Electrical filtering

Harmonic Analysis of Random Processes.—The response Y(t) of a linear, time-invariant electrical filter to an input X(t) can be expressed in the familiar form 66... 

Eigenstates of a crystal, 725 Eigenvalues of quantum mechanical angular momentum, 396 Electrical filter response, 180 Electrical oscillatory circuit, 380 Electric charge operator, total, 542 Electrodynamics, quantum (see Quantum electrodynamics) Electromagnetic field, quantization of, 486, 560... 

M5. Mierdel, G., Migration of dust particles in electric filters,Z. Tech.Physik 13,564 (1932). 

Whatever its source, the electrical signal usually contains noise components having frequencies far higher than those found in the spectrum itself. Electrical filtering is then called for to remove these high-frequency components. 

The design of optimum electrical filters is a highly developed discipline that we shall not address here. It is worthwhile, however, to discuss briefly the simple single-stage RC filter that is widely used. When all factors are... 

We see that the amplitude-transfer characteristic is given by 27r[l + (coRC)2] -1/2. The power-transfer characteristic is given by the square of this quantity. It has the form of a Cauchy function and attenuates high frequencies. Brodersen (1953) and Stewart (1967) have analyzed in detail the performance of other linear electrical filters applied in spectroscopy. 

The spectrum distortion introduced by all such filters limits the spectrometer s scanning rate. The subtleties of the scan rate s dependence on electrical filtering and slit width for constant signal-to-noise ratio are explored by Blass and Halsey (1981). 

In concluding this section, we point out that the effect of any electrical filter composed of purely linear elements, whether they be passive like resistors, capacitors, and inductors or active like linear amplifiers, can be represented as a convolution. The various other spreading phenomena that are described by convolution in the same domain may therefore be lumped together with the electrical contribution and comprehensively called the spectrometer response function. Even inherent line broadening may be included, provided that the convolution does not appear in an exponent, as in the case of absorption spectra. 

The resolution of overlapping spectral peaks depends on their separations, intensities, and widths. Whereas separation and intensity are predominantly functions of the sample, peak width is strongly influenced by the instrument s design. The observed line is a convolution of the natural line, a function characteristic of inelastically scattered electrons that produces a skewed base line, and the instrument function. The instrument function is, in turn, the convolution of the x-ray excitation line shape, the broadening inherent in the electron energy analyzer, and the effect of electrical filtering. This description is summarized in Table I. 

Figure 6. A diagram of the chopper/filter wheel used in the fast response, ln-sltu CO2 sensor. Combining both functions on a single wheel provides the precise timing necessary to minimize electrical filter interference and significantly reduces instrument weight and volume. Coating sample and reference...

We notice that the elements in series in the mechanical model are transformed in parallel in the electrical analogy. The converse is true for the Kelvin-Voigt model. The electrical analog of a ladder model is thus an electrical filter. 

A radiation detector is a device in which the photons absorbed are transformed ultimately into electrical energy. The efficiency with which the photons are transformed into electrical power is described by the responsivity of the detector, and it is expressed as the voltage generated by one watt of incident radiant power. The average time required for the incident power to be transformed and dissipated by the detector characterizes the response time, or time constant of the detector. To be specific, the electrical response of a detector to a radiation beam time-modulated at frequency / is similar to the frequency response R(/) of a low-pass electrical filter with time constant r ... 

Lubricants have a nonlinear viscosity coefficient against temperature. At very low or very high temperature this nonlinearity can create significant measurement failures. A careful analysis will show this effect within the transmission chain. Sticking is the worst case. It can happen that frozen water makes a short cut in torque sensors. In most cases damping factors are based on the electrical filter circuits (Fig. 7.12.13). 

Besides accidential or suicidal ingestion, there is occupational exposure of some groups of employees in the production and processing of heavy metal ores, manufacturing and use of thallium, its alloys and compounds, and in certain cement factories from roasting pyrites and ingestion of dust from the electric filter (Schaller et al., 1980). Whereas the excretion level in urine from persons without known occupational contact with thallium was found to be lower than 1.1 mg Tl/kg creatinine, it significantly increases upon exposure. No influence of the age of the person examined and the duration of employment, as well as no influence of alcohol and nicotine consumption was noted. 

Fig. 13.19 Schematic sketch of an electric filter 1 - body 2 to 4 -filtering section 5 to 8 - mesh electrodes 9 - drainage system 10 -damper.

The behavior of emulsions is considered in Section V in connection with the process of oil dehydration. Actual problems of drop integration in emulsions are discussed. It is shown that this process occurs most effectively if the emulsion is subjected to an electric field. In this context, the behavior of conducting drops in emulsions, the interaction of drops in an electric field, and the coalescence of drops in emulsions are examined in detail. In terms of applications, processes of emulsion separation in settling tanks, electro dehydrators, and electric filters are considered. 

Humpherys, D.S. 1970. The Analysis, Design, and Synthesis of Electrical Filters. Prentice-HaU, Englewood... 

Comb filter An electrical filter circuit that passes a series of frequencies and rejects the frequencies in between, producing a frequency response similar to the teeth of a comb. 

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