Electrical circuit, basic impedance

Resistance (R,r) is an clement of an electric circuit that reacts to impede the flow of current. The basic unit of resistance is the ohm (fi), which is defined m terms of Ohm s taw as the ratio of potential difference to current, i e, ... 

In order to understand electrochemical impedance spectroscopy (EIS), we first need to learn and understand the principles of electronics. In this chapter, we will introduce the basic electric circuit theories, including the behaviours of circuit elements in direct current (DC) and alternating current (AC) circuits, complex algebra, electrical impedance, as well as network analysis. These electric circuit theories lay a solid foundation for understanding and practising EIS measurements and data analysis. 

This chapter has provided basic electrical fundamentals, including concepts and definitions for circuit elements, and their relationships within electric circuits. Various basic AC electric circuits were also presented. Following upon primary circuit theories, the concept of electrochemical impedance spectroscopy and basic information about EIS was introduced. This chapter lays a foundation for readers to expand their study of EIS and its applications in PEM fuel cell research and development. 

The circuit elements can be connected in series or in parallel. The basic rule for the calculation of the circuits is for an electric circuit with elements in series connection, the total impedance is the sum of the impedances of the individual elements for an electric circuit with elements in parallel connection, the total... 

This method employs the basic principles previously described for the EIS method but with the use of two identical working electrodes. The method does not use an auxiliary electrode nor a reference electrode. With reference to Fig. 6.21, the two working electrodes (A and B), ideally, are identical in all aspects—geometry, chemical composition, microstructure, surface condition, etc. The method involves application of a low-amplitude (e.g., 20 mV) AC potential across the two electrodes, at a very low frequency (If) and at a very high frequency (hf), and measurement of the impedance of the system at each frequency, Z lf and Z hf. The assumed equivalent electrical circuit for the system also is indicated in Fig. 6.21. This circuit assumes that the simplest equivalent electrical circuit, as shown in Fig. 6.18, is applicable to each of the electrodes in the two-electrode method. In this case, Rs is the solution resistance (normalized with respect to specimen area, for example, ohms-m2) between the two electrodes. With reference to Fig. 6.21 (and also with reference to the previous discussion of the EIS method), it is seen that ... 

As per basic electrical laws, current flowing in an electrical circuit will create a voltage drop (A V) proportional to the impedance (Z) of this circuit. 

In an analysis of an electrode process, it is useful to obtain the impedance spectrum —the dependence of the impedance on the frequency in the complex plane, or the dependence of Z" on Z, and to analyse it by using suitable equivalent circuits for the given electrode system and electrode process. Figure 5.21 depicts four basic types of impedance spectra and the corresponding equivalent circuits for the capacity of the electrical double layer alone (A), for the capacity of the electrical double layer when the electrolytic cell has an ohmic resistance RB (B), for an electrode with a double-layer capacity CD and simultaneous electrode reaction with polarization resistance Rp(C) and for the same case as C where the ohmic resistance of the cell RB is also included (D). It is obvious from the diagram that the impedance for case A is... 

At the heart of impedance analysis is the concept of an equivalent circuit. We assume that any cell (and its constituent phases, planes and layers) can be approximated to an array of electrical components. This array is termed the equivalent circuit , with a knowledge of its make-up being an extremely powetfitl simulation technique. Basically, we mentally dissect the cell or sample into resistors and capacitors, and then arrange them in such a way that the impedance behaviour in the Nyquist plot is reproduced exactly (see Section 10.2 below on electrochemical simulation). 

Basically, the impedance behavior of a porous electrode cannot be described by using only one RC circuit, corresponding to a single time constant RC. In fact, a porous electrode can be described as a succession of series/parallel RC components, when starting from the outer interface in contact with the bulk electrolyte solution, toward the inner distribution of pore channels and pore surfaces [4], This series of RC components leads to different time constant RC that can be seen as the electrical response of the double layer charging in the depth of the electrode. Armed with this evidence, De Levie [27] proposed in 1963 a (simplified) schematic model of a porous electrode (Figure 1.24a) and its related equivalent circuit deduced from the model (Figure 1.24b). 

Transmission line — This term is related to a more general concept of electric -> equivalent circuits used frequently for interpretation of experimental data for complex impedance spectra (-> electrochemical impedance spectroscopy). While the complex -> impedance, Z, at a fixed frequency can always by obtained as a series or parallel combinations of two basic elements, a resistance and a capacitance, it is a much more compli-... 

Impedance models are constructed according to the electrochemical phenomena. The total impedance of an electrochemical system can be expressed by different combinations of the electrical elements. This section covers the features of basic equivalent circuits commonly used in electrochemical systems. In Appendix D, the effect of an element parameter change on a spectrum related to a given equivalent circuit is described in detail. 

First, the applied time-dependent stimulus (one-shot or repetitive — voltage or current) is mapped into the complex-frequency domain, that is, the s-plane. Then, by using the s-plane versions of the impedances, we can transform the entire circuit into the s-plane. To this transformed circuit we apply the s-plane versions of the basic electrical laws and thereby analyze the circuit. We will then need to solve the resultant (transformed) differential equation (now in terms of, v rather than t). But as mentioned, we will be happy to discover that the manipulation and solution of such differential equations is much easier to do in the s-plane than in the time domain. In addition, there are also several lookup tables for the Laplace transforms of common functions available, to help along the way. We will thus get the response of the circuit in the frequency domain. Thereafter, if so desired, we can use the... 

Whenever electricity flows across a circuit, there is a resistance to flow encountered by the electrons. For pacing systems, the resistance is determined by the complex interaction of multiple components. Because some of these components are also characterized by the ability to retain charge or capacitance, the term impedance is preferred. At the time of lead implantation, it is this complicated series of resistance and capacitance factors that are measured and are referred to as system impedance. For a pacing circuit, the system impedance has five basic components a low, purely resistive conductor impedance, a high cathode electrode impedance, complex polarization effects at the electrode-tissue interface, a low tissue impedance, and the anode electrode impedance (Fig. 1.3). 

Figure 11.13 illustrates a basic equivalent circuit to represent a general electrochemical reaction. Rs represents the electric resistance, which consists of the ionic, electronic, and contact resistances. Since the electronic resistance is typically much lower than the ionic resistances for a typical fuel cell MEA, the contribution of the electronic resistance to Rs is often negligible. Cj is the double-layer capacitance associated with the electrode-electrolyte interfaees. Since a fuel cell electrode is three-dimensional, the interfaces include not only Arose between Are surfaces of the electrodes and the membrane but also those between the catalysts and the ionomer within the electrodes. Ret is the resistanee associated with the charge transfer process and is called charge transfer resistanee. Z is called the Warburg impedance it deseribes the resistance arising from the mass transport processes. 

Electrical installation circuits usually carry in excess of 1A and often carry hundreds of amperes. Electronic circuits operate in the milliampere or even microampere range. The test instruments used on electronic circuits must have a high impedance so that they do not damage the circuit when connected to take readings. All instruments cause some disturbance when connected into a circuit because they consume some power in order to provide the torque required to move the pointer. In power applications these small disturbances seldom give rise to obvious emors, but in electronic circuits a small disturbance can completely invalidate any readings taken. We must, therefore, choose our electronic test equipment with great care, as described in Chapter 4 of Basic Electrical Installation Work 8th Edition and shown here at Fig. 4.16. 

Section 3.2 of Chapter 3 of the lET Electrical Installation Design Guide tells us that the basic design intent is to use standard final circuits wherever possible to avoid repeated design. Provided that earth fault loop impedances are below 0.35 ohm for TN-C-S supplies and 0.8 ohm for TN-S supplies the standard circuits can be used as the basis of all final circuits. 

---