High-frequency measurements

Impedance Some of the errors arising from the use of linear polarisation resistance led to interest and development in a.c. systems.An early development used a fixed a.c. frequency and a commercial instrument was produced in the UK. Inaccuracies still occurred, however, and were due to the electrode impedance which is fequency dependent. Electrode reactions have a capacitance component, in addition to resistance, resulting in a requirement to measure the impedance. However, the total impedance comprises values for the reaction, solution, diffusion and capacitance. Measurements at different frequency are more reliable, particularly where high solution resistances occur. Simplifications for industrial monitoring have been developed consisting of two measurements, i.e. at a high (10 kHz) and low frequency (0-1 Hz). The high-frequency measurement can identify the... 

For high-frequency measurements, normal photomultipliers are too slow, and microchannel plate photomultipliers are required. However, internal crosscorrelation is not possible with the latter and an external mixing circuit must be used. 

The two main techniques for measuring electrode losses are current interrupt and impedance spectroscopy. When applied between cathode and anode, these techniques allow one to separate the electrode losses from the electrolyte losses due to the fact that most of the electrode losses are time dependent, while the electrolyte loss is purely ohmic. The instantaneous change in cell potential when the load is removed, measured using current interrupt, can therefore be associated with the electrolyte. Alternatively, the electrolyte resistance is essentially equal to the impedance at high frequency, measured in impedance spectroscopy. Because current-interrupt is simply the pulse analogue to impedance spectroscopy, the two techniques, in theory, provide exactly the same information. However, because it is difficult to make a perfect step change in the load, we have found impedance spectroscopy much easier to use and interpret. 

Experimental methods are applicable for a wide range of frequencies. High-frequency measurements employ commercially available dielectric constant meters, Q-meters, and so on the impedance bridge method is widely employed at low frequencies. The levels of the frequencies applied experimentally are very important for data interpretation and comparison. 

Unfortunately, with most high-frequency measurement methods it is not possible to use a guarded electrode system and, in addition, lead inductances become appreciable at high frequencies. To meet the high-frequency requirement... 

It should be remembered that the curves shown in Fig. 13L are all simulated and therefore "ideal" in the sense that they follow exactly the equations derived for the given equivalent circuit. In practice, the points are always scattered as a result of experimental error. Also, the frequency range over which reliable data can be collected does not necessarily correspond to the time constant which one wishes to measure. For the case shown in Fig. 13L(a) the semicircle can be constructed from measurements in the range of 1 > o) > 20. In Fig. 13N(b) one would have to use data in the range of about 10 > to 200 to evaluate the numerical values of the circuit elements. From the Bode magnitude plots, can be evaluated from high-frequency measurements (to 100), while R can be obtained from low frequency data (to < 1). The capacitance can be obtained approximately as = l/co Z at the inflection point (which coincides with the maximum on the Bode angle plot), but this would be correct only if (p - 90 that is, if the... 

Hales, B., van Geen, A., and Takahashi, T. (2004). High-frequency measurement of seawater chemistry Flow injection analysis of macronutrients. Limnol. Oceanogr. Methods 2, 91—101. 

Numerical solutions have been presented for the impedance response of semiconducting systems that accoimt for the coupled influence of transport and kinetic phenomena, see, e.g., Bonham and Orazem. Simplified electrical-circuit analogues have been developed to account for deep-level electronic states, and a graphical method has been used to facilitate interpretation of high-frequency measurements of capacitance. The simplified approaches are described in the following sections. 

Double integration of the area under the first derivative reveals that 48 =i= 2% of the chemically determined copper (IS) is EPR detectable in frozen solution. Table I summarizes the experimental g and A values measured from the recorded spectra. A best fit of the EPR spectrum of oxidized ascorbate oxidase is obtained by computer simulation, using the high-frequency measurements at 35 GHz (28). The ratio of type 1 to type 2 copper is estimated by double integration of the first low-field line, which arises from the type 2 copper, at approximately 0.270 T (IS). Roughly 25% of the EPR-detectable copper in ascorbate oxidase is type 2, whereas 75% is blue type 1 copper. This ratio is confirmed by computer analysis (IS) and agrees with earlier results (28) (Figure 4). 

A laser system that delivers pulses in the picosecond range with a repetition rate of a few MHz can be considered as an intrinsically modulated source. The harmonic content of the pulse train - which depends on the width of the pulses - extends to several gigahertz. The limitation is due to the detector. For high frequency measurements, it is absolutely necessary to use microchannel plate photomultipliers (that have a much faster response than usual photomultipliers). The highest available frequencies are then about 2 GHz. As for pulse fluorometry, Ti sapphire lasers are most suitable for phase fluorometry, and decay times as short as 10-20 ps can be measured. 

Both extremes of frequency pose problems low-frequency measurements cannot be made on coatings in rational terms and high-frequency measurements tend to obscure the differences between liquid and solid states of matter. 

Electrochemical polarization curves, high frequency measurements... 

The study of the temperature effect is not easy to carry out and even if numerous works have been published on static conductivity behaviour, only a few with evolution of microwave properties with temperature. All the high-frequency measurements reported have been performed using cavity perturbation methods (6.5 GHz for polyaniline and polyorthotoluidine [50,51b] and 9.9 GHz for polyacetylene [33]). In parallel, low-frequency (from d.c. to 1 MHz) measurements have been performed at low temperature for a long time [4a]. 

This chapter has focused on the use of conventional X-band EPR spectrometers to measure EPR spectra of immobilized paramagnetic centers in proteins. However, a variety of other EPR methods, such as pulsed, double-resonance, and high-frequency measurements, are being increasingly applied to study biological systems (see V. J. EteRose and B. M. Hoffman, this volume [23]). These modem methods, in conjunction with conventional EPR measurement, provide a powerful array of techniques... 

Two basic contributions are expected to the variation of dielectric properties of a hydrated material with respect to those of a dry one that of the polar water molecules themselves and the second one due to the modification of the various polarization and relaxation mechanisms of the matrix material itself by water [37]. In the low frequency region of measurements, there is a third contribution, often ignored in works dealing with high frequency measurements, which arises from the influence of moisture on conductivity and conductivity effects. The increase of electrical conductivity of the sample is the major effect present in wet samples dielectric response is often masked by conductivity, and it superposes the dielectric processes in the loss spectra and demands a conductivity correction of the dielectric loss spectra [9]. This dc conductivity strongly affects the modifled loss factor, e". In this case, it can be expressed as shown in the following equation ... 

Retaining the second term of the expansion for inspection shows that at low temperature and high frequency measurements, it can have a significant influence on the calculated absorption coefficient ... 

A comparison of the TDR and the FR methods for fault detection/measurement suggests that high-frequency measurement of transmitted/reflected power (Sj/Sjj) and phase using the FR method is... 

Alternatively, as seen for the low-frequency range, high-frequency measurements can be performed in the time domain (time domain reflectometry methods [19]) that can be extended to 20 GHz, but with less accuracyrelative to network analysis [14]. 

Figure 6 (a) Sample cell for high-frequency measurements of liquids (b) sample cell for low-frequency measurements of liquids, solids, and powders. (From Ref 38. With permission from American Institute of Physics.)... 

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