Phase Incremented Adiabatic Pulses

Adiabatic pulses are usually composed of a number of back-to-back pulses of equal width Ar. The amplitude adopts a certain shape that is normally 

Phase incremented double adiabatic decoupling for 13C- and 15N-labelled proteins 

The procedure to combine any two phase modulated pulses is straightforward and is going to be discussed below. For the kth step of the two pulses (denoted by the two indices a and b), their amplitudes and phases can be described by A a, Wka and A b, respectively. The vector sum (denoted 

As with any other homonuclear decoupling, the transverse magnetization of the 13C , for example in the evolution time, is perturbed by the decoupling pulse, resulting in an additional precession virtually around the z axis. Since the adiabatic decoupling is applied during the entire evolution time of the 13C , a non-linear frequency shift rather than a phase shift appears in the spectrum. This is termed the Bloch-Siegert (frequency) shift in the NMR literature in honour of their discovery of the phenomenon. 

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A new adiabatic double quantum polarisation transfer experiment has been proposed, which is an adiabatic variant of the POST-C7 experiment. A continuous variation of the phase increment between pulses in this experiment leads to the introduction of a fictitious Zeeman field that allows for an adiabatic passage through the recoupling condition. This results in a chemical shift offset-compensated adiabatic experiment, which leads to an efficient and broadbanded polarisation transfer or to a double quantum excitation. 

The idea of using the linear phase increments to achieve frequency-shifted excitation can be adopted almost to any pulses, such as hard (amplitude fixed) pulses, shaped pulses, and even adiabatic inversion pulses. Unlike any other pulses, the adiabatic pulses have already used non-linear phase increments for tilting the effective RF field slowly compared with the Larmor frequency of the spins in the rotating frame in order to fulfill the adiabatic condition. 

The idea of using phase increment to achieve frequency-shifted excitation can be extended virtually to any sort of RF pulses, including the most complicated adiabatic inversion pulses where a non-linear phase increment has already been applied. Using the phase increment, double or multiple pulses can be constructed with only a single waveform generator in order to excite different regions of a NMR spectrum or to compensate the BSFS, BSPS, as well as BSOS. 

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