Phase-cycling

By use of the two-step phase cycle, it is therefore possible to compensate for the effects of imbalance in the two receiver channels. It is also possible to remove extraneous signals that may occur, such as from DC offsets in the receiver, by simultaneously inverting the phase of the rf pulse and the receiver thus, as shown in Fig. 3.27, a steps to c and likewise b becomes d. The NMR signals will foUow the phase of the pulse and so will add in the memory whereas offsets or spurious signals will be independent of this and so will cancel. This gives us a second possible two-step phase cycle which, when combined with the first, produces an overall four-step cycle known as CYCLOPS [8] (CYCLically Ordered PhaSe cycle. Table 3.1). This is the standard phase cycle used for one-pulse acquisitions on all spectrometers and is often nested within the phase cycles of 2D experiments again with the aim of removing receiver artefacts. 

Scan number Pulse phase Receiver phase 

In the general quadrature scheme one requires two signals to be digitised that differ in phase by 90° but which are otherwise identical. The digitised data from each is then stored in two separate memory blocks, here designated 1 and 

Experimentally it is rather difficult to ensure the phase difference is exactly 

Phase cycling is typically employed to suppress these, although recent hardware designs can eliminate them completely. 

FIGURE 3.3 Depiction of the quadrature signal in Eq. 3.8 for (a) reference frequency bjd a (b) (o,( = or, (c) etyf to. The inward spiral results from transverse relaxation at rate 1/T2. From Chen and Hoult,37 Biomedical Magnetic Resonance Technology by C.-N. Chen and D. I. Hoult. Copyright 1989 IOP Publishing Limited. Reproduced with permission. 

It is a simple matter to apply a low-pass filter to remove the high frequency component at (to + corf) and leave only the component at (a) — w. The remaining signal is thus 

A plot of Eq. 3.8 in the complex plane is shown in Fig. 3.3. Because the frequency of the output (a) — 0) is just the frequency at which Mxy precesses in the rotating frame, Fig. 3.3 also provides a visual depiction of this precession as viewed along the z axis. Note that the quadrature phase detection configuration permits us to differentiate between the frequencies (w — w ) and (o)rf — ), whereas such frequencies are indistinguishable with a single phase detector. The phase angle (4 — cf)r,-) can be chosen to provide the pure absorption mode on resonance, and in more complex experiments it can be adjusted as needed, as we shall see in detail later. 

The alternative method for obtaining quadrature phase detection with the use of a single phase-sensitive detector, developed initially by Redfield38 and used in some commercial spectrometers, has certain advantages in two-dimensional NMR. In this approach, the phase of the receiver is advanced by 90° after each measurement. The rationale can be better understood after we discuss digitization rates in Section 3.7. 

Phase cycling refers to the repetition of a pulse sequence a number of times, with the phase of the rf pulses and/or the receiver reference phase incremented each time, usually by 90° or 180°. As an FID is acquired in each of these steps, it is 

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Bain A D 1984 Coherence levels and coherence pathways in NMR. A simple way to design phase cycling procedures J. Magn. Reson. 56 418-27... 

TOCSY data are acquired in tbe pbase-sensitive mode using quadrature detection, and aU. tbe data phases are positive. Tbis increases the SNR for the matrix, and the time required for the experiment is short because very Htde, if any, phase cycling is necessary. In some cases a single scan per FID suffices, and the data can be acquired in approximately 10 min,... 

Blade Material Volt Phase Cycle Ratio ... 

Driver Number Kind Type Manufacturer Full Load Speed, RPM Elec. Char.—phase/cycles/volts Rated H.P. ... 

Type and specifications on fan driver, gear types, pow er voltage, phase, cycles. Motors should at least meet specifications equivalent to totally enclosed, fan cooled, or if in explosive hazardous area, TEFC Class I, Group D (except this not acceptable in hydrogen or acetylene atmosphere). Due to moisture conditions around this equipment, it should be protected against moisture penetration and corrosion. 

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.

What is the effect of phase cycling on the appearance of NMR signals ... 

Phase cycling is widely employed in multipulse NMR experiments. It is also required in quadrature detection. Phase cycling is used to prevent the introduction of constant voltage generated by the electronics into the signal of the sample, to suppress artifact peaks, to correct pulse imperfections, and to select particular responses in 2D or multiple-quantum spectra. 

In 2D NMR experiments, the FIDs are relatively short and with fewer data points, so dc correction is more difficult to carry out accurately. Phase cycling procedures are recommended whenever required to remove dc offsets before dc correction, which is carried out before the first (F2) Fourier transform. Since the data points in the transform arise from frequency-domain spectra, no dc correction is normally required (we expect to see unchanging dc components at Fi = 0). 

Pure 2D absorption line shapes are readily obtained in heteronuclear 2D /-resolved spectra. The incorrect setting of 90° and 180° pulses can, however, cause ghost peaks that can be removed by a phase cycling procedure, appropriately named Exorcycle (Rutar, 1984b). A... 

Gradient-Accelerated Spectroscopy (GAS)—An Alternative to Phase Cycling... 

Figure 7.25 Homoniiclear double-quantum filtered COSY spectrum (400 MHz) of 8-mMangiotensin II in H,0 recorded without phase cycling. Magnetic field gradient pulses have been used to select coherence transfer pathways. (Reprinted from J. Mag. Reson. 87, R. Hurd, 422, copyright (1990), with permission from Academic Press, Inc.)...

Gradient-enhanced 2D TOCSY spectrum of 10 mMof sucrose in D..,0 is shown in figure 7.26. The clean spectrum obtainable without any noise and without the nece.ssity of any phase cycling illustrates the power of this new technique in modern NMR spectroscopy. 

Coherence pathway selection Choosing a corresponding phase cycle so that undesired resonances are suppressed and only the desired magnetization is observed. 

CYCLOPS A four-step phase cycle that corrects dc imbalance in the two channels of a quadrature detector system. 

Phase cycling As employed in modern NMR experiments, repeating the pulse sequence with all the other parameters being kept constant and only the phases of the pulse (s) and the phase-sensitive detector reference being changed. The FIDs are acquired and coadded. The procedure is used to eliminate undesired coherences or artifact signals, or to produce certain desired effects (e.g., multiple-quantum filtration). 

Quadrature images Any imbalances between the two channels of a quadrature detection system cause ghost peaks, which appear as symmetrically located artifact peaks on opposite sides of the spectrometer frequency. They can be eliminated by an appropriate phase-cycling procedure, e.g., CYCLOPS. 

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