Impedance plot Argand

A mathematician would say that a plot of Z" (as y ) against Z (as jc ) forms an Argand diagram (or Argand plane ). As electroanalysts, we will call such a set of axes a Nyquist plot or simply an impedance plot (see Figure 8.9). 

We shall refer to it as the complex-plane impedance plot, recognizing that the same data can also he represented in the complex-plane capacitance or the complex-plane admittance plots. The terms Cole-Cole plot, Nyqidst plot and Argand plot are also found in the literature. 

Fig. 3.7 The complex-plane impedance plot representation (also called the Argand diagram or Nyquist diagram) of the ideal impedance spectra in the case of reflective boundary conditions. Effect of the ratio of the film thickness (L) and the diffusion coefiicient (D). L/D (7) 0.005 (2) 0.1 (2) 0.2 4) 0.5 and (5) 1 s /. i o = 2 Q, 7 ct = 5 Q, (7 = 50 cm fis / Cdi = 20 pFcm. The smaller numbers refer to frequency values in Hz...

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... 

It has to be mentioned that such equivalent circuits as circuits (Cl) or (C2) above, which can represent the kinetic behavior of electrode reactions in terms of the electrical response to a modulation or discontinuity of potential or current, do not necessarily uniquely represent this behavior that is other equivalent circuits with different arrangements and different values of the components can also represent the frequency-response behavior, especially for the cases of more complex multistep reactions, for example, as represented above in circuit (C2). In such cases, it is preferable to make a mathematical or numerical analysis of the frequency response, based on a supposed mechanism of the reaction and its kinetic equations. This was the basis of the important paper of Armstrong and Henderson (108) and later developments by Bai and Conway (113), and by McDonald (114) and MacDonald (115). In these cases, the real (Z ) and imaginary (Z") components of the overall impedance vector (Z) can be evaluated as a function of frequency and are often plotted against one another in a so-called complex-plane or Argand diagram (110). The procedures follow closely those developed earlier for the representation of dielectric relaxation and dielectric loss in dielectric materials and solutions [e.g., the Cole and Cole plots (116) ]. 

Figure 11.10 plots the imaginary -Z" vs. the real part Z" of the complex impedance (Argand plot) exemplary for undoped CoTi03/La at 400°C under synthetic air. All plots showed semicircles and could be described with the impedance function of a parallel RC circuit equivalent. 

S.3.3 Nyquist (or Argand) Complex-Plane Plots for Representation of Impedance Behavior... 

In addition to an examination of the frequency response of series and parallel components of the circuit impedance/admittance, another approach may be particularly valuable. This analysis method involves plotting the real versus imaginary parts of some such complex quantity as admittance or impedance as parametric functions of frequency. Such Argand or "circle diagrams" have been used for many years in electrical engineering when complex dielectric constant is the quantity considered, they are known as Cole-Cole plots. ... 

This implies that the complex impedance vector can be represented in the Argand plane, where we plot the imaginary component Im (Z) = Z" versus the real component Re (Z) = Z. Hence we can also write... 

The HFR corresponds to the extrapolated real-axis intercept for impedance spectra plotted on the Argand plane. The reported frequency ranges vary, but they usually include measurements at 1 kHz or larger frequencies. 

Figure 19-5. Different possibilities to represent impedance data. Left Argand plot Right ...

The complex impedance of a sample between inert electrodes is generally measured over a wide frequency range, e.g. 10 Hz to 10 Hz, and plotted as an Argand diagram with frequency as a parameter, e.g. Figure 6. 

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