Impedance imaginary components

Two difierent components contribute to impedance the resistive or real component due to resistors and the reactive or imaginary component from AC circuitry elements, such as capacitors, inductors, etc. Unlike the resistive component, the reactive impedance affects not only the magnitude of the AC wave but also its time-... 

Nyquist Plot a graph of the frequency response of an electrode in which the imaginary component of the impedance is plotted as a function of the real component for a range of frequencies. 

Equivalent Circuit Analysis. IS measurements yield values of V and Z the real and imaginary components of the impedance, as a function of f, the AC frequency. The data are usually displayed as Nvauist plots (Z, vs. Z ) or Bode plots (impedance modulus,... 

The ratio of the amplitudes of the applied and the response signal Vmlim) and the phase shift between these signals (0) can be used to determine the impedance, which can be represented as a complex number. The real component of impedance is known as the resistance, R, and the imaginary component, given by X, is known as the reactance [19]. 

In the impedance circuit analysis of an electrode/solution interface, the impedance and phase angle (or real and imaginary components) are measured at several frequencies. The imaginary component is plotted against the real component and the semicircle is then interpolated to those points. The solution resistance and the sum of solution and charge-transfer resistances, respectively, are then found by extrapolating the semicircle to = 0. 

For the two combinations to be equal, the real and the imaginary components of their impedances must be equal for all frequencies. Thus, from (D.3) and (D.7) for the real component... 

Figure 4 Cartesian coordinate system with imaginary j notation depicting an impedance vector Z and its real and imaginary components Z and Z" as well as phase angle 9.

The total equivalent resistance of a corroding surface may be estimated by integration of the imaginary component of the impedance over the measured frequency domain according to... 

In this expression, E and / are the magnitude of the potential and current noise at any given frequency, /. RRe and Rlm are the real and imaginary components of Rsn. Plots of spectral noise impedance versus frequency resemble Bode magnitude plots of EIS data as shown in Fig. 58. Meaningful phase angle information is not usually obtained, as this is not preserved by the MEM transform, and data are usually of insufficient quality for accurate phase information to be obtained from the EFT. 

Therefore, the real and imaginary components, Zre and Zim, in the AC impedance of the parallel RC circuit are given by... 

The Randles circuit is at the electrode/polymer interface (case a). The imaginary component of the impedance is dominated by the double-layer capacitance, and the real one is controlled by the double layer. The capacitance of the transmission line is shunted and the transmission fine is not involved. 

Figure C.l. K-K transforms of real and imaginary components of the electrochemical impedance for passive zinc in a borate solution of pH = 10.5, at 1.2 V (SCE) [13]. (Reproduced by permission of ECS—The Electrochemical Society, from Ismail KM, Macdonald DD. Characterization of the barrier passive film on zinc.)...

Further experiments have been conducted to confirm whether or not the presumed diffusion layer and its thickness, 8, as estimated from (95) corresponds to physical reality. First AC impedance spectroscopy has been used to find the frequency response of the real and imaginary components of the cell impedance and compared with the theoretical prediction for diffusion across a thinned diffusion layer. At very high AC frequencies, where the AC perturbation had insufficient time to probe to the edge of the diffusion layer, effectively the response expected for semi-infinite diffusion was seen ( Warburgian behaviour ). At lower AC frequencies, as expected, the cell impedance was greatly reduced in the presence of ultrasound. Moreover, not only was the quantitative behaviour as predicted theoretically... 

One-port FPW measurements, typically using a network analyzer, yield the input impedance of the transducer, the real and imaginary components of which can be used to determine the density and viscosity of a fluid contacting the device. 

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