Nmr Data Acquisition And Acquisition Parameters

The process of data acquisition results in an FID signal residing in the computer of the NMR instrument. In order to properly set up the acquisition parameters, it is helpful to understand a little about how this is accomplished. We will follow the sequence of events involved in the acquisition of the raw data for a simple 1D 1H spectrum on a 200-MHz instrument through a simplified diagram of the spectrometer:

(a) Wait for a period of time called the relaxation delay for spins to reach thermal equilibrium;

(b) send a high-power short-duration RF (200 MHz) pulse to the probe coil;

(c) receive the resulting FID signal from the probe coil;

(e) convert the RF (MHz) signal to a "stereo" audio (kHz) signal;

(f) sample the audio (analog) signal at regular intervals and convert it to a list of integers;

(g) add the digital FID "list" to a sum FID in memory;

(h) repeat steps (a)-(g) for as many "scans" or "transients" as desired.

Each of these steps will be discussed in more detail with the goal of understanding the basic parameters needed to set up an NMR experiment. The FID contains all of the frequencies of the sample protons, which represent a range of chemical shift values. The range of radio frequencies in the FID is extremely narrow: 199.999-200.001 MHz for a 10 ppm range of chemical shifts. We are only interested in this tiny slice of frequencies, so it is convenient to subtract out the fundamental frequency (200.000 MHz) and look only at the differences, ranging from -0.001 to +0.001 MHz, or from -1000 to +1000 Hz. These much lower frequencies are called "audio" frequencies, since they are in the range of sound waves that can be detected by the human ear. In fact, the audio signal of an NMR can be connected to a pair of speakers so that you can listen to the FID in stereo!

The audio signals must be converted into a list of numbers, which is the only language that a computer understands. This is done by sampling the voltage of each signal at regular intervals of time and converting each analog voltage level into an integer number. Thus, an FID becomes a long list of numbers, which is stored in the computer memory. As the same FID is acquired over and over again, repeating the sequence (relaxation delay—pulse-acquire FID), each new list of numbers is added to the list stored in memory. This process is called "sum to memory." As more and more "scans" or "transients" are acquired, the signal-to-noise ratio of this sum improves.

Now let's look in detail at each process, so that we can understand the NMR acquisition parameters needed to set up the experiment. After the pulse, we will follow through the hardware devices in a block diagram and try to understand a little about the NMR hardware. It turns out that processing of the NMR signal in the hardware is strictly analogous to the theoretical steps we will use in viewing the NMR experiment with the vector model, so it is essential to understand it in general.

3.6.1 Relaxation Delay: D1 (Varian) or RD (Bruker)

Usually the acquisition (pulse-FID) is repeated a number of times in order to sum the individual FIDs and increase the signal-to-noise ratio. In this case, a delay must be inserted before each pulse-FID sequence to allow the populations to return to a Boltzmann distribution ("relaxation"). Without this delay the nuclei will become saturated (equal populations in the two energy levels), and there will be little or no signal in each FID. Ideally, you should wait for about five times the characteristic relaxation time (Ti) before starting the next pulse, but in practice the relaxation delay is quite a bit less and you live with a certain reduction of signal. This is a compromise value because pulsing more often gives you more data per unit time. In this case, you rapidly reach a steady state where the nuclei are not completely relaxed but are at least at the same degree of relaxation each time a new pulse arrives. Relaxation is going on during the FID acquisition period as well, and sometimes with long FID acquisition times, there is no need for a specific relaxation delay. Another strategy for slow-relaxing nuclei (e.g., quaternary carbons in 13C-NMR) is to reduce the amount of RF excitation (the pulse width) so that the perturbation from equilibrium resulting from each pulse is reduced.

3.6.2 The Pulse

The RF pulse is simply a high-power RF signal turned on for a very short period of time, on the order of microseconds (^s). The duration of the RF pulse in microseconds is called the pulse width (PW) (Fig. 3.9). As with all sine waves, the pulse has characteristics of frequency, amplitude, and phase. The frequency of the pulse is set at the center of the

Increasing pulse width Figure 3.9

spectral window (range of resonant frequencies expected), but because of its short duration and high power it is capable of exciting all of the sample nuclei within the spectral window simultaneously. Using our example of a 200 MHz experiment, the pulse frequency would be 200.000 MHz, but all nuclei resonating in the range 199.999-200.001 MHz would be equally excited by it. The pulse shape is rectangular, meaning that the RF power turns on more or less instantaneously to full power, and then PW microseconds later turns off. A "90° pulse" is the pulse width required to exactly tip the sample magnetization from the z axis into the x-y plane, where it rotates at the resonant frequency in the x-y plane, leading to a maximum-intensity FID signal. The sample magnetization is just the vector sum of all the individual nuclear magnets. The amplitude of the pulse (height of the rectangular envelope) can be adjusted but is usually set near the maximum for simple 1D spectra. RF power is the square of the amplitude, and usually we talk about pulse power (in watts or decibels) rather than amplitude. The duration (pulse width) of the 90° pulse depends on the RF power and, to some extent, on the characteristics of the probe and the sample. With higher power (higher pulse amplitude) we need less time to rotate the magnetization by 90°, so the 90° pulse width is shorter. For some experiments, calibration of the 90° pulse width is essential for the experiment to work right. For simple one-pulse experiments, an approximate value is sufficient. In more sophisticated experiments that use more than one pulse separated by various time delays, the pulse duration parameters are P1, P2, P3, and so on for the various pulses in the sequence. Pulses are always entered in microseconds (^s) and should not be made very long (more than a few hundred microseconds) because at full power the amplifiers can "burn up" if left on continuously for too long. Finally, we have control over the pulse phase as well. Relative to an RF signal that starts at the zero degree point of the sine function, we can shift the phase by any amount we choose, although 90°, 180°, and 270° phase shifts are the most common. For example, a 90° phase shift means that the wave starts at the top of the cycle and goes down to zero and then to negative. We will see that setting the pulse phase is equivalent to placing the pulse vector on the x, y, —x, or —y axis of the rotating

frame of reference (0o, 90o, 180°, or 270° phase shifts, respectively). This gives us much more flexibility in controlling the complex "dance" of sample magnetization in advanced experiments. In the actual pulse sequence code, which is written to tell the spectrometer the exact sequence of events in an NMR experiment, the phases are represented by 0, 1, 2, and 3 for the x, y, -x, and — y axes, respectively, in the rotating frame of reference.

The remaining steps involved in receiving the FID signal are diagramed in Figure 3.10, showing the process of amplification, quadrature detection, digitisation, and summation to give the final FID in the computer.

3.6.3 Receiving the FID from the Sample

As the sample magnetization rotates in the x-y plane, the same probe coil that transmitted the high-power RF pulse to the sample experiences a very weak induced signal. This signal decays to nothing over a period of a second or two, and the full-time course of this induced signal is called the free induction decay or FID. Each type of nucleus in the molecule (e.g., the CH3, CH2, and OH protons in ethanol) has its own resonant frequency, so the FID consists of a superposition of a number of pure frequencies, corresponding to a number of peaks in the spectrum. All of the information of the NMR spectrum is contained in the FID, and a large part of the spectrometer is devoted to amplifying, recording, and analyzing this signal. In cryogenic probes (Chapter 12, Section 12.3), the probe coil is cooled to very low temperatures (e.g., 25 K) resulting in a 3-4 times reduction in thermal electronic noise and a concomitant 3-4 times increase in sensitivity (signal-to-noise ratio).

Analog Digital

Figure 3.11

Analog Digital

Figure 3.11

3.6.4 The Receiver

The receiver consists of preamplifier, detector, audio filters, analog-to-digital converter (ADC), and sum to memory. It amplifies the RF FID signal coming from the probe, converts it to an audio frequency signal by subtracting out the RF at the center of the spectral window, amplifies it some more, converts it to a list of numbers, and adds these numbers over a number of repeated scans (Fig. 3.10). The total amplification given to the FID in the receiver is called the receiver gain (Varian: GAIN or Bruker: RG). The intensity of the FID signal induced in the probe coil depends on the sample concentration, so the amount of gain or amplification in the receiver must be adjusted for each new sample. The audio signal coming into the digitization stage (ADC) should ideally be of the same magnitude for all samples, regardless of concentration. The ADC has a maximum range of integer values that it can give to the signal as it comes in, for example -32,767 to +32,768 (Fig. 3.11). If the signal is amplified too little before digitization, the numbers will get "grainy": they might range from — 1to +1 with only three possible values (Fig. 3.11, bottom). In this case, it would be very difficult to find a small peak in the spectrum in the presence of big ones (this is called a "dynamic range" limitation). If, on the contrary, the signal is amplified too much, it might exceed the digitizer limits and get truncated or "cut off" (Fig. 3.11, top). For example, a signal that would give a value of 52,314 would be read as 32,768 because the digitizer cannot respond to any larger value. This cutting off or "clipping" has very drastic effects on the spectrum: the baseline gets huge oscillations ("wiggles") that cannot be corrected in any way. So it is clear that the receiver gain has to be set correctly for each sample to get the best results. More concentrated samples (or samples with large solvent peaks) will require smaller receiver gain values, whereas dilute samples are best run with large gain. Both Varian and Bruker allow for an automatic receiver gain adjustment. On the Varian, simply set GAIN to "N" (not used) and start the acquisition; a number of trial FIDs will be recorded to determine the best gain value and then the acquisition will begin. On the Bruker, the command RGA (receiver gain adjust) will do the same thing but will not automatically start acquisition. To better understand how the NMR hardware works, we will look in detail at five essential stages of the receiver (Fig. 3.10).

3.6.4.1 The Preamplifier This is a physical box that sits on the floor next to the magnet or is part of the "magnet leg," which either supports the magnet (Varian Gemini-200) or stands alone next to the magnet (Varian Unity or Inova). Its job is to amplify the RF FID signal immediately, before any thermal electronic noise has accumulated from the connecting cables. That is why it is located very close to the magnet, so the cables from the probe are short. Once the FID has been amplified, any thermal noise that is added to it later will be less important relative to the NMR signal. In cryogenic probes (Chapter 12, Section 12.3) the preamplifier is actually moved into the probe head where it is cooled to the same low temperature (e.g., 25 K) as the probe coil. This further limits the introduction of thermal noise at the first stage of amplification. Any noise that comes into the preamplifier is there "forever" because amplification at that stage will amplify the noise just as much as the signal (the FID). Thus, it is essential to limit this noise as much as possible in the early stages.

The preamplifier also contains a "send-receive" switch that allows the high-power pulse going into the probe and the very low-power FID coming out to travel on the same cable connecting the preamp to the probe. This "switch" is actually a solid-state device with no moving parts.

3.6.4.2 The Detector This converts the RF FID signal into an audio frequency FID signal by "mixing" it with a reference RF signal that has a single pure frequency at the center of the spectral window (vr, the reference frequency). Subtraction of frequencies is accomplished by an electronic process called "mixing" using an analog device called a "mixer," "phasesensitive detector," or "modulator." It actually involves analog multiplication of the FID signal by a reference frequency signal (200.000 MHz in this example), with the resulting signal having frequency components representing both the sum and the difference of the FID frequency and the reference frequency.

(199.999 - 200.001 MHz range) x 200.000MHz reference

= -1000 to +1000 Hz range + 399.999 - 400.001 MHz range

(difference) (sum)

The multiplication sign represents a multiplication of the two signal amplitudes at each instant in time to give a momentary product amplitude. The sum frequency is eliminated by an electronic filter, leaving only the desired (difference) audio signal. In case any of you are wondering about this bit of electronic magic, it can be explained by high-school trigonometry as follows:

sin(at)cos(jt) = 1/2{[sin(at)cos(jt) + sin(jt)cos(at)]

+ [sin(at)cos(-jt) + sin(-jt)cos(at)]} = 1/2{[sin((a + j)t)] + [sin((a - j)t)]}

This just says that the product of two waves of different frequency a and j is the same as the sum of two waves of frequency a + j (sum) and a - j (difference).

In reality this is done twice, first to "mix down" to an intermediate frequency (IF) still in the megahertz range [e.g., 20.5 MHz (Varian) or 22 MHz (Bruker)] and then to mix to the final audio frequency by subtracting out the IF. The reason for this is that we want to detect a wide range of different NMR frequencies (different nuclei), but it is difficult to have all of the amplification stages "broadband" so that they can deal equally well with all frequencies. By mixing down to an IF that is the same regardless of which nucleus we are observing, the electronics can be optimized to that frequency alone (narrow band) with greater efficiency. For example, a 300-MHz spectrometer with an IF of 20.5 MHz will mix a XH FID (300 MHz) with a reference frequency (also called the "local oscillator" or "LO") of 320.5 to get an IF of 20.5 MHz. This signal is amplified and then split into two signals that are mixed with 20.5 MHz reference signals (0° and 90° phase) to give the real and imaginary audio FIDs. To observe 13C, the LO is changed from 320.5 to 95.5 MHz and mixed with the 75 MHz 13C FID to give the 20.5 MHz IF. As before, the IF is split and mixed with the 20.5-MHz reference signals to give the real and imaginary 13C FIDs. Regardless of the NMR frequency being observed (300 or 75 MHz), the IF (20.5 MHz) is the same. Radio receivers use the same principle of mixing to a common IF regardless of which station you are tuned to, and then mixing again to the audio frequency that you hear. The newest spectrometers produced today have an ADC that is fast enough to directly sample the RF FID, eliminating the need for analog mixing of any kind! The detection step (conversion to audio) is done by digital multiplication of the sampled RF FID.

The resulting audio signal has frequencies that represent the difference between the actual resonant frequencies of the sample nuclei and the reference frequency (vo - vr). This means that the audio frequency at the center of the spectral window is zero (reference frequency minus reference frequency = 0); the downfield half of the spectrum represents positive audio frequencies (FID frequency > reference frequency) and the upfield half represents negative audio frequencies (FID frequency < reference frequency). It is important to recognize that this audio frequency scale has nothing to do with the chemical shift (ppm) scale; that scale is added by the software after we find a reference peak and assign it a value on the ppm scale. Subtracting out the reference frequency from the RF FID corresponds to rotating the coordinate system used to represent the sample magnetization about the z (vertical) axis at the reference frequency. In this rotating frame of reference, a nucleus that resonates at the reference frequency (vr) would have its magnetization vector stand still in the x'-y1 plane after the pulse, since it is rotating in the same direction and at the same speed as the X and y axes of the rotating frame of reference. Nuclei that resonate in the downfield half of the spectral window have their magnetization rotating counter-clockwise in the X-y' plane after the pulse, and those that resonate in the upfield half give rise to magnetization that rotates clockwise in the rotating frame of reference (Fig. 3.12).

Placing the zero of our audio frequency scale in the center of the spectral window has many advantages, but it requires that we have a way to tell the difference between positive frequencies and negative frequencies. This is accomplished by using a technique called quadrature detection. The RF FID signal is split into two and mixed with two different reference RF signals, one of which is phase shifted by 90° (one fourth of a cycle) with respect to the other (Fig. 3.10). The different frequency is selected in both cases, resulting in two audio signals that are 90° out of phase with each other. These signals are traditionally called the "real" and the "imaginary" FIDs, but there is nothing more or less real about either one. The best way to think about these "stereo" signals is to imagine that there are two receiver coils in the spectrometer: one placed on the X axis of the rotating frame (recording the

Figure 3.12

Frequency scale

Figure 3.12

x-component Mx of the sample magnetization) and one placed on the /-axis of the rotating frame (recording the y-component My). If the magnetization vector resulting from a nucleus in the sample is rotating counter-clockwise in the rotating frame (i.e., faster than the axes are rotating), it will generate a maximum signal in the x-axis detector just before it reaches a maximum signal in the y-axis detector, so that the "real" (x-axis) signal will lead ahead of the "imaginary" (y-axis) signal by 90° (Fig. 3.12, left). We can thus determine that this frequency is a positive audio frequency, and place the peak in the spectrum in the downfield (left) half of the spectral window. If instead the magnetization vector is rotating clockwise in the rotating frame (i.e., slower than the x' and y' axes), it will generate a maximum signal in the y-axis detector just before it reaches a maximum signal in the x-axis detector, so the "imaginary" (y-axis) signal will lead ahead of the "real" (x-axis) signal by 90° (Fig. 3.12, right). In this case the frequency is a negative audio frequency, and the peak belongs in the upfield (right) half of the spectral window. Imagine a carrousel with one person riding on it near the edge. If you have two observers, one on the north side and one on the east side, and each observer calls out the direction as the rider goes by, you can tell which way the carrousel is rotating because you would hear "north east north east "for the clockwise direction and "east north east north "for the counter-clockwise direction. With only one observer you would hear, for example, "north north ...

" and you would not be able to tell which direction the carrousel is rotating. The direction of rotation of the carrousel is analogous to the sign of the frequency of an NMR peak in your spectrum. If we only had one "detector," which is the equivalent of having only one FID channel, we could not distinguish between positive and negative audio frequencies. The two FIDs, real and imaginary, are processed by the computer using a complex (i.e., both real and imaginary) Fourier transform, which sorts out the positive and negative frequencies mathematically and spits out the correct NMR spectrum.

3.6.4.3 Audio Filters The audio stage amplifies the audio signal and noise and also tries to block by analog filtering any signals that are outside of the spectral window, that is, which have frequencies greater than the maximum frequency you have set up to observe (set by the ADC, see below). Generally you would not have any signals outside these limits, but you do have noise frequencies that extend in both directions from zero to positive and negative infinity. If these noise frequencies are not blocked, they will "fold in" to the desired range of frequencies and add to the noise that is mixed in with your desired signals. Without audio filters, the signal-to-noise ratio would be very near to zero. The audio filter response should ideally be flat throughout the desired range of frequencies and fall to zero very rapidly beyond the maximum frequency. This is not possible with analog filter devices (made up of electronic components such as capacitors, inductors, and resistors), so there is a certain amount of reduction in response ("droop") within the spectral window near the edges, and the response falls to zero gradually rather than suddenly for frequencies above the maximum (see Fig. 3.20). There are no parameters to adjust since the computer automatically adjusts the audio filters to a response that fits the width of the spectral window, as defined by the parameter SW (spectral width).

3.6.4.4 The ADC The computer cannot understand anything but numbers. The audio frequency FID is a continuous, smooth function of voltage (electrical intensity) versus time. The ADC or digitizer samples the FID voltage at regular intervals of time and assigns an integer value (positive or negative) to the intensity at each sample time (Fig. 3.13). These numbers go into a continuous list of numbers that constitute the digital FID. The spectrometer does not actually just acquire a single value for each time point—it is more like a stereo receiver. There are two channels in the receiver, one that effectively records signals along the X-axis of the rotating frame and one that records signals along the /-axis (Fig. 3.10). So the list of numbers is really twice as long because both FIDs are sampled by the ADC, and the numbers are loaded into the list in pairs: real (1), imaginary (1), real (2), imaginary (2), ..., and so on. Bruker and Varian originally had different ways of sampling, which led to some differences in processing and interpretation of data. Varian samples the two FIDs simultaneously at each time value, and Bruker alternates between real and imaginary samples in time; for example,

Varian (simultaneous)

Bruker (alternate)

Real Imaginary Real Imaginary

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