Impedance phase angle

The tangent of the impedance phase angle for the capacitor is given by the imaginary component divided by the real component, tan 6= - Xc/0 = —00. Therefore, the impedance phase angle for the capacitor is —7t/2. 

Another method often used for plotting and evaluating EIS data involves plots of log Z and 8 versus log GO. These data presentations are known as Bode plots and are illustrated by the example in Fig. 6.20, again for the simplest equivalent circuit of Fig. 6.18. Bode plots have advantages in that the impedance and impedance phase angle are shown as explicit functions of the frequency, which is the independent experimental variable. Reference to Eq 6.68 shows that at very high go values, Z approaches Rs, and at very low frequencies, Z approaches (Rs + Rp). These limits are indicated in Fig. 6.20. In analyzing intermediate frequencies, that is, when (Rs + Rp) > Z ... 

Nagano, M., Suita, S., and Yamanouchi, T. (2000) The Validity of Bioelectrical Impedance Phase Angle for Nutritional Assessment in Children. 7. Pediatr. Surg. 35.1035 1039. 

Fig. 10 Comparison of the impedance phase angles of the Pt electrode and PEDOT-coated Pt electrodes. The PEDOT/PSS was coated potentiometrically at room temperature with variable polymerization charge densities from 20, 40, 80 to 160 mC/cm. AU four PEDOT-coated electrodes have reductions in phase angle at the frequency range of 100 Hz-10 kHz while significant reductions appear around 1 kHz...

Thus, in the range where the impedance phase angle approaches 7t/2, the value of the intercalation capacitance, Qn can be determined graphically from the slope of Eq. 3.3. 

Introducing the complex notation enables the impedance relationships to be presented as Argand diagrams in both Cartesian and polar co-ordinates (r,rp). The fomier leads to the Nyquist impedance spectrum, where the real impedance is plotted against the imaginary and the latter to the Bode spectrum, where both the modulus of impedance, r, and the phase angle are plotted as a fiinction of the frequency. In AC impedance tire cell is essentially replaced by a suitable model system in which the properties of the interface and the electrolyte are represented by appropriate electrical analogues and the impedance of the cell is then measured over a wide... 

For the impedance of the resistance and inductance in series, the current will lag the potential phase angle by... 

The impedance can be measured in two ways. Figure 5.23 shows an impedance bridge adapted for measuring the electrode impedance in a potentiostatic circuit. This device yields results that can be evaluated up to a frequency of 30 kHz. It is also useful for measuring the differential capacity of the electrode (Section 4.4). A phase-sensitive detector provides better results and yields (mostly automatically) the current amplitude and the phase angle directly without compensation. 

IZI=J(Z )2+(Z ), and phase angle shift,, vs. f). The electrochemical system is then simulated with an electrical circuit that gives the same impedance response. Ideally this electrical circuit is composed of linear passive elements, e.g. resistors and capacitors, each of which represents individual physicochemical steps in the electrochemical reaction. ... 

Figure 13.7 Absolute value of the impedance and phase angle as a function of the frequency.

A complication that occurs on a low at.% Ru electrode is that, owing to the low Faradaic currents (low Ru content) and hence large Rt value, currents due to other trace redox reactions, e.g. oxygen reduction, become more detectable. This reveals itself in a phase-angle of 45° as co 0 as trace oxygen reduction would be diffusion-controlled. The impedance corresponding to this situation can be shown to be the same as that in Equation 5.3, with U(p) expressed by the relationship ... 

At low frequencies the impedance is dominated by diffusion. Two regions may be identified in the complex impedance, a linear region with a phase angle of ti/4 corresponding to semiinfinite diffusion and... 

Perrin-Helmholtz theory, 873 Phase angle, impedance, 1129 Phase difference, impedance, 1127 Phase formation, one dimensional, underpotential deposition, 1316 Phenyl compounds, 979 Phonon spectra, 1463 Phonon, 1517... 

Warburg showed that this impedance would have a phase angle of 45° and be proportional in magnitude to to h. Its value was shown to be... 

Measurement of interfacial impedance and phase angle over a frequency range... 

Although not dealt with in this chapter, AC impedance measurements (sometimes called electrochemical impedance spectroscopy) are important in studying electrode dynamics. Generally in this method, a sinusoidal voltage (10 2 to 105 Hz) is applied to the cell, the phase angle and the amplitude of the response current are measured as a function of... 

This is the phenomenon of the so-called constant phase element (CPE) as it follows from eqn. (115) that Yc is composed of an imaginary and a real component, with a frequency-independent phase angle cor/2. Though the phenomenon is most clearly discovered in impedance or admittance analyses, its effect in time-domain methods should not be ignored. 

No simple combination of resistors correctly models the phase angle and current response of Zf at all frequencies, but it can be modeled at any single frequency by a resistor and capacitor arranged either in series or in parallel. This effective impedance, now termed the Warburg impedance (Zw), is a function of frequency and can be extracted from experimental data either numerically or... 

Figure 8.8 Series RC circuit (a) circuit (b) current-voltage relationships (c) frequency dependence of impedance Z and phase angle .

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