Pulse excitation bandwidth

The variable offset cumulative spectra (VOCS) method has been a major step forward for the acquisition of broad wideline and ultra-wideline SSNMR powder patterns, representing a time-efficient way to overcome the excitation limitations of rectangular rf pulses [51,53,54]. VOCS involves acquiring the broad overall SSNMR spectrum by collecting a series of individual subspectra at evenly spaced transmitter frequencies. The spacing between subspectra is typically set to be equal to or less than the pulse excitation bandwidth in order to ensure proper spectral excitation in each experiment. The resulting series of subspectra are then added together in the frequency domain to yield the overall broad powder pattern. In this marmer, even extremely broad powder patterns can be collected without any... 

PULSE excitation BANDWIDTH SPANS ALL ALLOWED TRANSITIONS... 

With broad-band pulses, pumping and probing processes become more complicated. With a broad-bandwidth pulse it is easy to drive fundamental and overtone transitions simultaneously, generating a complicated population distribution which depends on details of pulse stmcture [75], Broad-band probe pulses may be unable to distinguish between fundamental and overtone transitions. For example in IR-Raman experiments with broad-band probe pulses, excitation of the first overtone of a transition appears as a fundamental excitation with twice the intensity, and excitation of a combination band Q -t or appears as excitation of the two fundamentals 1761. 

HSQC rather than HMQC-based transfer schemes have recently in particular been employed in various indirectly detected two- and three-dimensional 111/X/Y correlation experiments involving multi-step coherence-transfer in either direction.38 40 43 44 The application of PFG s appears to be essential to obtain a sufficiently clean spectrum that is free of artefacts, and in many cases the pulse sequence shows only a satisfactory performance if composite pulses, with a larger excitation bandwidth than normal ones, are employed.21,38,39,43 The pulse schemes yield generally phase-sensitive spectra with pure absorptive lines and do not suffer from splitting or broadening of the cross peaks as a consequence of the undesired evolution... 

In pulse-echo-based techniques, the time of flight in a sample cannot be determined simply from the observation of the time span between adjacent echoes in the echo pattern if plane parallel transducers operated at resonant frequencies are employed. Transducers introduce substantial errors if the velocity is derived from such measurements, especially if relatively short samples are used. Various correction approaches have so far been developed in order to consider the influence of resonant transducers and the effects of diffraction [31-33]. The need for corrections can be avoided and a broad operational bandwidth obtained by using short pulses of duration equal to or shorter than the transduction [34] this requires a time resolution better than the transit time in the transducer. This short-pulse excitation (e.g. the maximum for a 10-MHz transducer is 50 ns) requires a high-power wide-band ultra-linear amplifier to ensure the detection of US signals with sufficient resolution under non-resonant conditions. 

The amplitude modulated pulses may require special equipment such as a waveform generator which, however, has become a standard constituent of the modem commercial spectrometers. The amplitude modulated pulses are usually windowless and the sidebands produced by these pulses, in most cases, are very weak and can be neglected. The simplest amplitude modulated pulses are Gaussian pulse, sine pulse or sine-square pulse [1]. The main drawback of these simple shapes is that they produce a phase gradient over the excitation bandwidth and their excitation profiles are non-uniform over the bandwidth of interest. The amplitude modulated pulses can easily be shifted off-resonance by applying a phase ramp over the pulse according to equation (4). 

Figure 3.4. A single monochromatic radiofrequency pulse has an effective excitation bandwidth that depends inversely on the duration of the pulse. A short intense pulse is therefore able to excite over a wide frequency window (a), whereas a longer weaker pulse provides a more selective excitation profile (b).

For those spins further from resonance, the angle 0 becomes greater and the net rotation toward the x-y plane diminishes until, in the limit, 0 becomes 90 . In this case the bulk magnetisation vector simply remains along the -f-z-axis and thus experiences no excitation at all. In other words, the nuclei resonate outside the excitation bandwidth of the pulse. Since an off-resonance vector is driven away from the y-axis during the pulse it also acquires a (frequency dependent) phase difference relative to the on-resonance vector (Fig. 3.6). This is usually small and an approximately linear function of frequency so can be corrected by phase adjustment of the final spectrum (Section 3.2.8). 

Universal pulses act equally on any initial magnetisation state whereas excitation and inversion pulses are designed to act on longitudinal magnetisation only. The bandwidth factor is the product of the pulse duration. At, and the excitation bandwidth, Af, which is here defined as the excitation window over which the pulse is at least 70% effective (net pulse amplitude within 3 dB of the maximum other publications may define this value for higher levels and so quote smaller bandwidth factors). Use this factor to estimate the appropriate pulse duration for the desired bandwidth. The attenuation factor is used for approximate power calibration and represents the amount by which the transmitter output should be increased over that of a soft rectangular pulse of equal duration. The Gaussian based profiles are truncated at the 1% level. 

The excitation profile of soft pulses is defined by the duration of the pulse, these two factors sharing an inverse proportionality. More precisely, pulse shapes have associated with them a dimensionless bandwidth factor which is the product of the pulse duration. At, and its effective excitation bandwidth, Af, for a correctly calibrated pulse. This is fixed for any given pulse envelope, and... 

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