Phase cycling schemes

A simple, two-step phase cycling scheme may therefore be employed The signals of 0° phase and 90° phase pass through signal channels (1) and (2) to sections A and B, respectively, of the computer memory during... 

To suppress other interference effects, the phase of the transmitter pulse is also shifted by 180° and the signals subtracted from sections A and B, leading to the CYCLOPS phase cycling scheme shown in Table 1.4, in which the two different receiver channels differing in phase by 90° are designated as 1 and 2 and the four different receiver pulses (90°, 90°, 90° and 90f,) are called x, y, — x, and —y, respectively. 

Figure 1.43 The first two steps of the CYCLOPS phase cycling scheme. Any imbalance in receiver channels is removed by switching them so they contribute equally to the regions A and B of the computer memory.

Fig. 5 Radio frequency pulse sequences for measurements of Sj and Si in DSQ-REDOR experiments. The MAS period rR is 100 ps. XY represents a train of 15N n pulses with XY-16 phase patterns [98]. TPPM represents two-pulse phase modulation [99]. In these experiments, M = Nt 4, N2+ N3 = 48, and N2 is incremented from 0 to 48 to produce effective dephasing times from 0 to 9.6 ms. Signals arising from intraresidue 15N-13C DSQ coherence (Si) are selected by standard phase cycling. Signal decay due to the pulse imperfection of 15N pulses is estimated by S2. Decay due to the intermolecular 15N-I3C dipole-dipole couplings is calculated as Si(N2)/S2(N2). The phase cycling scheme can be found in the original figure and caption. (Figure and caption adapted from [45])...

Technically, the inverse experiment used to be very demanding because the excess of protons not coupled to the nucleus of interest (e.g., protons coupled to the almost hundred-fold excess of 12C instead of 13C) needed to be suppressed. Originally, this was achieved by the use of elaborate phase-cycling schemes, but today the coherence pathway selection by gradient pulses facilitates this process. 

Fig. 19. Pulse scheme of the MP-HNCA-TROSY experiment. Delay durations A = 1/(4/hn) 2T a = 27 ms 2Ta= 18-27 ms 2TN = 1/(2JNC-) <5 = gradient + field recovery delay 0 < k < Ta/t2,inax- Phase cycling scheme for the in-phase spectrum is 0i = y 02 = x, — x + States-TPPI 03 = x 0rec = x, — x 0 = y. For the antiphase spectrum, f is incremented by 90°. The intraresidual and sequential connectivities are distinguished from each other by recording the antiphase and in-phase data sets in an interleaved manner and subsequently adding and subtracting two data sets to yield two subspectra.

Accurate measurements of the frequency-resolved transverse spin relaxation T2) of Rb NMR on single crystals of D-RADP-x (x = 0.20, 0.25, 0.30, 0.35) have been performed in a Bq field of 7 Tesla as a function of temperature. The probe head was placed in a He gas-flow cryostat with a temperature stability of 0.1 K. To obtain the spin echo of the Rb - 1/2 -o-+ 1/2 central transition we have used the standard (90 - fi - 180y -ti echo - (2) pulse sequence with an appropriate phase-cycling scheme to ehminate quadrature detection errors and unwanted coherences due to pulse imperfections. To avoid sparking in the He gas, the RF-field Bi had to be reduced to a level where the 7T/2-pulse length T90 equalled 3.5 ps at room temperature. 

Phase cycling scheme for the selective reverse INEPT pulse sequence of fig. 1. Phases are shown in multiples of 90° subscripts indicate that a given phase or bracketed block of phases should be repeated the stated number of times, e.g., the notation (01)2 (13)2 indicates the sequence 0101 1313. Phases in the sequence of fig. 1 other than those listed above remain unchanged in successive transients. 

In the future, gradient spectroscopy may prove to be a better approach to suppression of undesired components. At the time this review was written preliminary results obtained in our laboratory indicate this to be the case provided gradients are used in conjunction with the appropriate phase cycle schemes, which are then usually reduced to their minimum possible size. Spectra usually reveal less artefacts, and, in favourable cases, higher sensitivities. Systematic investigations are underway. 

In solution-state NMR, many important experiments incorporate the creation and evolution of MQ coherence (MQC).5,6,84-86 Since MQC cannot be directly detected, experiments that follow the evolution of a MQC are inherently at least two-dimensional. This is the case with H- H DQ MAS spectroscopy. Figure 7 shows a corresponding pulse sequence and coherence transfer pathway diagram first, a DQC is excited, which subsequently evolves during an incremented time period q the DQC is then converted into observable single-quantum (SQ) coherence (SQC), which is detected in the acquisition period, q. To select the desired coherence transfer pathways, e.g., only DQC during q, a phase cycling scheme is employed.79,80 Pure absorption-mode two-dimensional line shapes are ensured by the selection of symmetric pathways such that the time-domain... 

The mixed MQNQ scheme was first demonstrated on a spin- system acquiring a " A1 spectrum of AlPO-41. Both the 5Q1Q (conventional 5QMAS) and 5Q3Q (mixed 5Q3QMAS) spectra are shown in Fig. 8b and c, demonstrating the resolution enhancement offered by the MQNQ approach. The phase list used for this experiment, based on the nested phase cycle scheme, may be denoted as ... 

There are several general considerations for identifying appropriate two-dimensional (2-D) experiments to use for structural elucidation. First, most of the experiments described here are available both in gradient and nongradient versions. Gradients are used in these experiments to improve coherence selection that is otherwise performed using elaborate phase cycle schemes. It is therefore possible to achieve improved signal selectivity and reduced spectral... 

For selection of particular MQ coherences, phase cycling schemes can be used which are based on phase shifts (p of the complete pulse sequences (7.2.20) and... 

Fig. 11. Pulse sequence and phase-cycling scheme for the acquisition of a 3D data set, which separates the spectra of various MQ orders in one of the dimensions.

The CYCLOPS phase cycling scheme is commonly used in even the simplest pulse-acquire experiments. The sequence is designed to cancel some imperfections associated with errors in the two phase detectors mentioned above a description of how this is achieved is beyond the scope of this discussion. However, the cycle itself illustrates very well the points made in the previous section. 

Yip GN, Zuiderweg ER (2004) A phase cycle scheme that significantly suppresses offset-dependent artifacts in the R2-CPMG 15 N relaxation experiment. J Magn Reson 171 25-36... 

Fig. 10. Three types of DAS pulse sequence, phase cycling and rotor axis orientations, (a) A basic DAS experiment where all pulses are selective 90° pulses calibrated for the particular axis orientations (used from Mueller era/. with permission) (b) A more versatile pure-phase experiment, allowing axis flip to any angle 0 during acquisition. The Z filter mixes the two coherence orders during the flip. The time r for the Z filter is set equal to the storage time needed for the axis flip (from Mueller et al. with permission) (c) A combined shifted-echo and hypercomplex DAS experiment with two phase cycling schemes corresponding to the acquisition of real (upper) and imaginary (bottom) part of r, evolution, respectively (from Grandinetti et al. with permission).

Cogwheel phase-cycling schemes were applied by Ivchenko et al. to sideband suppression and sideband separation experiments in solid state NMR. It has been shown that cogwheel phase cycles lead to the elimination of most pulse imperfection effects, while using far fewer experimental signal acquisitions than conventional phase-cycling methods. 

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