Frequency-Dependent Losses

The advantages of a quasi-resonant converter over a classic PWM converter are smaller size and typically higher efficiencies. Although when a smaller size is pursued by increasing its operating frequency, the improvement in efficiency is sacrificed due to other frequency dependent losses. 

Thus, the wave equation has been extended by a first-order term, i.e., a term proportional to the first derivative of y with respect to time. More realistic loss approximations would append terms proportional to d3 yldt3, d5y/dt5, and so on, giving frequency-dependent losses. 

The frequency dependences of the storage and loss components of the complex moduli must be introduced (2-A). These must obey causality, as discussed by Hartmann in the present volume. Hence, a frequency dependent modulus always implies a frequency dependent loss factor and vice versa. 

Deutsch A, Kopcsay GV et al (2001) Frequency-dependent losses on high-performance interconnections. IEEE Trans Electromagn Compat 43 446-465... 

The third complicating factor specific to ROESY is the attenuation of cross-peak intensities as a function of resonance offset from the transmitter frequency [69]. Off-resonance spins experience a spin-lock axis that is tipped out of the x-y plane (Section 3.2.1) resulting in a reduction in observable transverse signal in addition to a reduction in cross-relaxation rates. This is more of a problem for quantitative measurements, although fortunately mid-sized molecules show the weakest dependence of ROE cross-relaxation rates on offset. The so-called compensated ROESY sequence [69] eliminates these frequency-dependent losses should quantitative data be required. 

For wire fault detection many requirements for modeling have to be fulfilled. The transmission line should be modeled with high accuracy and efficiency. The frequency-dependent losses of the conductors and dielectric must be considered and the complexity and size of the transmission line models should be reduced. In [24] the ABCD matrix model is applied to simulate the transmission line. 

According to (5.8) the gain factor Go(v) = exp[—2a(y)L] depends on the line profile g v — vq) of the molecular transition Ei E. The threshold condition can be illustrated graphically by subtracting the frequency-dependent losses from the gain profile. Laser oscillation is possible at all frequencies vl where this subtraction gives a positive net gain (Fig. 5.22). 

Fig. 5.38. Some possible schemes of coupled resonators for longitudinal mode selection, with their frequency-dependent losses. For comparison the eigenresonances of the long laser cavity with a mode spacing Av = cjld are indicated...

The frequency-dependent increase in storage modulus to 1 GPa and the frequency-dependent loss peaks signify vitrification during cure. Vitrification, as expected, is frequency-dependent since it is the cure-induced glass transition. Gelation, however, is an event that is independent of frequency. It is important to note that the shear sandwich experiment is useful primarily for B-staged resins whose viscosity is sufficient so that the resin does not flow out of the gap between the parallel-plate shear sandwich fixtures. 

Long, A.R. Frequency-dependent loss in amorphous semiconductors. Adv. Phys. 1982 31 553-637... 

Fig. 10 Mechanical properties of polymeric hydrogels based on catechol-functiomalized PEG at different pH and comparison of a chemical and a physictil hydrogel, assessed by their elastic (GO and viscous (G O shear moduli, a Frequency-dependent loss (G") and storage (GO moduli of gels at pH 5 (green), pH 8 (blue), and pH 12 (red) (C circles-, G" triangles), b Comparison of physically (red) and chemically (black) crosslinked hydrogels, c Recovery of stiffness and cohesiveness after tearing by shear stress (same color code as in b). Modified from Waite et al. [121]. Copyright 2011 National Academy of Sciences of the United States...

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