Frequency, carrier Larmor

For a spin whose chemical shift is exactly at the center of the spectral window, we call the pulse an on-resonance pulse because the pulse (or carrier ) frequency is exactly equal to the resonant frequency (precession frequency or Larmor frequency vG) of the spin. During the pulse, we can use the vector model to show the B field (the pulse) as stationary in the rotating frame of reference, because the x and y axes are rotating about the z axis at exactly the frequency of the pulse. The position of the B field in the x -y plane depends on the phase of the pulse, which is just the place in the sine function (0-360°) where the radio frequency oscillation starts at the beginning of the pulse. This can be controlled by the spectrometer and is written into the pulse sequence by the user ... 

A very effective signal sensitivity enhancement scheme for MQMAS as well as for MAS is the DFS introduced by the group of Kentgens.The underlying principles of DFS and FAM are similar and they have been exphcitly dealt with already. In a nutshell, a cosine amplitude modulated RF carrier wave irradiates the sample at two frequencies, namely, ioq -F w, and aio — Larmor frequency of the spins and is the frequency of modulation. This means that if satellite transitions of a static spins-1 system will be simultaneously... 

Let us imagine that the frame of reference is not static but is rotating clockwise around the z axis at the carrier frequency vx. In Figure 4.7b, we are looking down the z axis toward the xy plane and place the vx vector on the x axis, where it apparently remains even though it is really precessing at the carrier frequency of, say, 300 MHz. The two faster Larmor vectors (vLl and vl 2) appear to precess clockwise, whereas the slowest vector (vl3) appears to precess counterclockwise, that is, at their difference frequencies 2000 Hz, 800 Hz, and (—) 1000 Hz—precisely those used to produce the FID. 

The third advantage of the heterodyne system is the possibility of performing phase "shifting at the IF rather than at the carrier frequency. This is because the phase of the heterodyned signal is just the difference of the phases of the two original frequencies so that when the IF phase is changed by a certain amount, so is the phase of the resultant. Therefore, we can set up a phase shift network, say, with 0°, 90°, 180°, and 270° phase shifted outputs at the intermediate frequency once and for all and use them at any Larmor frequency provided that we adjust the overall phase at each frequency. 

Carrier frequency. Syn. NMR frequency, Larmor frequency, on-resonance frequency, transmitter frequency. The frequency of the RF being generated by a particular channel of the spectrometer. The carrier frequency is located at the center of the observed spectral window for the observed (detected) nuclide. 

The principle of Fourier transform (FT) NMR spectroscopy is the observation of the so-called free induction decay (FID) after the application of radio frequency (rf) pulses to the resonating nuclei. The carrier frequency of the rf-pulses is the Larmor frequency. In many cases, the FID is observed after single-pulse (SP) excitation, e.g., after application of a so-called 7r/2-pulse which rotates the magnetization by 90° from the direction of the external magnetic field (z-direction) into the x,y-plane. The characteristic time constant for the free induction decay is the transverse relaxation time, T2, which is given by T2=(2/M2) =0.53 (A Vi/2)" for Gaussian lines. Fourier transformation of the FID yields the common absorption spectrum. 

It may be noted that refocusing occurs only in the heteronuclear system, i.e., when a selective 180° pulse is applied. Field inhomogeneities or differences of chemical shift cause an additional fanning out of the magnetic vectors which can be eliminated by the application of the 180° pulse to the X nucleus. This is important for practical purposes since the Larmor frequency of the X nucleus is not normally identical to the carrier frequency Vq, as assumed in the above discussion. 

At 500 MHz, moderate-sized (more than six residues) oligosaccharides lie within the spin-diffusion limit. However, for smaller molecules, as the value of the function (OqT (where (Oq is the Larmor frequency of protons, and is the correlation time of the molecule) approaches 1 then the value of the NOE tends towards 0. Cross-peak intensities of NOESY spectra of smaller oligosaccharides (2-5 residues) may thus become too small to measure accurately. In such cases, the rotating frame Overhauser effect spectroscopy (ROESY, originally referred to as CAMELSPIN) experiment is commonly used to measure NOE values. To reduce the appearance of HOHAHA-like cross-peaks, a low power spin-lock field should be used, and the transmitter carrier offset to the low-field end of spectrum. The offset dependency of cross-peak intensities should also be removed by 90° pulses at either end of spin-lock period. 

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