance [7,10,11,18], one can speculate that the time variation in the skin s impedance may be a strong function of the time variation of the skin s hydration. The reason for the skin s profound dependence on hydration results from the skin s hydroscopic nature [15] coupled with water s significant impact on the skin s dielectric constant [12]. The skin s hydroscopic characteristic is speculated to be in part due to the presence of amino acids in the skin [15]. Hydration probably influences the skin s dielectric constant because the following components are sensitive to an electric field [7] (a) The keratin protein chains contained in the stratum comeum have a dipole moment. Thus, as the stratum comeum becomes more hydrated, the keratin becomes more flexible and responsive to an applied electric field, (b) As the stratum comeum becomes more hydrated, the ions in the stratum comeum become freer to move and thus more responsive to an applied electric field. 

Figure 4.7 Real and imaginary parts of the impedance response for a 10 fl resistor in parallel with a 0.1 F capacitor. The characteristic time constant for the element is 1 s.

The frequency K = 1 at which the current distribution influences the impedance response is shown in Figure 13.7 with k/Co as a parameter. As demonstrated in Example 13.2, the influence of high-frequency geometry-induced time-constant dispersion can be avoided for reactions that do not involve adsorbed intermediates by conducting experiments below the characteristic frequency given in equation (13.57). The characteristic frequency can be well within the range of experimental measurements. The value k/Cq = 10 cm/s, for example, can be obtained for a capacitance Co = 10 (corresponding to the value expected for the dou-... 

Add normally distributed stochastic errors to the time-domain potential and current signals for the system described in Example 7.1. Then apply the Fourier analysis to calculate the impedance response at the characteristic frequency. Repeat this process, refreshing the random numbers used, so as to calculate the standard deviation of the resulting impedance. How does this result depend on the number of cycles used for the integration ... 

PDEIS is a new technique based on fast measurements of the interfacial impedance with the virtual instruments [3] that benefits from the efficient synchronization of direct hardware control and data processing in the real-time data acquisition and control [4], The built-in EEC fitting engine of the virtual spectrometer divided the total electrochemical response into its constituents those result from different processes. Thus, just in the electrochemical experiment, we come from the mountains of raw data to the characteristics of the constituent processes - the potential dependencies of the electric double layer capacitance, charge transfer resistance, impedance of diffusion, adsorption, etc. The power of this approach results from different frequency and potential dependencies of the constituent responses. Because of the uniqueness of each UPD system and complex electrochemical response dependence on the frequency and electrode potential, the transition from the PDEIS spectrum (Nyquist or Bode plot expanded to the 3D plot... 

The characteristic time constant Tc in the form of tz and xyof Eqs (9.26) and (9.29) deserves some explanation. A two-component RC circuit with ideal components has a time constant t = RC. A step excitation results in an exponential response. With a CPE, the response will not be exponential. In Section 9.2.5, the time constant was introduced simply as a frequency scale factor. However, the characteristic time constant Tc may be regarded as a mean time constant because of a DRT. When transforming the Colez impedance Z to the Coley admittance Y or vice versa, it can be shown that the as of the two Cole Eqs 9.26 and 9.29 are invariant, but the characteristic time constants Tc are not. In fact ... 

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