Definition of Impedance

From the preceding section we can write a general definition of impedance. The general operational definition of impedance is described by Eq. (2.88)  

Applying the laws for the connections of impedances in series and in parallel, and substituting the impedance of the elements from Table 2.1, the total impedance of this circuit may be written as 

Erom the preceding examples one can see that writing the impedance of the circuits is straightforward. 

The foregoing examples are valid for any potential perturbation. In the particular case of ac impedance, that is, when the applied potential perturbation is sinusoidal, one uses the ET (Eq. 2.127)  

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For two passive elements in series, the same current must flow through the two elements, and the overall potential difference is the sum of the potential difference for each element. Thus, according to the definition of impedance given as equation (4.19), the impedjmce for the series arrangement shown in Figure 4.2(a) is given by... 

A brief discussion on applying IS to investigate the electrical properties of polymer electrolytes has been dealt with in Chapter 7. This chapter, on the other hand, aims to introduce and provide the necessary background for beginners to use IS as a method of analysis. Thus, we begin the chapter with the definition of impedance, and then discuss the basic principles of IS followed by impedance data presentation and interpretation. Ideal and real impedance data will be presented, compared and discnssed in order to enable the readers to grasp a clearer picture on the electrical properties and electrochemical processes in a polymer electrolyte system. 

An overview on the topic of IS, with emphasis on its application for electrical evaluation of polymer electrolytes is presented. This chapter begins with the definition of impedance and followed by presenting the impedance data in the Bode and Nyquist plots. Impedance data is commonly analyzed by fitting it to an equivalent circuit model. An equivalent circuit model consists of elements such as resistors and capacitors. The circuit elements together with their corresponding Nyquist plots are discussed. The Nyquist plots of many real systems deviate from the ideal Debye response. The deviations are explained in terms of Warburg and CPEs. The ionic conductivity is a function of bulk resistance, sample... 

Propagation constant F and characteristic impedance Zq of a conductor are frequency dependent as they are functions of the impedance of the conductor, as explained in Section 1.2. It should be noted that a and p in Section 1.3.4.1 (see Figure 1.10) are not frequency dependent (in the sense discussed in this section). The frequency dependence of the attenuation constant a(co) and phase constant P(co) in Section 1.3.4.1 comes from the definition of impedance Z and admittance Fof a conductor ... 

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