Frequency response measurements functions

For the SCC of type II an example of a RTD modelled is shown in Figure 7, The model used is the dispersion model (sec Esq. 6). The values of the model parameters determined arc a Bodenstein number of 8.8 and a mean residence time of 0.6 s. It clearly shows that the model for the RTD explains the frequency response measurement up to a frequency of 2 Hz, At the frequency of 2 Hz the signal-to-noise ratio of 100 is reached. Any mixing processes which affect the transfer function above this frequency cannot be identified. 

The power spectra may be directly obtained using dynamic signal analyzers that measure signals as a function of time and perform the fast Fourier transform. The coherence function takes values betweaen 0 and 1 and characterizes statistical validity of the frequency response measurements ... 

An important difference between analysis of stability in the. v-plane and stability in the frequency domain is that, in the former, system models in the form of transfer functions need to be known. In the latter, however, either models or a set of input-output measured open-loop frequency response data from an unknown system may be employed. 

Frequency Response Analysis the response of an electrode to an imposed alternating voltage or current sign of small amplitude, measured as a function of the frequency of the perturbation. Also called Electrochemical Impedance Spectroscopy. 

The time variations of the effluent tracer concentration in response to step and pulse inputs and the frequency-response diagram all contain essentially the same information. In principle, any one can be mathematically transformed into the other two. However, since it is easier experimentally to effect a change in input tracer concentration that approximates a step change or an impulse function, and since the measurements associated with sinusoidal variations are much more time consuming and require special equipment, the latter are used much less often in simple reactor studies. Even in the first two cases, one can obtain good experimental results only if the average residence time in the system is relatively long. 

Many different techniques are available for flow measurement and for recording of respiratory functions or flow parameters in particular (e.g. [115,116]). However, not all methods are appropriate for measurement of inhalation flows, either because they have low frequency responses or they influence the shape of the inspiratory flow curve by a large volume or by the inertia of the measuring instrument (e.g. rotameters). They may also interfere with the aerosol cloud from the inhalation device during drug deposition studies. 

The van der Waals interaction depends on the dielectric properties of the materials that interact and that of the medium that separates them. ("Dielectric" designates the response of material to an electric field across it Greek Si- or Si a- means "across.") The dielectric function e can be measured experimentally by use of the reflection and transmission properties of light as functions of frequency. At low frequencies, the dielectric function e for nonconducting materials approaches a limit that is the familiar dielectric constant. The dielectric function actually has two parts, one that measures the polarization properties and the other that measures the absorption properties of the material. 

Dielectric test methods are used to measure the cure of epoxy adhesives between two conducting electrodes. This method is especially appropriate for metal-to-metal joints because the substrates themselves can be used as the electrode. The adhesive is treated as a capacitor during the test. Its response (dielectric constant, dissipation factor, etc.) over a range of electrical frequencies is measured as a function of curing time. 

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. 

In general terms, the frequency response of a device is the magnitude and phase of its output signal as a function of the fi quency of a (constant amplitude) input signal. The nature of the output signal varies from one type of device to the next, as discussed in detail in the following. The two related variations on the instrumentation that can be used to measure frequency response are discussed next as well. 

T25 to 181 C were examined by the DSA technique. Figure 2 shows the composite loss tangent response as a function of the natural logarithm of time for a cure at 147 C at several frequencies. Two tan 6 peaks are observed. At fixed temperature both peaks become smaller, shift to longer times, and exhibit Improved resolution as the frequency Is decreased. Figure 3 displays the composite loss tangent as a function of the natural logarithm of time at a fixed frequency of 3.5 Hz for cures at several temperatures. At this, the lowest frequency of measurement, the two peaks are best resolved, smallest, and occur soonest In time as the temperature is Increased. 

Ultrasound-based sensors for metal-coated fiber optic measurements based on interferometric determination of the displacement using a Michelson interferometer have also been designed. The input acoustic field can be detected by using two reference methods, namely (a) time-delay spectroscopy with a calibrated hydrophone (a hydrophone with known frequency response determining the sound pressure, the input displacement being obtained by simple algebra) and (b) the interferometric foil technique (the displacement of a metallized foil situated at the surface of the fluid measured by the interferometer used for fibre tip measurements). The frequency dependence of the transfer function compared well with the theoretical models [51]. 

We have performed optically heterodyne-detected optical Kerr effect measurement for transparent liquids with ultrashort light pulses. In addition, the depolarized low-frequency light scattering measurement has been performed by means of a double monochromator and a high-resolution Sandercock-type tandem Fabry-Perot interferometer. The frequency response functions obtained from the both data have been directly compared. They agree perfectly for a wide frequency range. This result is the first experimental evidence for the equivalence between the time- and frequency-domain measurements. 

Figure 2 The imaginary part of frequency response function, Im (Au ). obtained by the OHD-OKE (dots) and the light scattering measurements by the double monochromator (dashed line). In the insert is shown Im.R(Au ) obtained by the tandem interferomator (solid line). A small peaic appearing at 3.3 cm (shown as a symbol of ) is the ghost due to the tandem interferometer.

The potentials and currents were measured and controlled by a Solatron 1286 potentiostat, and a Solatron 1250 frequency response emalyzer was used to apply the sinusoidal perturbation and to calculate the transfer function. The impedance data analyzed in this section were taken after 12 hours of immersion and were found by the methods described in Chapter 22 to be consistent with the Kramers-Kronig relations. 

Cancer risk assessment involves a quantitative estimate of the carcinogenic activity of a carcinogen. For genotoxic carcinogens, this estimate is derived from the cancer potency of the carcinogen. Cancer potency is defined as the slope of the dose-response curve for induction of tumors, and is a function of the dose and the magnitude of response, measured as a slope. The endpoint is the cancer incidence or frequency of occurrence of cancer (tumor induction) in... 

Time-resolved fluorometry fahs into one of two categories, depending on how the fluorescence emission response is measured (1) pulse fluorometry, in which the sample is illuminated with an intense brief pulse of light and the intensity of the resulting fluorescence emission is measured as a function of time with a fast detector system, or (2) phase fluorometry, in which a continuous-wave laser illuminates the sample, and the fluorescence emission response is monitored for impulse and frequency response. ... 

Instead of the application of a low pass filter in the frequency domain itself (multiplication with 1 in the low-frequency range and above that with 0, i.e. multiplication of the frequency response with a rectangle function), one can use in the amplitude domain (i.e. for the measurement itself) the mathematically fully equivalent convolution with the Fourier transform of that rectangle function. 

There are two main sources of error in this type of measurement. The first arises from the failure of the approximation Y jcoCsd if the sample has a poor ohmic contact or the frequency is too high. If this is the case, the out-of-phase component is no longer a linear function of Csd. The error, which usually manifests itself as an unexpected frequency dependence of Csd, can be avoided by making frequency-dependent impedance measurements with a frequency response analyser (as discussed in Section 12.2.2). The other source of errors arises from the frequency response of... 

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 ... 

Typically, in dynamic oscillatory testing, a sinusoidal (oscillatory) small-amplitude stress is applied to the sample and the mechanical response measured as functions of both oscillatory frequency and, in some instances, temperature. 

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