Low-frequency sidebands

So far unexplained by theoretical calculations are the low-frequency sideband for the H—Al pair (and perhaps the H—B pair). Stress-induced splittings also are not fully understood [e.g., the peculiar behavior of the H—Al pair (Bergman et al., 1989) and the low symmetry deduced for H—B in Raman studies (Herrero and Stutzmann, 1988b)]. 

High-frequency to low-frequency delay is a distortion caused by the difference in time delay presented to high-frequency sidebands compared to low-frequency sidebands when it is important that their time... 

In spin relaxation theory (see, e.g., Zweers and Brom[1977]) this quantity is equal to the correlation time of two-level Zeeman system (r,). The states A and E have total spins of protons f and 2, respectively. The diagram of Zeeman splitting of the lowest tunneling AE octet n = 0 is shown in fig. 51. Since the spin wavefunction belongs to the same symmetry group as that of the hindered rotation, the spin and rotational states are fully correlated, and the transitions observed in the NMR spectra Am = + 1 and Am = 2 include, aside from the Zeeman frequencies, sidebands shifted by A. The special technique of dipole-dipole driven low-field NMR in the time and frequency domain [Weitenkamp et al. 1983 Clough et al. 1985] has allowed one to detect these sidebands directly. 

In polarization modulated ENDOR spectroscopy (PM-ENDOR)45, discussed in Sect. 4.7, the linearly polarized rf field B2 rotates in the laboratory xy-plane at a frequency fr fm, where fm denotes the modulation frequency of the rf carrier. In a PM-ENDOR experiment the same type of cavity, with two rf fields perpendicular to each other, and the same rf level and phase control units used in CP-ENDOR can be utilized. To obtain a rotating, linearly polarized rf field with a constant magnitude B2 and a constant angular velocity Q = 2 fr (fr typically 30-100 Hz), double sideband modulation with a suppressed carrier is applied to both rf signals. With this kind of modulation the phase of the carrier in each channel is switched by 180° for sinQt = 0. In addition, the phases of the two low-frequency envelopes have to be shifted by 90° with respect to each other. The coding of the two rf signals is shown in Fig. 8. 

We have thus far treated the K (n + 2)s states as having no Stark shifts. While they have no first order Stark shift, they do have a second order shift due to their dipole interaction with the p states, which are removed from the s states by energies large compared to the microwave frequency. The microwave field does not produce appreciable sidebands of the s state since it has no first order Stark shift. However, it does induce a Stark shift to lower energy. Not surprisingly the Stark shift produced by a low frequency microwave field of amplitude E is the same as the second order Stark shift produced by a static field Es/j2, they have the same value of (E2). Careful inspection of Fig. 10.9 reveals that the resonances observed with high microwave powers shift with power. 

Using amplitude or frequency modulation of a carrier at frequency tog, we can achieve exact frequency division if we make sidebands of the carrier to such low frequency that we can force the condition wg-nQ = (n+2) 2-a>g = 2 so that tog/ 2 = n+1. For example, if we examine Fig. 2, we can achieve exact frequency division by any means which locks the phase of the carrier to the phase of the amplitude modulation that is, the undulations of the carrier do not "slip" under the envelope of the amplitude modulation. A divider based on these principles would be quite useful if 2 is in the microwave region (or below) where precise frequency synthesis is possible. Since 2 and n could be freely chosen, any value of uig could be measured in a single device. 

Because the modulation frequency is so low, it is never necessary to carry out a full sideband analysis to interpret the results. Instead one may treat the low-frequency demodulated signal as arising from the Fourier components of the slowly varying response of the system to a tracked MMW source. ... 

For low-frequency motions (10 -10 s), the 2D exchange experiments are useful techniques (19). Other exchange experiments are also informative, e.g., the one-dimensional exchange spectroscopy by sideband alternation (ODESSA) (151), time-reversed ODESSA (152), and centerband-only detection of exchange (CODEX) (153). Many advanced techniques are given in a recent, excellent review by Brown and Spiess (14). 

The study performed has shown convincingly that H-bonding does not play any significant role in the adsorption of a PDMS oligomer on a fumed silica surface. However, the question arises how to explain a vividly seen intensification of a low-frequency IR sideband located in the region of... 

In radio communication systems, the signal with frequency wi is called the carrier and W2 the modulation, and Wi >> W2. The amplitude modulated signal from a perfect multiplier under these conditions does not contain the low-frequency signal W2. just the upper and lower sideband frequencies wi -b W2 and wi — W2- They are very near to the carrier frequency and can therefore be transmitted through the ether. 

This problem can be partially addressed by creating a DSB-SC signal at a low intermediate frequency /if, where /f /c > as shown in Fig. 12.21. A sharp sideband filter (which is much easier to implement at low frequency) is used to create a SSB-SC signal at frequency /p. This signal is modulated up to the desired carrier frequency where there are again two sidebands present. Since these are separated by a distance of 2/f, the undesired sideband can be removed using an easily implemented BPF with gentle rolloff response as in Fig. 12.22. 

Electron nuclear-nuclear Special TRIPLE resonance [21 ] was used as an extension of ENDOR. In this technique the respective high- and low-frequency NMR transitions v+ and v are pumped simultaneously by sweeping two RF frequency sidebands symmetrically about the proton Zeeman frequency vjj [21 ]. The obtained signals (changes of EPR intensity) are much larger and - even more important - less dependent on the ratio of electron and nuclear relaxation rates than in a conventional ENDOR experiment. Additionally, the relative line intensities approximately... 

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