Amplifiers, Bridges, Analyzers

Circuitry for impedance measurements has changed dramatically since the first measurements were performed on biological tissue. The development of digital electronics and the incorporation of computer power in almost all instruments have had an important impact on the possibilities of studying the passive electrical behavior of biomaterials over a wide frequency range, and with a speed that was not feasible only a few years ago. Only a brief summary of some of the techniques will be given in this section. 

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This operation determines the values of R and C that, in series, behave as the cell does at the measurement frequency. The impedance is measured as a function of the frequency of the ac source. The technique where the cell or electrode impedance is plotted V5. frequency is called electrochemical impedance spectroscopy (EIS). In modem practice, the impedance is usually measured with lock-in amplifiers or frequency-response analyzers, which are faster and more convenient than impedance bridges. Such approaches are introduced in Section 10.8. The job of theory is to interpret the equivalent resistance and capacitance values in terms of interfacial phenomena. The mean potential of the working electrode (the dc potential ) is simply the equilibrium potential determined by the ratio of oxidized and reduced forms of the couple. Measurements can be made at other potentials by preparing additional solutions with different concentration ratios. The faradaic impedance method, including EIS, is capable of high precision and is frequently used for the evaluation of heterogeneous charge-transfer parameters and for studies of double-layer structure. 

FIGURE 7.51 The Class A transistor amplifier is modeled as a resistive load to its driver whereas the output impedance seen at the output port is equal to the standard load resistance. The input and output impedances may be measured from the outside looking in with a network analyzer or impedance bridge. 

The AC impedance technique coupled to the complex plane method of analysis is a powerful tool to determine a variety of electrochemical parameters. To make the measurements, instrumentation is somewhat more complex than with other techniques. It requires a Wheatstone bridge arrangement with series capacitance and resistance in the comparison arm, a tuned amplifier/detector, and an oscillator with an isolation transformer. A Wagner ground is required to maintain bridge sensitivity, and a suitably large inductance should be incorporated in the electrode polarization circuit to prevent interference from the low impedance of this ancillary circuitry. Sophisticated measurement instruments or frequency response analyzers with frequency sweep and computer interface are currently available such as the Solartron frequency response analyzers. Data obtained can be analyzed or fitted into proper equivalent circuit using appropriate software. 

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