Sinusoidal operation

Most Mossbauer spectrometers use triangular velocity profiles. Saw-tooth motion induces excessive ringing of the drive, caused by extreme acceleration during fast fly-back of the drive rod. Sinusoidal operation at the eigen frequency of the vibrating system is also found occasionally and... 

Another resonant frequency instmment is the TA Instmments dynamic mechanical analy2er (DMA). A bar-like specimen is clamped between two pivoted arms and sinusoidally oscillated at its resonant frequency with an ampHtude selected by the operator. An amount of energy equal to that dissipated by the specimen is added on each cycle to maintain a constant ampHtude. The flexural modulus, E is calculated from the resonant frequency, and the makeup energy represents a damping function, which can be related to the loss modulus, E". A newer version of this instmment, the TA Instmments 983 DMA, can also make measurements at fixed frequencies as weU as creep and stress—relaxation measurements. 

Natural frequency When an object is mounted in shu (as in normal operation) and given an initial external displacement or velocity in any direction and then released, the body will oscillate about its initial position in a sinusoidal wavefonn as illustrated in Figure 14.20. 

As noted from general experience, except for specific large inductive loads such as of furnace or rectifiers, the fundamental content of the load current is high compared to the individual harmonic contents. In all such cases, it is not necessary to provide a filter-circuit for each harmonic unless the current is required to be as close to a sinusoidal waveform as possible, to cater to certain critical loads or instruments and devices or protective schemes operating in the system, where a small amount of harmonics may lead to malfunctioning of such loads and devices. Otherwise only the p.f. needs be improved to the desired level. Also to eliminate a parallel resonance with the... 

Quasi-resonant converters are a separate class of switching power supplies that tune the ac power waveforms to reduce or eliminate the switching loss within the supply. This is done by placing resonant tank circuits within the ac current paths to create pseudo-sinusoidal voltage or current waveforms. Because the tank circuits have one resonant frequency, the method of control needs to be modified to a variable frequency control where the resonant period is fixed and the control varies the period of the non-resonant period. The quasi-resonant converters usually operate in the 300 kHz to 2 MHz frequency range. 

The zero current switching (ZCS) quasi-resonant (QR) switching power supply forces the current through the power switch to be sinusoidal. The transistor is always switched when the current through the power switch is zero. To understand the operation of a ZCS QR switching power supply, it is best to study in detail the operation of its most elementary topology—the ZCS QR buck converter (and its waveforms) as seen in Figure 4-10. 

I will be using a seeond order, eommon-mode filter. The diffieulty in eonsider-ing an input eondueted EMI for this power faetor eorreetion eireuit is its variable frequency of operation. The lowest instantaneous frequency of operation occurs at the crests of the sinusoid voltage waveform. This is where the core requires the longest time to completely discharge the core. The estimated frequency of operation has been 50 kHz, so I will use this as an assumed minimum frequency. 

Circuits that carry AC current employing two, three, or more sinusoidal potentials are C2 ed polyphase circuits. Polyphase circuits provide for more efficient generation and transmission of power than single-phase circuits. Power in a three- (or more) phase circuit is constant rather than pulsating like the single-phase circuit. As a result, three-phase motors operate more efficiently than single-phase motors. 

Figure 1, Forcing functions for monomer (fu) and initiator (fi) feeds (a) sinusoidal (b) square-wave (c) reception vessel valve operating sequences which are synchronized with the feed policies (see Figure 2 for the location of the valves...

The general mode of operation in dynamic tests is to vary the stress sinusoidally with time. A viscoelastic solid in which the viscous element is that of a Newtonian liquid (as defined earlier) responds with a sinusoidal strain of identical oscillation frequency. However, because of the time-dependent relaxation processes taking place within the material, the strain lags behind the stress, as illustrated in Figure 7.9. 

The third block in Fig. 2.1 shows the various possible sensing modes. The basic operation mode of a micromachined metal-oxide sensor is the measurement of the resistance or impedance [69] of the sensitive layer at constant temperature. A well-known problem of metal-oxide-based sensors is their lack of selectivity. Additional information on the interaction of analyte and sensitive layer may lead to better gas discrimination. Micromachined sensors exhibit a low thermal time constant, which can be used to advantage by applying temperature-modulation techniques. The gas/oxide interaction characteristics and dynamics are observable in the measured sensor resistance. Various temperature modulation methods have been explored. The first method relies on a train of rectangular temperature pulses at variable temperature step heights [70-72]. This method was further developed to find optimized modulation curves [73]. Sinusoidal temperature modulation also has been applied, and the data were evaluated by Fourier transformation [75]. Another idea included the simultaneous measurement of the resistive and calorimetric microhotplate response by additionally monitoring the change in the heater resistance upon gas exposure [74-76]. 

Theoretically, it is not relevant, whether the quantification is performed in the frequency or in the time domain, since Fourier transform is a linear operator. The Fourier transform of a sinusoidal, exponentially damped signal in time... 

LPSVD is a non-iterative linear fitting procedure where all model parameters are estimated in a single step without need of any start values. This makes this method very fast and operator-independent. Disadvantages of this method are the very limited incorporation of prior knowledge and the limitation to exponentially decaying sinusoids. For this reason, LPSVD is not always appropriate for in vivo spectra. A more detailed description of LPSVD can be found in Ref 33. 

For example, biotransformation of naphthalene in an operating actiyated sludge treatment system (after correction for abiotic processes) was modelled a priori by an elementary first-order (in naphthalene concentration) rate equation (24). The complex actiyated sludge system was perturbed by induction of sinusoidal naphthalene feed concentrations for eight sinusoidal frequencies while the naphthalene in the reactor offgas was measured eyery ten minutes. Abiotic fates (stripping, and sorption) were accounted for and... 

This operation was modelled using a sinusoidal representation of the daily and seasonal power fluctuations. The Cost-Benefit equation contains four terms ... 

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