Sine Wave Oscillators

This version of the harmonic neutralized sine-wave oscillator uses a series of flip-flop gates, configured as a shift register (supplied by a 74HC174 IC) and an inverter (supplied by a CD4049) to provide the... 

A particularly interesting feature of gas flow in a tube wetted by a wavy film is that the pressure drop for a given gas velocity is considerably larger than in the case of flow in a dry tube (M4), as shown very clearly by the data of Feind (F2). In an attempt to explain this effect, Laird (L3) investigated gas flows along tubes with flexible walls which performed sine wave oscillations. It was concluded that a large part of the increase in the... 

Laird (L3), 1954 Experimental study of pressure drop in gas stream in tubes with sine-wave oscillations of tube wall. Shows that large pressure drop is partly due to change in shape of gas velocity profiles. 

How Many Fractional Phase Register Bits are Needed. The choice of how many bits to make the phase register is an important issue in computer music design. While other authors have covered this issue in relation to traditional sine wave oscillators, there are some subtle differences in the design of sample playback oscillators. Here, the fractional part of the phase register essentially determines how much pitch resolution is available, while the integer part determines how many octaves up the waveform can be transposed (pitch shifted). 

A more sensitive rheological techniques for following the stability of multiple emulsions is to use oscillatory techniques. In this case, a sinusoidal strain or stress is applied to the sample, which is placed in the gap of the concentric cylinder or cone-and-plate geometry the resulting stress or strain sine wave is followed at the same time. For a viscoelastic system, as is the case with multiple emulsions, the stress and strain sine waves oscillate with the same frequency, but out of phase. 

Schematic diagrams of the instrumentation for the ANL capacitive flowmeter are given in Fig. 6.20. A 100-kHz sine-wave oscillator, with stable frequency and amplitude controls, was used to pulse the drive electrode. Each sensing electrode was connected to a current-to-voltage converter preamplifier. The preamplifier outputs were bandpass filtered at 100 kHz 5 Hz and amplitude-demodulated. The demodulated signals were amplified and DC-coupled to a first-order low-pass filter to give density signals.

EXTAR 6000 Dynamic Mechanical Spectrometer This instrument applies various deformations, such as bending, tension, compression, and shear, to a solid sample and operates in the oscillatory mode as well as the static mode for stress relaxation and creep. For dynamic measurements, a new synthetic oscillation mode has been added to the existing high-precision sine wave oscillation mode. The synthetic oscillation mode can measure multiple frequencies at an extremely fast rate, which allows the instrument to measure samples with extremely rapid elastic modulus transformations. Measurements from -150 °C are fully automatic using the automatic gas cooling unit. 

What sort of instrumentation would be needed for electrochemical experiments A potentiometry experiment requires little more than a pH meter. A potentiostat or galvanostat can be used for the controlling potential or current in an experiment. In a coulometric procedure, a device to integrate the current (i.e., a coulometer) would also be needed. A hydrodynamic voltammetry [e.g., a rotating disk electrode (RDE)] experiment would require an electrode rotor (to spin the electrode at a precisely known rotation speed), and the rotating ring-disk or RRDE refinement (see below) would necessitate the use of a bipotentiostat so that the disk and ring potentials can be independently controlled. An ac impedance measurement involves the use of a sine-wave oscillator and... 

The interaction of electromagnetic radiation with matter can be explained using either the electric field or the magnetic field. For this reason, only the electric field component is shown in Figure 10.2. The oscillating electric field is described by a sine wave of the form... 

The m/z values of peptide ions are mathematically derived from the sine wave profile by the performance of a fast Fourier transform operation. Thus, the detection of ions by FTICR is distinct from results from other MS approaches because the peptide ions are detected by their oscillation near the detection plate rather than by collision with a detector. Consequently, masses are resolved only by cyclotron frequency and not in space (sector instruments) or time (TOF analyzers). The magnetic field strength measured in Tesla correlates with the performance properties of FTICR. The instruments are very powerful and provide exquisitely high mass accuracy, mass resolution, and sensitivity—desirable properties in the analysis of complex protein mixtures. FTICR instruments are especially compatible with ESI29 but may also be used with MALDI as an ionization source.30 FTICR requires sophisticated expertise. Nevertheless, this technique is increasingly employed successfully in proteomics studies. 

Figure 12.2 Sine wave representation of electromagnetic radiation. It consists of two in-phase waves, with oscillation of the electric field in the xy plane, and the magnetic field perpendicular to it, in the vz plane.

Fig. 7. MR detection of ultrasonic waves oscillating at 515 kHz. (a) Phase image of a phantom without insonation. (b) Phase image with 40 W peak power insonation. In the NMR sequence 50,000 cycles of synchronized sine-shaped motion-sensitizing gradient were applied. Arrows indicate the null-gradient positions of the dedicated gradient coil system. Wavelength is around 2.9 mm and peak matter displacement is around 120 nm. From Ref. 30, reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.

So far we have seen that if we begin with the Boltzmann superposition integral and include in that expression a mathematical representation for the stress or strain we apply, it is possible to derive a relationship between the instrumental response and the properties of the material. For an oscillating strain the problem can be solved either using complex number theory or simple trigonometric functions for the deformation applied. Suppose we apply a strain described by a sine wave ... 

The curve shows the amplitude of oscillation of an object or system as the frequency of the input oscillation is steadily increased. Start by drawing a normal sine wave whose wavelength decreases as the input frequency increases. Demonstrate a particular frequency at which the amplitude rises to a peak. By no means does this have to occur at a high frequency it depends on what the natural frequency of the system is. Label the peak amplitude frequency as the resonant frequency. Make sure that, after the peak, the amplitude dies away again towards the baseline. 

You might remember from your physics that this is the differential equation that describes a harmonic oscillator. The solution is a sine wave with a frequency of l/ip. We will discuss these kinds of functions in detail in Part V when we begin our Chinese" lessons covering the frequency domain. 

If the system is initially at rest (all derivatives equal zero) and we start to force it with a sine wave the output x, will go through some transient period as shown in Fig. 12,3 and then settle down to a steady sinusoidal oscillation. In the Laplace domain, the output is by definition... 

Now we are interested only in the steadystate response after the initial tran sients have died out and the system has settled into a sustained oscillation. As time goes to infinity, all the exponential terms in the summation shown in Eq. (12.24) decay to zero. The system is stable so all the poles pj must be negative. The steadystate output with a sine-wave input, which we called is... 

The main disadvantage of direct sine-wave testing is that it can be very time-consuming when applied to typical large time-constant chemical process equipment. The steadystate oscillation must be established at each value of frequency. It can lake days to generate the complete frequency-response curves of a slow process. 

Equations (4) and (8) can be used to simulate the reactor at point P3 of Figure 5 in [1]. Remember that point P2 is unstable, so if the initial conditions are those corresponding to this point, it is easy to show [16], [28], the reactor evolves to points P or P3. Then, two forcing actions on the reactor are considered 1) when the coolant flow rate and the inlet stream temperature are varied as sine waves, and 2) reactor being in self-oscillating mode, an external disturbance in the coolant flow rate can drive it to chaotic behavior. 

It is well known that a nonlinear system with an external periodic disturbance can reach chaotic dynamics. In a CSTR, it has been shown that the variation of the coolant temperature, from a basic self-oscillation state makes the reactor to change from periodic behavior to chaotic one [17]. On the other hand, in [22], it has been shown that it is possible to reach chaotic behavior from an external sine wave disturbance of the coolant flow rate. Note that a periodic disturbance can appear, for instance, when the parameters of the PID controller which manipulates the coolant flow rate are being tuned by using the Ziegler-Nichols rules. The chaotic behavior is difficult to obtain from normal... 

It has been shown recently [25] that concentrations of NOj, tend to reduce with increase in the amplitude of discrete-frequency oscillations. The mechanisms remain uncertain, but may be associated with the imposition of a near-sine wave on a skewed Gaussian distribution with consequent reduction in the residence time at the adiabatic flame temperature. Profiles of NO, concentrations in the exit plane of the burner are shown in Fig. 19.6 as a function of the amplitude of oscillations with active control used to regulate the amplitude of pressure oscillations. At an overall equivalence ratio of 0.7, the reduction in the antinodal RMS pressure fluctuation by 12 dB, from around 4 kPa to 1 kPa by the oscillation of fuel in the pilot stream, led to an increase of around 5% in the spatial mean value of NO, compared with a difference of the order of 20% with control by the oscillation of the pressure field in the experiments of [25]. The smaller net increase in NO, emissions in the present flow may be attributed to an increase in NOj due to the reduction in pressure fluctuations that is partly offset by a decrease in NOj, due to the oscillation of fuel on either side of stoichiometry at the centre of the duct. 

This time-variant signal (usually referred to as an AC signal) is found in a multitude of electronic circuits. Power delivered to homes and businesses is nearly universally transmitted using an AC signal. Communications circuits require exact sine waves in order to transmit information over large distances with low loss of signal integrity. Just as numerous as the amount of potential uses for oscillator circuits is the amount of circuits that can create these oscillators. In this chapter we will examine several oscillator circuits in detail. 

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