Frequency response analyzers

An EG G PARC 273 Potentiostat/Galvanostat was used in both the electrolysis and the CV experiments, coupled with an HP 7044B X/Y recorder. A Solartron 1255 HF Frequency Response Analyzer and a Solartron 1286 Electrochemical Interface were employed for the a.c. impedance measurements, using frequencies from 0.1 to 65 kHz and a 10 mV a.c. amplitude (effective) at either the open circuit potential (OCP) or at various applied potentials. As the RE can introduce a time delay at high frequencies, observed as a phase shift owing to its resistance and capacitance characteristics, an additional Pt wire electrode was placed in the cell and was connected via a 6.8 pF capacitor to the RE lead [32-34]. 

As an example, we present below a typical experimental arrangement suited for EHD measurements in a wide frequency range, with a frequency response analyzer as for any impedance measurement. 

Figure 3.19 Intensity-modulated photocurrent spectroscopy, showing (a) the layout of a typical spectrometer, and (b) the response obtained AOM, acousto-optic modulator RE, reference electrode WE, working electrode CE, counter electrode FRA, frequency response analyzer...

Impedance measurements performed with PAR M398 software in conjunction with a potentiostat and a lock-in amplifier or frequency response analyzer are obtained using one or both of two techniques, depending on the frequency range... 

The impedance can be measured using various instalments and techniques, ranging from a simple oscilloscope display to a fast Fourier transform (FFT) analyzer. The most common instrument used is a frequency response analyzer (FRA), e.g., the Solartron FRA. A potentiostat or a load bank combined with a frequency response analyzer can perform the EIS measurements. The electrical connection between the FRA, the potentiostat (or the load bank), and the fuel cell is illustrated in Figure 3.19. 

The different behaviours of gas diffusion electrodes with different catalyst loadings were studied by Paganin et al. [4], EIS measurements of 0.5 and 1 cm2 single cells were conducted with H2/02 (air) as fuel/oxidant. In their measurements, a Solartron 1250 frequency response analyzer and a 1286 electrochemical interface were employed. The amplitude of the AC signal was 10 mV and the frequency range was typically from 10 mHz to 10 kHz. Representative EIS results are shown in Figures 6.1 and 6.2. 

The LF measurements (a) are provided by means of impedance/admittance analyzers or automatic bridges. Another possibility is to use a frequency response analyzer. In lumped-impedance measurements for a capacitor, filled with a sample, the complex dielectric permittivity is defined as [3]... 

Impedance spectroscopy (IS) is a measurement of the conductive and dielectric properties of electroactive systems over a wide range of frequencies. Its popularity and applicability has increased dramatically over the past 25 years with the advent of fast-response potentiostats and frequency response analyzers. Impedance spectroscopy has been applied extensively in electrochemistry, especially in battery and sensor research, and it has been used to study active transport in biological membranes. Skin impedance has also been investigated with IS, but many of these studies attempted to correlate impedance with hydration and provided no insight into the mechanism of charge transport. More recent studies have used IS to elucidate the pathways of ion transport through skin, with special emphasis on understanding the mechanism... 

An impedance measurement can be made either by applying an electrical potential and monitoring the current response or, conversely, by passing current and monitoring the potential response. Several decades of frequencies can be scanned rapidly and accurately using a frequency response analyzer [4]. An alternative approach applies multiple frequencies simultaneously (white noise) and deconvolutes the response with a lock-in amplifier. The use of an... 

Consider, for example, a test sample of material with a well-defined geometry as shown in Fig. 2. Reversible electrodes are attached to opposite planar faces of the test article, and a sinusoidal electrical potential (V ) is applied via a waveform generator. The current response is monitored with a frequency response analyzer (FRA), which converts the signal to the frequency domain. The amplitude (A) of the input wave is adjusted to the range in which the system responds linearly, about 10 mV. Thus, the perturbation can be described by the following equation ... 

The best method to measure the double-layer capacitance is to use a phase-sensitive voltmeter. This instrument is sometimes incorporated into a frequency response analyzer, designed to make electrochemical impedance spectroscopy measurements, but it can also be used independently. In Part Two we devote a full section to the operation of such instruments and the analysis of results obtained by them. Here we shall limit the discussion to the measurement of capacitance. 

The frequency response analyzer may be the best instrument for double-layer-capacitance measurements, but it is also the most expensive one. Other methods are available, which are faster and cheaper, but less accurate. For example, the charge on the double layer is related to the potential as ... 

The impedance spectroscopy method in electrochemistry has been greatly developed in recent years by the availability of state-of-the-art frequency-response analyzers capable of measuring ac impedance over wide frequency... 

The third approach is to use experimental methods to assess the error structure. Independent identification of error structure is the preferred approach, but even minor nonstationarity between repeated measurements introduces a significant bias error in the estimation of the stocheistic variance. Dygas emd Breiter report on the use of intermediate results from a frequency-response analyzer to estimate the variance of real and imaginary components of the impedance. Their approach allows assessment of the variance of the stochastic component without the need for replicate experiments. The drawback is that their approach cannot be used to assess bias errors and is specific to a particular commercial impedance instrumentation. Van Gheem et have proposed a structured multi-sine... 

Experiments were carried out under potentiostatic conditions using an 1172 Solartron Frequency Response Analyzer and 1186 Solartron Electrochemical Interface. A small (input) amplitude (10 mV) sine wave (P sin wt) was applied to the system under study. The response of the system to the applied perturbation was monitored as a sine wave current [Y sin (wt + 6 )] and a sine wave potential [X sin (tot + 0 )]. These were transformed into the complex form A + i B and A + i B, respectively. The real and imaginary part of th impedance were computed using the relation t=(A +iB)/(A +iB)... 

The DC potential of the working electrode was controlled either by means of the potentiostat or the Frequency Response Analyzer. A 1000 ohm standard resistor was used to measure the DC current. Ten readings were averaged at each frequency. The frequency range used was from 0.1 Hz to 9999 Hz. Ten readings were recorded per decade of frequency with a delay time of 10 sec between readings taken at each frequency. 

Frequency response analyzers are instruments that determine the frequency response of a measured system. Their functioning is different from that of lock-in amplifiers. They are based on the correlation of the studied signal with the reference." " The measured signal [Eq. (29)], is multiplied by the sine and cosine of the reference signal of the same frequency and then integrated during one or more wave periods ... 

ACIS measurements were performed at frequencies between 1 mHz and 1 kHz using a Solartron Model 1250 Frequency Response Analyzer. Output from the comb specimens was amplified with a Keithley Model 427 Current-to-Voltage Converter before waveform analysis. Reference electrodes were not used owing to the geometry of the encapsulated test specimens. The data reported herein were obtained with a 0.1 V rms amplitude sinusoidal excitation waveform. In one experiment, DC bias was superimposed on this waveform. 

This work was supported by Seed Funds from the Stanford Center for Integrated Systems. The authors thank Ford Motor Company for use of the fluorescence microscope and imaging system, and Professor C.W. Bates, Stanford Dept, of Materials Science and Engineering, for use of the Solartron frequency response analyzer. 

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. 

Impedance measurements can be made in either the frequency domain with a frequency response analyzer (FRA) or in the time domain using Fourier transformation with a spectrum analyzer. Commercial instrumentation and software is available for these measurements and the analysis of the data. 

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