Figure 1. Basic Spectrometer
The nmr spectrometer consists of various pieces of equipment that provide the capability to a variety of experiments. The basic spectrometer consists of a transmitter, a probe, a magnet, a receiver and a computer.
Figure 1. Basic Spectrometer
During the nmr experiment, essentially what happens is that the computer instructs the transmitter to issue a radio frequency pulse to the probe. The probe is inside the magnet, of course and the sample is inside the probe. This rf pulse excites the spins in the sample and after the pulse the computer instructs the receiver to turn on and 'listen' to the rf energy being radiated back from the spins. There is a close analogy between this and hitting a bell with a hammer. The hammer strikes the bell (a pulse) and then one listens to the resulting sound (turn on the receiver). The incoming signal is digitized and stored in the computer's memory.
Of course, the actual situation is more complex than this. For example there is generally a set of preamplifiers situated very close to the magnet whose purpose is to amplify the very small signals coming from the spins. If we were to not do this then when the unamplified signals arrive at the receiver they could very well be drowned in the thermal noise from the signal cable. Signal-to-noise ratios have always been of primary concern to nmr spectroscopists, nmr not being an inherently sensitive technique. Also, at the receiver there are not one but two receivers called phase sensitive receivers that receive the signals with a 90o phase difference to each other. Yet another example is the in the internal workings of the receiver and the digitizer. There is no digitizer available today that can properly digitize signals in the megahertz frequency range, and certainly not at 300-800 MHz. Most digitizers will function adequately from 0 to 250,000 Hz. Therefore, what happens to the signal before it is digitized is that it has a reference signal subtracted from it that is in the appropriate frequency range. For example, the raw signal from a resonance in the sample may be at 300.1335695 MHz and this might be mixed with a reference signal of 300.134689 MHz to produce a difference frequency of 0.0011195 MHz or 1119.5 Hz which is easily digitized. Notice that this is a frequency in the audio range ... it is quite possible to hear these frequencies if an audio amplifier is hooked into the receiver.
Modern pulse spectrometers generally use cyromagnets. These are ones in which there is a superconductiong coil immersed in liquid helium that is charged (the coil of course, not the helium!) in order to produce the required field strength. In order to prevent excessive boiloff off the liquid helium there is a radiation shield to prevent ingress of infrared radiation and an outer container of liquid nitrogen. The liquid nitrogen acts as a 'heat sink'. Heat entering the magnet from the surroundings is absorbed by the nitrogen, the nitrogen evaporates and carries off most of the heat with it. You will see on all cryomagets exit ports where there is a build up of ice as a result of the evaporation of the cold liquid nitrogen. This is good. No ice is bad. It means no evaporation of nitrogen and that something is wrong.
The reason that we use cryomagnets is that in order to achieve the high fields required for high resolution nmr spectroscopy we must pass an extremely large current through a conductor. The highest field possible in a room temperature electromagnet is approximately that corresponding to a 100 MHz spectrometer magnet. You simply can't push any more current through the electromagnet coils economically. However, using superconductors, the practical upper limit on current is much higher and thus much higher fields can be achieved. One major difference between electromagnets and cryomagnets is the stray field. Elecromagnets generally have a yolk through which most of the field lines pass but the cryomagnet has no such thing so the stray field extends for some distance from the magnet. Thus, it is important not to approach the cryomagnet with any magnet-sensitive objects such as credit cards. Also, a ferromagnetic object that is attracted to the cryomagnet can damage the magnet coils if it becomes stuck to the side of the magnet. Be careful.
When filling a cryomagnet it is necessary to top up the liquid nitrogen first. If this is not done then the (very) cold liquid He will slow down and stop the liquid nitrogen evaporation. This will result in a backflow of air into the nitrogen dewar and there will be a buildup of ice in the nitrogen exit ports. After the liquid He fill, the liquid nitrogen will again begin to evaprate but may not have any way to exit from the magnet. Actually, this is not so, or should not be. There should be a pressure relief valve somewhere, usually on the cap to the liquid nitrogen inlet port.
When the nmr experiment is started the computer sets all of the appropriated hardware parameters, usually dealing with timing values for such things as the digitizer and the interpulse delay and then begins to execute the pulse sequence. The standard 1D data acquisition pulse sequence is as follows:
Figure 2. 1D Pulse Sequence
Here, the appropriate Bruker parameters for each of these is given in brackets. We see that there is a delay time, D1, to begin with. This is to allow the spin system to relax back to equilibrium between pulses and is on the order of 1 to 2 seconds usually. Note, however, that in exceptional circumstances this can rise to much longer times, especially for carbon-13. The pulse is then issued at the appropriate frequency. On a 300 MHz system this would be 300.13 + the offset frequency (O1). The offset frequency is added to the basic spectrometer frequency so that the spectral window will be in the proper place. Using different deuterated lock solvents requires changing the field strength in order to position the lock signal for lock. Changing the field strength also changes the resonant frequency meaning that the spectral window moves around, depending on which solvent is used. This, in turn, means that a different offset frequency must be used for each solvent. The basic spectrometer frequency plus the offset frequency is also the reference frequency discussed above. Using quadrature detection (two phase sensitive receivers), The reference frequency corresponds to the exact center of the spectrum. After the pulse is the 'dead' time, DE. This time is usually from 6 to 100 usec in duration and is to allow the sensitive electronic circuitry time to recover from the pulse. This has some importance to the way that the spectrum is processed ... more on this later. Finally there is the acquisition time during which the receiver is on and the incoming signal, after being compared to the reference, is digitized. and stored in memory. The sequence is then repeated for as many times as the user has specified with the NS parameter (number of scans). It is also possible that there will be a series of 'dummy' scans performed at the beginning of the pulse sequence that are identical to the acquisition scans that come later except that the receiver is not turned on. These are to get the spin system into a steady state so that each fid that is acquired will be comparable in magnitude to those previous to it. The number of dummy scans performed is DS.
For more information on pulse sequences, see the pulse sequences document.
The signal that comes from the probe is an analogue signal that varies continuously with time. Digital computers cannot handle analogue signals ... they must be in the form of digital numbers. Therefore there must be a device to convert from analogue to digital called, oddly enough, an analogue to digital converter or ADC. This device uses what is known as a sample-and-hold circuit that samples its input signal, holds it for a period of time and allows the digitizer to convert from the analogue signal to a digital one. It is as though someone with their eyes closed at a race track suddenly opens them for an instant and then closes them again. The image of the horses running on the track are sampled by the eye and temporarily held by the retina after the eye is closed again. An important pararmeter in this process is the time between samples or the dwell time, DW. This time determines the maximum frequency that can be sampled according to the Nyquist theorem. This states that in order to properly digitize an oscillating signal so that it can be faithfully be reproduced there must be at least two samples per cycle. Any less than this and there will be problems reproducing the original signal. It is the width of the spectral window (SW) in hertz that determines the sampling rate.
DW = 1/2SW
If a signal lies outside of the spectral window, the dwell time will not be set in order to properly digitize the signal. The signal will be digitized but when it is reproduced at a later time (after Fourier transforming) it will not be at its proper place in the spectrum ... it will be 'folded' or aliased into some place in the spectrum. If it lies 50 Hz outside of the window it will be aliased at a point 50 Hz inside the window. Thus, it is important to have the spectral window open wide enough to include all resonances. This is a problem when doing a new nucleus on the spectrometer since you don't know where the resonant peaks lie and must guess at an offset value and a spectral width. Generally in this case you would open up the spectral width to its widest possible value and look for peaks and then 'zero' in on them with a smaller spectral width and offset frequency.
The newer spectrometers have 'digital' filtering which, unlike analogue filters, have an infinite rolloff factor ... they basically cut off any signals above or below the spectral window. This has the effect of getting rid of aliasing or folding. Generally, this is a good thing because noise above and below the spectral window is not folded into the spectrum making the signal-to-noise ratio much better than for spectrometers using analogue filters. However, it can also fool you. If a signal lies outside of the spectral window then you will not see it if digital filtering is used. If analogue filters are used you will see the signal as a 'folded' signal that can't be properly phase corrected. You would then simply increase the width of the spectral window to inlcude the signal. In this respect, the use of digital filters requires more care. It is probably best to start with a very wide spectral width and narrow it in as necessary.
Newer machines also employ 'oversampling' in their acquisition schemes. This means that, instead of sampling at the appropriate Nyquist frequency to adequately digitize the data, the data are digitized at four times the required frequency (hence the name, oversampling). Why do this? Well, as with almost all technical advances in the field of nmr spectroscopy, it has to do with increasing sensitivity. If one samples four times in a given time period instead of one time then there will be essentially four times the data (ie. four identical spectra). These are then used, after the appropriate data processing, to construct a spectrum that has a higher signal to noise ratio than would otherwise be the case. Needless to say, older machines that do not have the appropriate software cannot process oversampled data. This is the case with our AMX-300 spectrometer. Uxnmr cannot deal with oversampled data sets.
There is an issue concerning digitizers that deals with dynamic range. Suppose that the maximum voltage level that the digitizer can accomodate is 10v and that the ADC is a 16 bit digitizer. The highest voltage that can be digitized is 10 volts and the lowest is 1.54 x 10-4 volts (allowing for 1 sign bit). If the input voltage is greater than 10 volts the digitizer will digitize is if it were 10 volts. This is call overload or clipping. It is as though the extra signal voltage is clipped off and thrown away. If the input voltage is less than 1.54 x 10-4 then the digitizer will represent it as zero. This is underflow. Because of this the receiver gain must be set to avoid both clipping and underflow. On the Bruker this is done easily with the RGA (receiver gain automatic) command.
As mentioned earlier there actually two phase sensitive detectors on most modern nmr spectrometers. These are set to detect signals that are out of phase by 90o which leads to a sin- cosine relationship. This is done for a number of reasons. First doing this rather than having a single detector allows us to determine whether the frequency of the detected signal is above or below the reference signal. This is not possible with a single detector. Second, since random noise is equivalent to random frequency signals it means that less noise at frequencies outside of the spectral window is aliased into the spectrum since the analogue filters can be set to tighter tolerances. This, in turn means better signal to noise ratio which is the ultimate goal of all nmr spectroscopists.
Figure 3. Phase Sensitive Receivers
In order to understand why it is that quadrature detection is used, imagine that you are a signal detector and that you 'detect' signals by looking at a projection of the rotating magnetic vector on a screen. Essentially, a 3 dimensional process is being projected on a 2 dimensional screen with loss of information, specifically, the direction of rotation. In other words, you cannot see whether the magnetic vector is precessing clockwise or counterclockwise, just that it is precessing. Now, if you have two projections of the precession at 90o to each other you will now be able to tell which direction the precession is occurring in.
Figure 4. Monural Projection
Figure 5. Quadrature Projection
Notice that we can now place the magnetization vector in a particular quadrant and that we can say in which way it is rotating. In other words, using the rotating reference frame, we can say whether the magnetization is rotating in a positive or negative sense with respect to the rotating frame frequency, which is just the reference frequency mentioned earlier.
The original impetus for placing the offset frequency in the middle of the spectrum was so that one could get away with using a slower analogue to digital converter. The speed of the converter in this case need only be half of that required if the offset frequency is at one side of the spectrum. Slower digitizers are cheaper and it means that a wider spectral width can be achieved, an important consideration for some heteronucleii which have extremely wide frequency ranges.
The disadvantage of quadrature detection is that unwanted 'ghost' image peaks appear, especially in samples with a large dynamic range. You can see the reason for this if you look at the Fourier transform of the quad data. Since there are two sets of data detected 90o out of phase with each other this leads to a sin-cosine relationship between them. The sin function is classed as an odd function since f(-x) = -f(x) for the sin function and the cosine function is even, f(-x) = f(x). This even-oddness is carried over into the frequency domain when the Fourier transform is applied so that the transform of the cosine and sin functions leads to:
Figure 6. Even and Odd Transforms
Summing these then gives us:
Figure 7. Sum of Even and Odd Transforms
You can see here how it is that the negative or positive nature of the signal with respect to the reference signal in the center of the spectrum is observed. However, since the signal must pass through two different set of hardware (Figure 3) there will inevitably be differences in signal amplitudes due to imbalances in amplifiers. This leads to imperfect summation that shows up in the spectrum as 'ghost' peaks. You can see this phenomenon if you use a sample with a very strong peak and only use one scan. The transformed spectrum will have a ghost peak mirrored through the center of the spectral window. There will also very likely be a dc offset voltage difference between the amplifiers that translates into a zero frequency peak at the center of the spectrum. This is the 'quadrature glitch'.
Ghost peaks and the quadrature glitch are substantially reduced by phase cycling of the pulse program. This is a method of data acquisition whereby the signals from each receiver are switched and pulse phases are changed by 90o on alternate scans. This has the effect of each receiver contributing equally to each data set, imaginary and real, in memory (figure 3). On, say, the first scan the pulse phase may be x and the magnetization is rotated onto the +y axis (see theory section). The y component of this signal will be a simple cosine function and the x component of the signal will be a simple sin function. These are digitised into channels A and B, respectively. Now, we change the pulse phase to y and issue the next pulse, the magnetization rotates onto the -x axis (see theory section). The y channel now 'sees' a sin function signal and the x channel a inverted cosine function signal. The y channel is stored in memory B and the x channel signal is inverted and stored in memory A. Thus the same signal is stored in each location but has travelled through the two different receiver channels on two successive scans. The quadrature glitch results from a dc offset and can be effectively suppressed by adding two more phase changes to the cycle. Scan 3 has a pulse phase of -x and scan 4 a pulse phase of -y. The signals from scan 3 are inverted and stored in memory A and B. The x signal from scan 4 is stored in memory B and the y signal from scan 4 is inverted and stored in memory A. This has the effect of eliminating signal due to dc offset from scans 1 and 2. This entire phase cycling procedure is refered to as the CYCLOPS phase cycling procedure (figure 8.). In practice, on the Bruker spectrometer we tend to scan in multiples of eight and simply use two CYCLOPS cycles bundled into one large phase cycling routine.
Figure 8. CYCLOPS Phase Cycle
This is accomplished by passing heated or cooled air through the probe. To go above ambient temperature the air is simply heated by a heater coil until the desired temperature is reached. A thermocouple senses the temperature and feeds this information back to the temperature controller. To go below ambient tempterature requires the use of a cold gas, usually evaporated from liquid nitrogen, in place of the air. The temperature of the sample in the probe drops until the set point is reached and then the heater coil turns on to prevent further temperature decrease.
Calibration is done with methanol at or below room temperature and ethylene glycol above room temperature. One measures the difference in chemical shifts between peaks and relates this to previously published data for these compounds.
There are two sources of phase error in the spectrum that results from a transform of raw data. First, the phase sensitive receivers aren't usually set at exactly 90o from each other. This introduces a frequency independent phase error to the spectrum (in other words, the same error to every frequency in the spectrum) and can be corrected by the 'zero' order phase correction process in which the same correction is applied everywhere in the spectrum. Second, during the dead time mentioned earlier, the spins are evolving and becoming out of phase with each other in a frequency dependent manner. The higher the frequency the more out of phase the signal is after the dead time. To correct for this, we do a frequency dependent phase correction. In other words the amount of correction is dependent on where in the spectrum it is being done. No correction is applied at the 'pivot' point and more at points further from this point. This is the 'first' order phase correction.
Since the phase sensitive detectors are 90o degrees out of phase (theoretically) we can model the signals with respect to each other as real(R) and imaginary(I) signals. Ideally, we want, say, detector A to give us the real signal and detector B to give us the imaginary signal:
R = A
I = B
However, since this is not the case in practice, as mentioned above, what we actually see at each detector is a mixture of real and imaginary signals, as though the real-imaginary coordinate system has been rotated by some angle, f:
R = Acos(f) + Bsin(f)
I = Asin(f)- Bcos(f)
It is possible to separate the A and B components by linear combination or R and I:
A = Rcos(f) + Isin(f)
B = Rsin(f) - Icos(f)
This is the essence of the zero order, frequency independent phase correction. The first order correction is applied by adjusting the parameters of the frequency dependent equation:
f(v) = a + bv
where v is frequency and a and b are the equation parameters.
When the sample is inserted into the probe we can receive a deuterium nmr signal from the deuterated solvent (you did use a deuterated solvent didn't you?). The spectrometer has a 'little' independent spectrometer whose only function is to do a deuterium nmr experiment by scanning the magnetic field back and forth, looking for a deuterium resonance signal. This is what you see in the lock window. We then 'lock' the spectrometer onto this signal. What this does is compare the deuterium signal to a reference frequency and make any changes in the field that might be necessary to make the field/frequency ratio constant. Obtaining a highly stable reference frequency is relatively easy to do and so maintaining the field/frequency ratio results in very low field drift during the nmr experiment. Also, remembering that the nmr resonant frequency is dependent upon field strength and knowing that the field/frequency ratio is constant for any given solvent means that a reference compound in the sample, such as TMS or DSS is not necessary. By locking onto the deuterium resonance for, say, D2O you will have to set the field to the appropriate value for D2O which means that the resonances in the sample will always occur in the same place in the spectrum, provided you have correctly set the offset frequency (which is done for you when you read a parameter file). You need only do a sample with a reference compound once, when the spectrometer is first installed. Newer spectrometers have digital lock in which it is not necessary to adjust the field and read a parameter file.
When it is not possible to use deuterium as the lock nucleus, when you are doing deuterium nmr experiments, it is possible to use fluorine as the lock nucleus. It is also quite possible to run the spectrometer unlocked, however field drift limits the time that this type of experiment can be done to an hour or two. Running unlocked overnight will result in broadened signals due to field drift. If you want to do this type of experiment remember to push the 'sweep off' button on the scm to turn off the deuterium lock sweep, otherwise the field will be swept during your experiment and your results will be scrambled!
The function of the probe is to efficiently transfer the energy of the rf pulse to the sample where the spins are and to receive the signals coming back from the spins after the pulse. From an electronic point of view the probe is just another impedence in the system and from the theory of impedences and power transfer it is necessary that the impedence of the probe and the transmitter be matched for maximum power transfer to occur. This is important largely in decoupling applications where the decoupled nucleus, usually 1H, is perturbed by a series of low power 90o pulses and in the reception of signals where the maximum signal coming from the sample is desired. Also, to apply accurate 90o pulses the probe's impedence should be matched properly.
Figure 9. Tune and Match Circuit
Two parameters must be adjusted, the tuning and the match. The tuning adjusts the resonant frequency of the coil and the match adjusts the impedence match to the external circuit. The circuit is sensitive enough that changing samples will change these parameters somewhat. Most often the change is very small and we don't generally tune and match for each sample (although there was a time not so long ago ...). In figure 9, adjusting C1 tunes the circuit to the proper resonant frequency and C2 adjusts the impedence to match the external circuitry. These are not independent adjustments, changes in one affect the setting of the other so it is necessary to adjust them iteritively until the proper setting is reached. Once the probe is tuned, usually only minor adjustments are needed from sample to sample since most samples don't affect the probe impedence much. Highly concentrated ionic solutions are an exception to this ... each sample should be tuned and matched.
Adjusting these parameters can be accomplished in a several ways. First, an rf bridge, a sweep generator and an oscilloscope can be used to look at the resonant frequency and the match. Some spectrometers are equipped with this type of tune/match measurement in software making it a relatively easy adjustment. Second, a directional coupler and a reflection meter to measure reflected power can be used. If the probe is not properly tuned then some of the transmitted power will be reflected back to the transmitter. A minimum of reflected power is an indication of a properly tuned probe. The third method is to use a 'wobble' generator. Here you can view the effect of tuning and matching on the spectrometer's computer screen and is the most convenient way of accomplishing the task.