Flat frequency response

If the observed surface is moving, the modulator/demodulator output varies in direct proportion to the peak-to-peak movement of the observed surface. Having a flat frequency response from DC to 10,000 Hz, the transducer is able to accurately follow motion at frequencies in excess uf those typically encountered. 

Photomultipliers are used as detectors in the single-channel instruments. GaAs cathode tubes give a flat frequency response over the visible spectrum to 800 nm in the near IR. Contemporary Raman spectrometers use computers for instrument control, and data collection and storage, and permit versatile displays. 

Treffer s model system consists of signal power P (in watts) falling on the input aperture of the modulator (i.e., the spectrophotometer) that modulates the input power as a function of time by a factor M(t) such that 0 < M(t) < 1. The modulation function M(t) is not the modulation of the signal due to chopping but modulation of the signal due to scanning. The modulated signal falls on a detector with responsivity R (in volts per watt) (Kruse et al., 1962 Stewart, 1970) and flat frequency response. The idealized instantaneous... 

Schroeder determined that the comb filter could be easily modified to provide a flat frequency response by mixing the input signal and the comb filter output as shown in figure 3.13. The resulting filter is called an allpass filter because its frequency response has unit magnitude for all frequencies. The z transform of the allpass filter is given by ... 

A set of ten microphones was set up in an arc that had a radial distance of iO diameters from the nozzle exit. The arc covered the polar angle, 0, range from 90 to 150 relative to the upstream jet axis. Each of the microphones had a relatively flat frequency response up to 100 kHz and was subsequently sampled at 250 kHz. The dataset for each microphone contained 409.600 samples (1.6 s). This allowed for a fast Fourier transform (FFT) of 4096 points over 100 subsets. Averaging the results for the 100 subsets reduced the random error in the calculation to within 0.1%. The resulting narrowband spectrum had a spectral resolution of 61 Hz. 

The limiting frequency shown in Table 4.2 represents the frequency at which the error in amplitude reaches 10%. It should be noted that the limiting frequencies listed in the table are considerably lower than the values sometimes claimed by pressure transducer manufacturers. Some transducer suppliers claim a flat frequency response up to 100 Hz however, the data in Table 4.2 does not substantiate that number. As mentioned before, the dynamic response of piezo pressure transducers is far better (several orders of magnitude) than membrane-type pressure transducers. 

Cottet et al. (2003) report the use of copper threads with diameter of 40 pm and insulated with a polyesterimide coating. The copper threads follow a helical path within the yam in a similar manner as the one chosen by the ancients. It is reported that the thread can be used as transmission lines, with length for 10 cm and 100 cm for frequencies of 1.2 GHz and 120 MHz, respectively. Using wires of similar dimensimis coated with polyurethane varnish, Locher and Troster (2007) report that transmissirm lines within a textile have a flat frequency response up to 2 GHz. 

The FBA principle is the basis not only of servo-accelerometers but also of broadband seismometers (BB). These instruments have a flat frequency response for ground velocity in a band from 0.01 to several tens of Hz. The feedback loop keeps the mass almost at rest relative to the ground, but the signal is integrated in the loop, and the output is taken from a point where it is proportional to ground velocity in a wide band. For more details, see the entry Principles of Broadband Seismometry. ... 

With such a detector a flat frequency response is achieved by operating below the critical frequency, coc = ( To obtain a large AT for a given AW the heat capacity of the detector element must be made as small as possible and, at the same time, must be chosen as large as possible however, M is often limited by the need to achieve a desired time constant. 

The responsivity falls off as the reciprocal of a> to obtain a flat frequency response, amplification proportional to a> has to be provided. 

Given that the ultrasonic back-wall echo from the synthesized beam and from the single element output may differ due to the coherent summing, time and frequency response of synthesized beam outputs may be achieved. Therefore, flat wall must be in the far-field or at the focus point as recommended by the standard [1]. 

The first filter in the chapter is one of the most popular. The schematic of the fourth-order Butterworth response low pass filter is shown in Fig. 3.1. The frequency response of the filter to an AC sweep is shown in Fig. 3.2. Note the flat response in the pass band and the stop band frequency of 100 kHz. 

An allpass filter has a flat magnitude response, and we might expect it to solve the problem of timbral coloration attributed to the comb filter. However, the response of an allpass filter sounds quite similar to the comb filter, tending to create a timbral coloration. This is because our ears perform a short-time frequency analysis, whereas the mathematical property of the allpass filter is defined for an infinite time integration. 

A consequence of incorporating the absorptive filters into the lossless prototype is that the frequency response envelope of the reverberator will no longer be flat. For exponentially decaying reverberation, the frequency response envelope is proportional to the reverberation time at all frequencies. We can compensate for this effect by associating a correction filter t(z) in series with the reference filter, whose squared magnitude is inversely proportional to the reverberation time [Jot, 1992b] ... 

After applying the correction filter, the frequency response envelope of the reverberator will be flat. This effectively decouples the reverberation time control from the overall gain of the reverberator. The final reverberator structure is shown in figure 3.27. Any additional equalization of the reverberant response, for instance, to match the frequency envelope of an existing room, can be effected by another filter in series with the correction filter. 

Aromatic polyimides have found extensive use in electronic packaging due to their high thermal stability, low dielectric constant, and high electrical resistivity. Polyimides have been used as passivation coatings, (1) interlayer dielectrics, (2) die attach adhesives, (3) flexible circuitry substrates, (4) and more recently as the interlevel dielectric in high speed IC interconnections. (5) High speed applications require materials with a combination of low dielectric constant, flat dielectric response versus frequency and low water absorption. 

In order to construct a magnitude and phase vs. frequency plot of the transfer function, the nondimensional time will be converted back to real time for use on the frequency axis. For the conversion to real time the following physical variables will be used po = 1350 kg/m, b = 15 p.m, and /Hf = 0.85 mPa/sec. The general frequency response is shown in Figure 64.4. The flat response from DC up to the first corner frequency establishes this system as an accelerometer. This is the range of motion frequencies encountered in normal motion environments where this transducer is expected to function. 

The shear stress sensor for turbulent flow needs to accurately capture the complete turbulent fluctuation spectrum. Therefore, the shear stress sensor should possess a large bandwidth with flat and minimum frequency-phase relationship. For direct measurement, i.e., floating point sensors, the resonant frequency of the floating element and the fluidic damping determines the usable bandwidth. For the thermal sensor, the thermal inertia of the sensor element and the frequency-dependent heat conduction to the substrate influence the usable bandwidth. It is complicated to analytically predict the frequency response of the thermal sensor. Therefore, dynamic calibration is essential to characterize the frequency response of the sensor. 

EMG noise in evoked bioelectric recordings often does not strictly meet the criteria of randomness and flat frequency spectrum since it is somewhat peaked at certain frequencies. Line-frequency interference has a single, large-frequency peak but is otherwise uncorrelat with the evoked waveform. Despite these variations from the optimum, signal averaging can still be quite useful in improving the SNR when bioelectric responses can be repetitively evoked. 

Figure 4.3.15. Mott-Schottky plots of the space charge capacitance (curve 1) as derived from data like those shown in Figure 4.3.9a and the capacitance associated with the high-frequency response, Q (curve 2) derived from data like those shown in Figure 4.3.96. The flat-band potential is the same in both cases (0.69 V), but the doping level, as calculated from the slope of the lines, is an order of magnitude lower for curve 2 (polished + etched + oxidized sample) than for curve 1 (polished + etched sample). (Shen et al. [1986]). Reprinted by permission of the publisher, The Electrochemical Society, Inc.

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