Electrical circuits responses

Combustible gas detection systems are frequently used in areas of poor ventilation. By the early detection of combustible gas releases before ignitible concentration levels occur, corrective procedures such as shutting down equipment, deactivating electrical circuits and activating ventilation fans can be implemented prior to fire or explosion. Combustible gas detectors are also used to substantiate adequate ventilation. Most combustible gas detection systems, although responsive to a wide range of combustible gases and vapors, are normally calibrated specifically to indicate concentrations of methane since most natural gas is comprised primarily of methane. 

Inductance (L) is the property of an electric circuit that produces an emf in the circuit in response to a change in the rate of current, i.e.. 

Eigenstates of a crystal, 725 Eigenvalues of quantum mechanical angular momentum, 396 Electrical filter response, 180 Electrical oscillatory circuit, 380 Electric charge operator, total, 542 Electrodynamics, quantum (see Quantum electrodynamics) Electromagnetic field, quantization of, 486, 560... 

IZI=J(Z )2+(Z ), and phase angle shift,, vs. f). The electrochemical system is then simulated with an electrical circuit that gives the same impedance response. Ideally this electrical circuit is composed of linear passive elements, e.g. resistors and capacitors, each of which represents individual physicochemical steps in the electrochemical reaction. ... 

This impedance response, in general, is similar to that elicited from an Armstrong electrical circuit, shown in Figure 3, which we represent by Rfl+Cd/(Rt+Ca/Ra). Rfl is identified with the ohmic resistance of the solution, leads, etc. Cj with the double-layer capacitance of the solution/metal interface Rfc with its resistance to charge transfer and Ca and Ra with the capacitance and resistance... 

Equivalent Electrical Circuit, In spite of the complex nature of the inhibition process, the inhibited systems actually display simple impedance responses. 

With analogy to electric circuits, a transfer function of the antenna can be calculated and the response of the antenna to an incoming wave obtained. The output signal is usually expressed as antenna cross-section. It is defined as the ratio between the total energy absorbed by the antenna and the incident spectral density function of the incident wave. In the case of Nautilus antenna (2300 kg, 3 x 0.6 m) the cross-section is of the order of 10 25m2 Hz. 

Fabrication of the prototype is an important step in product development. It demonstrates that the various components can indeed be physically integrated to form the final product with the desired functionalities. Consider a UV sensor. While its functionality depends on the physical response of a certain nanomaterial in the presence of UV light, an electric circuit and a display system are required for a functional consumer product. The availability of a prototype is essential in test marketing, safety tests, reliability tests and so on. However, the development of consumer-oriented products often involves a considerable amount of trial-and-error, which can lead to costly delays in product launching [10]. 

Further information on this subject can be obtained by frequency response analysis and this technique has proved to be very valuable for studying the kinetics of polymer electrodes. Initially, it has been shown that the overall impedance response of polymer electrodes generally resembles that of intercalation electrodes, such as TiS2 and WO3 (Ho, Raistrick and Huggins, 1980 Naoi, Ueyama, Osaka and Smyrl, 1990). On the other hand this was to be expected since polymer and intercalation electrodes both undergo somewhat similar electrochemical redox reactions, which include the diffusion of ions in the bulk of the host structures. One aspect of this conclusion is that the impedance response of polymer electrodes may be interpreted on the basis of electrical circuits which are representative of the intercalation electrodes, such as the Randles circuit illustrated in Fig. 9.13. The figure also illustrates the idealised response of this circuit in the complex impedance jZ"-Z ) plane. 

To summarize there are two learning paradigms in the context of a reflex action controlled by a single ganglion in an experimental animal in which electrical measurements of nerve action are relatively easy. This experimental system permitted Kandel to map the neural circuit responsible for the gill-withdrawal reflex. The neural... 

Frequency as an experimental variable offers additional design flexibility. This approach has several advantages. The most important one is the lack of polarization of the contacts. The second one is the fact that equivalent electrical circuit analysis can be used that aids in elucidation of the transduction mechanisms. Perhaps the most important distinguishing feature of this class of conductometric sensors is the fact that their impedance is measured in the direction normal to their surface. In fact, there may be no requirement on their DC conductivity and their response can be obtained from their capacitive behavior. In the following section, we examine so-called impedance sensors (or impedimetric sensors see Fig. 8.1b). 

The form of the frequency response of the electrical circuit, shown in Fig. 6.4, has the following characteristic frequencies ... 

Rather than continue so formally, consider dielectric susceptibilities in terms of illustrative models. Conceptually the simplest picture of a dielectric response is that in an electric circuit. Think about a capacitor as a sandwich of interesting material between two parallel conducting plates (see Fig. L2.22). 

Since the unloaded QCM is an electromechanical transducer, it can be described by the Butterworth-Van Dyke (BVD) equivalent electrical circuit represented in Fig. 12.3 (box) which is formed by a series RLC circuit in parallel with a static capacitance C0. The electrical equivalence to the mechanical model (mass, elastic response and friction losses of the quartz crystal) are represented by the inductance L, the capacitance C and the resistance, R connected in series. The static capacitance in parallel with the series motional RLC arm represents the electrical capacitance of the parallel plate capacitor formed by both metal electrodes that sandwich the thin quartz crystal plus the stray capacitance due to the connectors. However, it is not related with the piezoelectric effect but it influences the QCM resonant frequency. 

The advantage of network analysers is the possibility of impedance measurement near resonance with evaluation of the parameters R, L, C and C0 and test of the equivalent electrical circuit. However frequency response and network analysers are relatively slow with 1-10 s per measurement in typical experiments. A new generation of faster instruments has come to the market like the HP E5100 Network Analyzer with 40 (is per point in the impedance spectrum which allows us to obtain the impedance of the system in less than 10 ms. 

EIS data analysis is commonly carried out by fitting it to an equivalent electric circuit model. An equivalent circuit model is a combination of resistances, capacitances, and/or inductances, as well as a few specialized electrochemical elements (such as Warburg diffusion elements and constant phase elements), which produces the same response as the electrochemical system does when the same excitation signal is imposed. Equivalent circuit models can be partially or completely empirical. In the model, each circuit component comes from a physical process in the electrochemical cell and has a characteristic impedance behaviour. The shape of the model s impedance spectrum is controlled by the style of electrical elements in the model and the interconnections between them (series or parallel combinations). The size of each feature in the spectrum is controlled by the circuit elements parameters. 

Any electrochemical interface (or cell) can be described in terms of an electric circuit, which is a combination of resistances, capacitances, and complex impedances (and inductances, in the case of very high frequencies). If such an electric circuit produces the same response as the electrochemical interface (or cell) does when the same excitation signal is imposed, it is called the equivalent electric circuit of the electrochemical interface (or cell). The equivalent circuit should be as simple as possible to represent the system targeted. 

The a.c. impedance technique [33,34] is used to study the response of the specimen electrode to perturbations in potential. Electrochemical processes occur at finite rates and may thus be out of phase with the oscillating voltage. The frequency response of the electrode may then be represented by an equivalent electrical circuit consisting of capacitances, resistances, and inductors arranged in series and parallel. A simplified circuit is shown in Fig. 16 together with a Nyquist plot which expresses the impedance of the system as a vector quantity. The pattern of such plots indicates the type and magnitude of the components in the equivalent electrical network [35]. 

Fig. 16. Nyquist plot of the impedance response of an electrode. The equivalent electrical circuit is shown above the plot. Ra is the solution resistance, Cp the electrode/solution interface capacitance, and Rp the electrode/solution interface polarization resistance.

Fig. 5.18 Electrical circuits for DC step-response methods (a) measure- ment of a current transient, (b) measurement of the time integral of current, with compensation for the large instantaneous component of the response.

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