Quadrature detection

Quadrature detection is universally employed in all modem spectrometers. However, there exist two experimental schemes for implementing this and which of these you are likely to use will be dictated by the spectrometer hardware and perhaps by the age of the instrament (on some modem instmments the operator can choose between the two methods). 

Notice that in the calculation of the acquisition time we need only consider 

For either scheme, the total number of data points digitised, acquisition times and spectral widths are identical, so the resulting spectra are largely equivalent. The most obvious difference is in the appearance of aliased signals, that is, those that violate the Nyquist condition, as described below. Experimentally, flatter baselines are observed for the simultaneous method as a result of the symmetrical sampling of the initial data points in the FID and this is the recommended protocol. 

In Section 3.2.3 it was shown that a resonance falling outside the spectral window (because it violates the Nyquist condition) will still be detected but will appear at an incorrect frequency and is said to be aliased or folded back into the spectrum. This can be confusing if one is unable to tell whether the resonance exhibits the correct chemical shift or not. The precise location of the aliased signal in the spectrum depends on the quadrature detection scheme in use and on how far outside the window it truly resonates. With the simultaneous (complex FT) scheme, signals appear to be wrapped around the spectral window and appear at the opposite end of the spectrum (Fig. 3.24b), whereas with the sequential (real FT) scheme signals are folded back at the same end of the spectrum (Fig. 3.24c). If you are interested to know why this difference occurs see reference [7]. 

Fortunately, in proton spectroscopy it is generally possible to detect the presence of an aliased peak because of its esoteric phase which remains distorted when all others are correct. In heteronuclear spectra that display only a single resonance such phase characteristics caimot provide this information as there is no other signal with which to make the comparison. In such cases it is necessary to widen the spectral window and record any movement of the 

So far we have been concerned with a single detector measuring only the yKomponent of the magnetization. In such a single-detection system 

Since quadrature detection involves the cancellation of an unwanted component by adding two signals that have been processed through different parts of the detection system, they will cancel out completely only if their phases differ by precisely 90° and if their amplitudes are exactly equal. 

In practice this may not be achieved perfectly, so weak quad images may be produced. They can be readily recognized as they show different phases than the rest of the spectrum. 

After a single excitation pulse or a series of pulses the signal detection period begins where the response of the spin system to the pulse sequence is recorded. The basic configuration for quadrature detection [2.32, 2.33] is two detectors in the x,y-plane with a 90° phase difference where each detector may be assigned to the x- or y-axis. As illustrated in Fig. 2.6 there are two detection methods, in simultaneous detection both detectors are sampled at the same time whilst in sequential detection the detectors are sampled alternatively. 

If a 90° pulse with phase y is applied to the equilibrium magnetization the signal recorded by the detectors aligned along the x- and y-axis, see Fig. 2.6 is given by  

X = intensity scaling factor which is a function of experimental parameters 

The components Sx and Sy can be combined into a single complex function  

The Fourier transformation of the complex time domain signal in equation [2-12] yields  

Meakin and J. P. Jesson, Computer simulation of multipulse and Fourier transform NMR experiments. I. Simulations using the Bloch equations , J. Magn. Resonance 10, 290-315 (1973). 

Fourier Transform N.M.R. Spectroscopy (Elsevier, Amsterdam, 1976). 

Now we show you a sketch of what is happening in the frequency domain. The rf carrier frequency is at which is chosen so that the entire spectrum of interest is bracketed between and v +Av or v -Av (but not both) where 2Av is the digitizing rate. In a single phase detection experiment the folding problem is avoided by deliberately locating the carrier frequency to one side of all spectral features and ignoring the other side of There are a couple of fairly 

For the record, we point out that the Nyquist frequency is occasionally taken to be the minimum allowable sampling frequency rather than the highest frequency feature uniquely 

Because the reference frequency for the detector cannot be set within the spectrum without aliasing real lines in a single phase detection experiment, it is difficult to perform selective saturation experiments wherein only a small part of the spectrum is irradiated. We will see that it will be trivial to irradiate anywhere in the spectrum with quadrature detection. For such selective irradiation experiments, usually to saturate an unwanted water line, the reader is referred to the papers by Redfield (1976) and Hoult (1976). 

With the additional information provided by the sinusoidal response of the second channel, the sense of rotation can be determined, and vectors moving at +1/ Hz can be distinguished (Fig. 3.21). Technically, the FT is then complex, with the x and y components being handled separately as the real and the imaginary inputs to the transform, following which the positive and negative frequencies are correctly determined. In the case of the single channel, the data are used as input to a real FT. 

Notice that in the calculation of the acquisition time, we need only consider half the total time-domain data points since now two points are sampled at the same time. 

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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,... 

Figure 1.34 (a) Reduced S/N ratio resulting from noise folding. If the Rf carrier frequency is placed outside the spectral width, then the noise lying beyond the carrier frequency can fold over, (b) Better S/N ratio is achieved by quadrature detection. The Rf carrier frequency in quadrature detection is placed in the center of the spectrum. Due to the reduced spectral width, noise cannot fold back on to the spectrum. 

A serious problem associated with quadrature detection is that we rely on the cancellation of unwanted components from two signals that have been detected through different parts of the hardware. This cancellation works properly only if the signals from the two channels are exactly equal and their phases differ from each other by exactly 90°. Since this is practically impossible with absolute efficiency, some so-called image peaks occasionally appear in the center of the spectrum. How can you differentiate between genuine signals and image peaks that arise as artifacts of quadrature detection ... 

The image peaks resulting from quadrature detection can be easily distinguished from small genuine peaks since they show different phases and move with changes in the reference frequency. 

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. 

Bruker instruments use quadrature detection, with channels A and B being sampled alternately, so the dwell time is given by ... 

In quadrature detection, the transmitter offset frequency is posidoned at the center of the F domain (i.e., at F2 = 0 in single-channel detection it is positioned at the left edge). Frequencies to the left (or downfield) of the transmitter offset frequency are positive those to the right (or upheld) of it are negative. 

Quadrature detection A method for detecting NMR signals that employs two phase-sensitive detectors. One detector measures the jc-component of... 

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. 

Quadrature detection Preferred system of signal detection using two detection channels with reference signals offset by 90°. 

Thus, the magnetization is transferred from the amide proton to the attached nitrogen and then simultaneously to the intra- and interresidual 13C spins and sequential 13C spin. The 13C chemical shift is labelled during /, and 13C frequency during t2. The desired coherence is transferred back to the amide proton in the identical but reverse coherence transfer pathway. The 15N chemical shift is frequency labelled during t3, and implemented into the 13C 15N back-INEPT step. The sensitivity of the HNCOmCA-TROSY experiment is excellent and nearly similar to HNCA-TROSY except for the inherent sensitivity loss by a factor of /2, arising from additional quadrature detection needed for 13C frequency discrimination in the fourth dimension. The excellent sensitivity is due to a very efficient coherence transfer pathway,... 

The NMR experiments were performed using the quadrupolar echo pulse sequence 7i/2x—Ti—7i/2y—T2—acquisition with phase-cycling and quadrature detection. A Bruker MSL 400 spectrometer was used for the high pressure studies operating at a resonance frequency of 61.4 MHz. In the liquid-crystalline phase, perdeuterated lipids display NMR spectra, which are superpositions of axially symmetric quadrupolar powder patterns of all C-D bonds.From the sharp edges, the quadrupolar splittings... 

A pre-requisite for the successful extraction of key NMR parameters from an experimental spectrum is the way it is processed after acquisition. The success criteria are low noise levels, good resolution and flat baseline. Clearly, there are also experimental expedients that can further these aims, but these are not the subject of this review per se. In choosing window functions prior to FT, the criteria of low noise levels and good resolution run counter to one another and the optimum is just that. Zero filling the free induction decay (FID) to the sum of the number acquired in both the u and v spectra (in quadrature detection) allow the most information to be extracted. 

Proton-proton homonuclear decoupling has been performed by the ESLG decoupling sequence [46]. Quadrature detection in coj was achieved by using the time proportional phase increment method (TPPI) [47]. During the acquisition period, two pulse phase modulation (TPPM) heteronuclear decouphng ]48] was applied (Figure 7.6). 

Figure 9. Selective irradiation of dioxane. Homonuclear irradiation of a homogeneously broadened resonance at 67.9 MHz. Spectral details PW = 40 ysec (90° C), D2 = 10 sec, 4 scans accumulated, quadrature detection 15% acetone-dc,...

Figure 10. Selective irradiation of linear PE (2 X 10 mol wt, 1 — K 0.5). Spectral details are 35°C 67.9 MHz sweep width 5 KHz (quadrature detection) line broadening 9.7 Hz pulse width 35 jisec (90°C = 48 /jsec) delay = 1.0 sec, 4K data points 1024 scans accumulated 10-mm sample tube. Decoupling 7W (forward), 0.4W (reflected), broad band noise modulated decoupling.

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. 

The carrier position in the directly detected dimension may seem to be important however, in most cases it is not critical whatsoever. The one exception is when no quadrature detection in the remote dimension is desired (see below). In a general scenario the carrier can be placed anywhere in the spectral region of interest with no significant penalty on overall acquisition time. The only important requirement to be fulfilled is that the pulse(s) should cover the desired frequency range with sufficient uniformity (see also below). 

One may use no quadrature detection in the remote dimension at all, thereby accepting some degree of overlap of correlation regions [22]. By judicious placing of the carrier within the spectral region of interest, one can solve many correlation patterns. This approach is, however, limited to relatively sparse spectra and needs careful planning ahead. 

One can avoid overlap in the remote dimension if the carrier was moved away sufficiently from the spectral region of interest. In this case there will be no need for explicit quadrature detection neither in the direct, nor in the remote dimension, while pure phase character is still retained. Two-channel (e.g., quadrature) detection in the direct acquisition dimension offers, however, a sensitivity advantage of factor of /2 [23] with no extra cost in acquisition time, so it is worthwhile to retain. 

Fig. 2. Pulse scheme for the gradient-selected, sensitivity-enhanced X/Y se-HSQC experiment as employed for 31P/15N correlation spectroscopy in Ref. 25. 90° and 180° hard pulses are denoted by solid and open bars, respectively. 2 are delays of length 1/(4 /x,y)> and is a short delay of the same length as the gradient pulse (typically rj 1 ms). Pulse phases are x, unless specified. The ratio of gradient pulse strengths is set to G2/Gi = Yy/Yx, and quadrature detection in Fi is achieved by recording every transient twice and changing the sign of G2 in the second scan.

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