Impedance plot Bode diagram

A Bode plot is an alternative representation of the impedance. There are two types of Bode diagram, log z log (or z log ) and 9 log , describing the frequency dependencies of the modulus and phase, respectively. A Bode plot is normally depicted logarithmically over the measured frequency range because the same number of points is collected at each decade. Both plots usually start at a high frequency and end at a low frequency, which enables the initial resistor to be found more quickly. 

A line of 45° versus the coordinate axis represents the Warburg impedance in the complex plain presentation (Nyquist plot. Figure 5.7a). The representation in the Bode diagram is shown in Figure 5.7b. The phase shift has a constant value of 45°, whereby the modulus of the impedance, IZI is linearly decreasing with increasing frequency. 

Nyquist plot. A shift of the 45° line and a small deviation from the linear behavior at highest frequencies indicate that an impure diffusion impedance is represented in the diagram. A characteristic double layer behavior dominates the high-frequency part of the Bode diagram (Figure 5.10b). At low frequencies the diagram approaches the characteristic form of diffusion. 

A comparison of these cases shows that the two representations of impedance measurements provide different information. While low-frequency components dominate in the Nyquist plot, high-frequency components dominate the character of the Bode diagram. 

Dynamic Methods in Solid-State Electrochemistry, Fig. 2 Impedance plot for a simple Rj R2C) combmatimi, Nyquist diagram (left). Bode diagram (right)... 

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... 

Figure 2.37 shows an example impedance spectrum of an electrochemical system with two time constants. Figure 2.37a, b, and c are the equivalent circuit, simulated Nyquist diagram, and Bode plot, respectively. 

The most common graphical representation of experimental impedance is a Nyquist plot (complex-plane diagram), which is more illustrative than a Bode plot. However, a Bode plot sometimes can provide additional information. 

FIGURE 46.19 Impedance spectroscopy, (a) Schematic diagram of the impedance measurement device analysis plots (b) Nyquist plot and (c) Bode plot. 

When a range of frequencies is applied to the DUT, both El and ECI techniques are called spectroscopies, i.e., electrical impedance spectroscopy and electrochemical impedance spectroscopy. Electrochemical impedance spectroscopy (EIS) profiles, measured as a function of the interrogating frequency, can be presented by two popular plots complex plane impedance diagrams, sometimes called Nyquist or Cole-Cole plots, and Bode (I Z I and 6) plots (Fig. 2). As the impedance, Z, is composed of a real and an imaginary part, the Nyquist plot shows the relationship of the imaginary component of impedance, Z" (on the Y-axis), to the real component of the impedance, Z (on the X-axis), at each frequency. A diagonal line with a slope of 45° on a Nyquist plot represents the Warburg... 

Fig. 2 Representative (a) complex plane diagrams (Nyquist or Cole-Cole plots) and (b) Bode plots from electrochemical impedance spectroscopy measurements...

Fig. 5 (a) Nyquist and Bode (b) total impedance and (c) ZiM and phase angle plots, (d) Rsol- RctICdl circuit diagram... 

The measured frequency characteristics of electrochemically produced iron and S235JR steel in corrosive environment of 0.5M NaCl solution are presented in the form of Nyquist diagrams (Fig. 14) and Bode plots of impedance spectra (Fig. 15). 

FIGURE 4-1 A. R-Ccircuit diagram and corresponding B. Nyquist and Bode C. totai impedance D. phase angle plots... 

FIGURE 4-4 A. (R -Cj circuit diagram B. Nyquist and Bode C total impedance D and phase angle E. modulus plots F. modulus plots... 

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