Modulation of frequencies

Flow which fluctuates with time, such as pulsating flow in arteries, is more difficult to experimentally quantify than steady-state motion because phase encoding of spatial coordinate(s) and/or velocity requires the acquisition of a series of transients. Then a different velocity is detected in each transient. Hence the phase-twist caused by the motion in the presence of magnetic field gradients varies from transient to transient. However if the motion is periodic, e.g., v(r,t)=VQsin (n t +( )q] with a spatially varying amplitude Vq=Vq(/-), a pulsation frequency co =co (r) and an arbitrary phase ( )q, the phase modulation of the acquired data set is described as follows ... 

Figure Bl.19.39. Schematic of the themiocoiiple probe in a scaiming themial profiler. The probe is supported on a piezoelectric element for modulation of tip-sample distance at frequency oi and to provide positioning. The AC thennal signal at oi is detected, rectified, and sent to the feedback loop, which supplies a voltage to the piezostack to maintain the average tip-sample spacing constant. (Taken from [209], figure 1.)...

Lau K T, Bar-Chaim N, Ury I and Yariv A 1983 Direct amplitude modulation of semiconductor GaAs lasers up to X-band frequencies Appi. Phys. Lett. 43 11... 

Frequency-Modulation Spectroscopy. Frequency-modulation spectroscopy (tins) is a high sensitivity null-background infrared technique for measuring absorbances down to 10 with fast acquisition speeds. Fms involves frequency-modulating a laser source at COq to produce a carrier frequency having sidebands at cJq where is an integral multiple of the modulation frequency. Dye lasers and many other single-line sources can... 

The most popiilar form of motor speed control for adjustable-speed pumping is the voltage-controlled pulse-width-modulated (PWM) frequency synthesizer and AC squirrel-cage induction motor combination. The flexibility of apphcation of the PWM motor drive and its 90 percent- - electric efficiency along with the proven ruggedness of the traditional AC induction motor makes this combination popular. 

Frequency converters constructed for use with three-phase motors less than 4 kW can therefore be delivered with a single-phase supply from the electrical mains. For greater power requirements, it is most common to use a three-phase power supply. Through switches and potentiometers or the programming module of the frequency converter, the important parameters of electrical motors can be adjusted as needed. 

Sum This type of modulation, which is described in the example above, generates a series of frequencies that include the fundamental shaft speeds, both input and output, and fundamental gear-mesh profile. The only difference between the real frequencies and the ghost is their location on the frequency scale. Instead of being at the actual shaft-speed frequency, the ghost appears at frequencies equal to the sum of the input and output shaft speeds. Figure 44.40 illustrates this for a speed-increaser gearbox. 

The above description refers to a Lagrangian frame of reference in which the movement of the particle is followed along its trajectory. Instead of having a steady flow, it is possible to modulate the flow, for example sinusoidally as a function of time. At sufficiently high frequency, the molecular coil deformation will be dephased from the strain rate and the flow becomes transient even with a stagnant flow geometry. Oscillatory flow birefringence has been measured in simple shear and corresponds to some kind of frequency analysis of the flow... 

The quantum theory must describe not only the shape of a resolved rotational structure of the Q-branch but its transformation with increase of pressure to a collapsed and well-narrowed spectrum as well. A good example of such a transformation is shown in Fig. 4.6. The limiting cases of very low and very high pressures are relatively easy to treat as they relate to slow modulation and fast modulation limits of frequency exchange. 

With t = 0 the present expression reduces to the result obtained in Eq. (3.28). If, e.g., t = 2, then spectral exchange takes place both within the branches of an isotropic scattering spectrum (Fig. 6.1) and between them. The latter type of exchange is conditioned by collisional reorientation of the rotational plane, whose position is determined by angle a. As a result, the intensity of adsorbed or scattered light is redistributed between branches. In other words, exchange between the branches causes amplitude modulation of the individual spectral component, which accompanies the frequency modulation due to change of rotational velocity. 

The measurement of the electrode impedance has also been ealled Faradaie impedanee method. Since measurements are possible by applying either an electrode potential modulated by an AC voltage of discrete frequeney (which is varied subsequently) or by applying a mix of frequencies (pink noise, white noise) followed by Fourier transform analysis, the former method is sometimes called AC impedance method. The optimization of this method for the use with ultramicroelectrodes has been described [91Barl]. (Data obtained with these methods are labelled IP.)... 

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