Frequency response analyser methods

The entry into the measurement scene of efficient, commercial frequency response analysers, combined with digital signal processing capability, 

13 Block diagram, showing frequency response analyser method of measurement. 

The integration over many cycles of the generator is highly effective in averaging out random noise from the input signal. Also, only the response at the fundamental frequency is detected, since terms like cos (mot+ntp) sin tot with n = 2, 3,4. .. average to zero over a complete cycle harmonics are totally 

14 Circuit for connecting sample to a frequency response analyser. 

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In passive methods, the quartz crystal is perturbed with a sinusoidal high frequency ac voltage in a few kHz frequency range around resonance. The most commonly used instrument is the Frequency Response Analyser (FRA) at I-lOMHz. Several commercial instruments can measure automatically a range of frequencies and evaluate the BVD circuit parameters. 

Another passive method is the transference function method (TFM) introduced by Muramatsu [6]. The method consists of an oscillator that drives a crystal through a known measuring impedance and a radiofrequency voltmeter which measures the transference modulus of the system. Muramatsu [6] neglected the effect of the parasitic capacitance and his expression for the quartz impedance resulted in a nonlinear relationship between the measured resistance R with the ac voltage divider and the value of R measured by an impedance analyser. Calvo and Etchenique [74] improved the method and introduced an analytical expression to fit the entire transfer function around resonance in order to obtain the same values of R, L and C as measured by a frequency response analyser. 

Abstract Theoretical, experimental principles and the applications of the frequency response (FR) method for determining the diffusivities in microporous and bidispersed porous solid materials have been reviewed. Diffusivities of hydrocarbons and some other sorbates in microporous crystals and related pellets measured using the FR technique are presented, and the FR data are analysed to demonstrate the identification of the FR spectra. These results display the ability of the FR method to discriminate multi-kinetic mechanisms, including a surface resistance or surface barrier occurring simultaneously in the systems, which are difficult to be determined using other microscopic or macroscopic methods. The FR measurements also showed that the diffusivity of a system depends significantly on the subtle differences in molecular shape and size of sorbates in various... 

Kochenburger, R. J. Trans. AIEE 69 (1950) 270. A frequency response method for analysing and synthesising contactor servomechanisms. 

The consideration of general missile effects on the barrier should include the possible deformation of the structure by local missile effects. If there is no major local deformation of the structure by penetration, then methods of energy balance and momentum balance can be used to predict the deflections or stresses in principal members for the purpose of determining whether the barrier can contain the missile and continue to perform its design function. If, however, local missile effects are severe, as they often are, an appUed force-response time history should be developed and the structural response should be analysed as for an impulse load. The dynamic loads induced by missile impacts should be considered with due attention to the frequency response of the target structure. This is particularly important when the response of the barrier may interfere with the operability of equipment either mounted directly on the barrier or installed in the vicinity of the barrier. 

There are also a number of more sophisticated non-destructive techniques (NDT) which measure the frequency response of the bonded component part and can thus identify the presence (or absence) of adhesive in the joint. These NDT methods use ultrasonic testing, whereby high-frequency, highly directional sound waves analyse the adherends and find hidden internal flaws [2]. 

Becanse there are many factors involved in the dynamic mechanical compression of polyolefin foams, the Taguchi method was employed in a Perkin Elmer DM A7 dynamic mechanical analyser to establish a method to improve the measurement process. The signal-to-noise ratio was measured to determine how the variability could be improved. Control and noise factors were evaluated and levels chosen, with details being tabulated. Appendix A describes some of the factors. Tests were conducted on two closed cell foams. NA2006 foam is 48 kg/cu m LDPE and NEE3306 foam is 32 kg/cu m EVA. Different factors were shown to influence results for E and tan delta but an optimum combination is proposed for the simultaneous measurement of both properties. The results were less variable as frequency was increased. Small differences in the dynamic response of different materials should be measurable because of the low variability in the experimental results. 18 refs. 

Of importance for any experimental technique which is to be used to fit some complex reaction model is the way in which experimental errors influence the result [93]. The error structure for the EHD method utilising the RDE has been analysed in detail by Orazem et al. [94]. These authors showed that information could reliably and accurately be extracted even at high modulation frequencies (up to 20 Hz). In principle the determination of Sc should only require data at low modulation frequency. They demonstrated that extraction of accurate values for Sc required data which had been recorded over a relatively wide frequency range and had been weighted according to a reliable model for the errors. They also showed that the EHD (7 - Cl) response could be fitted empirically to the form ... 

As the readers may see, quartz crystal resonator (QCR) sensors are out of the content of this chapter because their fundamentals are far from spectrometric aspects. These acoustic devices, especially applied in direct contact to an aqueous liquid, are commonly known as quartz crystal microbalance (QCM) [104] and used to convert a mass ora mass accumulation on the surface of the quartz crystal or, almost equivalent, the thickness or a thickness increase of a foreign layer on the crystal surface, into a frequency shift — a decrease in the ultrasonic frequency — then converted into an electrical signal. This unspecific response can be made selective, even specific, in the case of QCM immunosensors [105]. Despite non-gravimetric contributions have been attributed to the QCR response, such as the effect of single-film viscoelasticity [106], these contributions are also showed by a shift of the fixed US frequency applied to the resonator so, the spectrum of the system under study is never obtained and the methods developed with the help of these devices cannot be considered spectrometric. Recent studies on acoustic properties of living cells on the sub-second timescale have involved both a QCM and an impedance analyser thus susceptance and conductance spectra are obtained by the latter [107]. 

The specific conductance of a water sample provides a simple method to determine the total dissolved ionic solids present in the sample. It is also an inexpensive technique, which lends itself to continuous monitoring of a river or waste stream for the total ion content (Fig. 4.1), and can be easily used to check the accuracy of analyses conducted for specific ions. Specific conductance is measured via a pair of carefully spaced platinum electrodes, which are placed either directly in the stream to be measured or in a sample withdrawn from it [22]. The water temperature should be 25 °C, or the result corrected to this temperature. Voltages in the 12 to 14 range, and frequencies of 60 to 1000 Hz AC are used, plus a Wheatstone bridge circuit to obtain a conductivity reading in xmho/cm or xS/cm (microsiemen/cm). The response obtained is linear with the total ion content over a wide range of concentrations (Fig. 4.1). Examples of the conductance ranges and seasonal variation of some typical Canadian rivers are... 

Conventional kinetics is largely concerned with the description of dynamic processes in the time domain, and in consequence few conceptual problems are encountered in understanding time resolved experiments. By contrast, frequency resolved measurements often pose more of a challenge to understanding, in spite of the obvious correspondence between the time and frequency domains. This conceptual difficulty may explain why the only frequency resolved method to achieve universal acceptance in electrochemistry is electrochemical impedance spectroscopy (EIS) [27-29], which analyses the response of electrochemical systems to periodic (sinusoidal) perturbations of voltage or current. It is clear that EIS is a very powerful method, and there... 

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