Commercial frequency response analyzers

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... 

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. 

Response times of 15-40 ms seem to be currently in use. Fry et al. (1957) analyzed the dynamic characteristics of three types of commercially available, differential-pressure pneumotachographs which employed concentric cylinders, screen mesh, and parallel plates for the air resistors. Using a high-quality, differential-pressure transducer with each, they measured total flow resistance ranging from 5 to 15 cm HjO. Frequency response curves taken on one model showed fairly uniform response to 40 Hz the second model showed a slight increase in response at 50 Hz, and the third exhibited a slight drop in response at this frequency. 

A few solutions exist for 3-D PZT bodies. Most well-known solutions for finite PZT plates were obtained from approximated two-dimensional (2-D) equations of extended Mindlin s solutions (Herrmann 1974). But, these solutions are not directly applicable to the analysis of AE sensors commercially available. In order to clarify the frequency response of AE sensor (function W(f) in eq. 3.5) and to optimize the design of PZT elements, resonance characteristics of PZT element were analyzed by using the finite element method (FEM) (Ohtsu Ono 1983). 

In virtually all types of experiments in which a response is analyzed as a function of frequency (e.g., a spectrum), transform techniques can significantly improve data acquisition and/or data reduction. Research-level nuclear magnetic resonance and infra-red spectra are already obtained almost exclusively by Fourier transform methods, because Fourier transform NMR and IR spectrometers have been commercially available since the late 1960 s. Similar transform techniques are equally valuable (but less well-known) for a wide range of other chemical applications for which commercial instruments are only now becoming available for example, the first commercial Fourier transform mass spectrometer was introduced this year (1981) by Nicolet Instrument Corporation. The purpose of this volume is to acquaint practicing chemists with the basis, advantages, and applications of Fourier, Hadamard, and Hilbert transforms in chemistry. For almost all chapters, the author is the investigator who was the first to apply such methods in that field. 

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