In the Laboratory
Fourier Transform Nuclear Magnetic Resonance Spectroscopy Experiment for Undergraduate and Graduate Students Matthew A. Doscotch, John F. Evans, and Eric J. Munson* Department of Chemistry, University of Minnesota, 207 Pleasant St. S.E., Minneapolis, MN 55455
Commercial Fourier transform (FT) NMR spectrometers have been incorporated into many analytical instrumentation courses to teach students about FTNMR spectroscopy. However, what students learn from using a commercial NMR spectrometer is often limited to placing an NMR tube into a probe that is hidden inside the superconducting magnet dewar, typing several commands into a computer attached to the console, and observing the resulting spectrum on the computer monitor. In few if any of these courses is the NMR spectrometer disassembled to show the students its basic components, such as the frequency synthesizers, mixers, and switches. To alleviate this situation, we have designed an FTNMR spectrometer such that each of the components is self-contained and visible to the students. The units are connected by coaxial cables, which allows the students to easily modify the configuration of the spectrometer, for example by changing phase delay cables. This is in contrast to other PC-based FTNMR spectrometers that have been proposed as teaching instruments (1), whose components are still located on one or more circuit boards inside the computer, and which do little to instruct the students about how the spectrometer works. The cost of the spectrometer described here is comparable to these PC-based instruments with the added advantage of accessibility of the spectrometer components to the students. The total cost of constructing the spectrometer, excluding the probe and magnet, and provided that a suitable Macintosh computer is available, is approximately $20,000. The spectrometer is currently used in an undergraduate instrumental analysis laboratory course as well as a graduatelevel analog instrumentation course that has a lab component associated with it. The FTNMR spectrometer used for these experiments is shown in Figures 1 and 2 and depicted in the block diagram in Figure 3. The spectrometer itself has been divided into five sections for teaching purposes: transmitter, probe/matching network, receiver, audio filters, and pulse generation/data acquisition. These sections are discussed in detail in the Experimental section. The spectrometer incorporates most of the features found in current commercial spectrometers, including heterodyne operation using an intermediate frequency (IF) of 20 MHz; four-phase generation in the transmitter of 0, 90, 180, and 270° phase shifts; and quadrature detection of the receiver signal for a factor of 1.41 increase in signal-to-noise (S/N) ratio. In the first part of the undergraduate-level experiment, students became familiar with the operation of the software that controls data acquisition and spectral processing, and the experimental parameters that are adjusted when acquiring and optimizing a spectrum. They examined various portions *Corresponding author.
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of the spectrometer circuit to gain an understanding of the function of each component in an FTNMR spectrometer. They also learned how to operate the spectrometer, including shimming the magnet and phasing a spectrum. In the second part of the experiment the amount of ethanol in an unknown
Figure 1. Photograph of the FTNMR spectrometer showing the permanent magnet (foreground) and main component board (center). The frequency synthesizer, pulse programmer digitizer, and computer are located on the lab bench (right center). The individual sections of the spectrometer are divided by colored tape.
Figure 2. Photograph of an individual component module with its operational description.
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ethanol/water sample was quantitatively determined. Students were required to plan the procedure for the determination of the unknown. In the graduate-level analog instrumentation course, students were given the same components that were used in the undergraduate course, but these were not connected, and they were required to construct the spectrometer in two 4hour laboratory sessions. Some introductory information was provided and the task of constructing the five sections of the spectrometer was divided among the students. The demonstration of the success of the project for the graduate students was the observation of a phase-cycled NMR signal of H2O. Experimental Procedure
Equipment The permanent magnet and probe were obtained from a Perkin-Elmer R-24B nuclear magnetic resonance spectrometer that was being discarded. Permanent magnets are becoming available as many institutions replace old continuous-wave systems with Fourier transform spectrometers equipped with superconducting magnets. The magnet has an approximate
field strength of 1.4 tesla and an operating frequency of about 60 MHz for protons. The spinner housing, magnet insulation, and shim controls should be kept in addition to the probe and magnet to avoid difficulties with spinning the sample, magnetic field drift, and obtaining maximum field homogeneity, respectively. Golay shim controls similar to those used in the R-24B were reconstructed from the original spectrometer schematics for about $300. The following is a listing of components purchased from Mini-Circuits (Brooklyn, NY) that were used to construct the spectrometer. The cost of each component with either BNC or SMA connections was ca. $50. Each component listed is followed by its model number in parentheses and then a brief description of its characteristics. •
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• AF - Audio Filters PD - Phase Detectors PS/C - Power Splitter/ Combiner
X
•
- Amplifier
Receiver Section
- Diodes
Tecmag Aries Unit 0-100 kHz
AF
AF
Doubler 10 MHz Frequency Synthesizer
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PD
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Transmitter Section
Filter
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•
PS/C 0/0
21.4 MHz BP
• 20 MHz
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40 MHz (variable)
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Probe and Matching Network
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λ/4
Cable 60 MHz
Filter 60 MHz BP
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Probe/ Magnet Shim Controller
Figure 3. Block diagram of the FTNMR spectrometer.
Frequency doubler (GK-3): doubles the frequency of the input signal but reduces the strength of the signal by several dB. The frequency doubler has an input range of 0.05–150 MHz and an output range of 0.1– 300 MHz. Single pole double throw (SPDT) switch (ZYSWA-250DR): one signal input and two outputs. Gating of the switch is controlled by the pulse programmer. The switches have 50 Ω of impedance at all times. SPDT switch (ZYSW-2-50DR): the same as the ZYSWA except that the open switch has infinite impedance, which helped to eliminate noise. Both types of switches have a typical switching time of 1.5 nanoseconds. 2-Way power splitter/combiner (ZCS-2-1): either equally divides the RF input power, generating two outputs with the same amplitude and phase, or combines two input signals into one output. In the former case, the two signal outputs are highly isolated. 4-Way PS/C (ZCS-4-1): the same characteristics as the 2-way PS/C but there are four outputs or inputs instead of two. 2-Way PS/C (ZCSJ-2-1): the same characteristics as the other 2-way PS/C, except the two output signals consist of a 0° and a 180° phase shift of the input signal. Frequency mixer (ZAD-1H): two signal inputs and one output. The output consists of the sum and the difference of the input frequencies; could also be used as phase-sensitive detectors. Bandpass filters (BBP-60 and BBP-21.4): center frequencies of 60 and 21.4 MHz with bandwidths of 49.8–70.5 and 17.9–25.3 MHz at 3 dB of attenuation, respectively. Attenuators (CAT-20, 10, 6, 3): provide 20, 10, 6, and 3 dB of attenuation as needed.
Control of the logic lines to the switches and digitization of the NMR signal was accomplished using an Aries unit (Tecmag, Inc., Houston, TX). The Aries unit, costing approximately $15,500, was interfaced to a Power Macintosh 7100/80 computer. The Macintosh computer ran the data acquisition software, MacNMR 5.2 (provided with the Aries unit), for Fourier transformations of the acquired transients. The frequencies used in the spectrometer circuit were generated by a used Programmed Test Service (R&D Electronics, Cleveland, OH) 160 frequency synthesizer purchased for ca. $2,000 with a frequency range of 0.1–160 MHz. Frequency control was provided by the computer through the Aries unit. Amplification was done using modular home-built amplifiers (Motorola; MHW-592) that increased the signal
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by 35 dB. The amplifiers ($50 ea.) had 50 Ω of impedance and a bandwidth of 5–400 MHz. The 25-dB low noise preamplifier ($200) was obtained from Advanced Receiver Research (Burlington, CT) and had a narrow bandwidth centered at 60 MHz. Fifty-ohm RG-58 coaxial cables of 2, 4, 6, 8, and 10 feet were made in-house using either BNC or SMA connectors. Alternatively, pre-made cables, connectors, and other equipment necessary to construct coaxial cables can be purchased from Pasternack Enterprises, Irvine, CA. Approximately 50 cables were necessary to connect the components, at a cost of about $500. All components had BNC connections except for the switches, which had SMA connections. Frequency Devices Inc. (Haverhill, MA) model 844P8B4 audio filters ($500) with a frequency range of 100 Hz to 25.6 kHz were used to construct computer-controlled audio filters from circuit diagrams provided by Tecmag, Inc. Home-built series diodes and diodes to ground were used. It should be noted that in the graduate-level course the students were required to find their own information on audio filters and diodes, and then construct those components. A general power supply ($300) providing 5 and 15 volts of power was built for the switches, amplifiers, and audio filters. The small package components (Mini-Circuits and amplifiers) were mounted on a sheet of plywood, along with labels that describe the component, frequency, and purpose of each stage of the circuit (see Figs. 1 and 2). The samples were spun by connecting the probe to a tank of compressed air. Absolute ethanol and deionized water were used for unknown samples.
Description of Spectrometer Transmitter The transmitter section began with a frequency synthesizer, which generated the two frequencies used in the spectrometer (see Fig. 3). The frequency synthesizer produced a sine waveform from 0.1 to 160 MHz and could be controlled to within 1-Hz resolution. The frequency synthesizer also had a built-in stable frequency reference source that operated at 10 MHz. The fixed 10-MHz signal, in addition to providing a reference source for the frequency synthesizer, was also frequency-doubled to 20 MHz and used as the intermediate frequency (IF). The IF signal was filtered with a 21.4-MHz bandpass filter, then amplified and sent to a 4-way power splitter/combiner (PS/C), which produced four signals of equal phase and amplitude. Two of these signals were sent to the phase-sensitive detectors (PD) in the receiver circuit. One of the remaining signals was sent to a single-pole doublethrow switch (SPDT). The input signal was directed to either of the two outputs under the control of the Aries pulse programmer unit (see the section entitled Pulse Generation/Data Acquisition). Attached to the output of the switch were two cables of different lengths such that one cable was λ/4 (at 20 MHz) longer than the other, which provided either a 0 or 90° phase shift at 20 MHz. The signal was then redirected down a single coaxial line using a PS/C. A second switch directed the output to another PS/C unit, which performed either a 0 or 180° phase shift depending on the selection of input ports. Using these combinations it was possible to generate a 0, 90, 180, or 270° phase shift depending upon the signal path through the switches. The signal was then sent to a frequency mixer. The mixer took the IF and the second frequency generated by the frequency synthesizer and mixed 1010
them together, producing the sum and difference of the two frequencies. Since the second frequency was approximately 40 MHz (this was the frequency that can be changed in increments of 1 Hz from 0.1–160 MHz), the two frequencies that emerged from the mixer were approximately 20 MHz (40 – 20) and 60 MHz (40 + 20). Finally, the signal passed through another switch after the mixer, and then through a 60-MHz-bandpass filter, which eliminated the extraneous 20MHz signal. Probe and Matching Network The purpose of the matching network will be explained in detail, because its operation may be less familiar to many readers. A more detailed description may be found in Fukushima and Roeder (2). The signal that entered the matching network passed through a set of crossed diodes in series. Crossed diodes are simply two diodes that are connected in opposite directions. Crossed diodes allow signals greater than about 0.5 V to pass through them, but greatly attenuate signals less than 0.5 V. The series diodes served to block any of the signal that might continue to pass through the amplifier and into the probe after the switch is turned off. Since the detected signal was on the order of microvolts, any signal that leaked through the switch from the transmitter side would have overwhelmed the signal from the sample. As the signal from the amplifier was much greater than 0.5 V, it passed through the diodes unaffected. When the excitation pulse was turned off, the signal was much less than 0.5 V, and any residual signal was further attenuated by the diodes. Often it is necessary to connect several pairs of diodes in series to ensure adequate suppression of signal leaking through the transmitter. Crossed diodes that were connected to ground were used later in the matching network to protect the preamplifier. Because the preamplifier was easily saturated, it was necessary to shield it from the pulse generated by the high-power amplifier. When crossed diodes are connected to ground, any signal that is greater than 0.5 V goes to ground, whereas signals less than 0.5 V (such as an NMR signal) see the diodes as an open circuit and continue on to the preamplifier. A quarter-wave cable, employed as an impedance transformer, was used to properly route the signal to the probe and preamp. For the frequency corresponding to the quarter wavelength of the cable, if one end of the cable is at zero resistance (or shorted), the other end appears to be at infinite impedance (or open circuit). At the end closest to the series diode, the quarterwavelength cable appeared as infinite resistance during the high-power pulse and zero (or 50 Ω) for the NMR signal coming from the probe. Diodes to ground were placed at the end of the quarter-wavelength cable to produce the infinite resistance. For high-power signals (> 0.5 V), the diodes passed the signal to ground (short circuit), which transformed at the other end of the quarter-wave cable to an infinite impedance. The high-power signal, given a choice between a 50-Ω (the probe) and infinite (the preamp) impedance, delivered most of its power to the probe. When the NMR signal (microvolt level) returned from the probe, the series diodes appeared as infinite impedance, and the quarter wavelength cable appeared as 50 Ω impedance, so the NMR signal passed to the preamplifier. As a quarter-wavelength cable is an essential part of this spectrometer, it is important to understand how to construct
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and test one. The equation to roughly calculate the proper length of the cable is: cable length in meters = 180/(4 × resonance frequency in MHz)
For example, for a quarter wavelength cable at 60 MHz, the length is 180/(4 × 60) = 0.75 m, or about 29 inches. This equation is typically accurate to within 15%, which is adequate for the matching network. To test the length of the cable, a frequency source and an oscilloscope are required, both of which are capable of operating at the desired quarter-wavelength frequency. The PTS synthesizer can be used as a frequency source. The circuit is connected as follows. Two cables, one from the PTS and the other from the input of the oscilloscope, are connected to a BNC three-way “T” connector. One end of the quarter-wavelength cable is connected to the third port (a barrel connector may be necessary). Since the unconnected end of the quarter wavelength cable is at infinite impedance, the end connected to the T connector should be at zero impedance (i.e., ground), and no signal should be observed at the oscilloscope if the frequency from the PTS corresponds to the quarter wavelength for the cable. The frequency can be changed on the PTS to determine the minimum signal intensity, and the quarter-wavelength cable length adjusted to correspond to the desired frequency. Receiver The receiver circuit was one of the most critical parts of the NMR spectrometer because it must amplify a signal from the nanovolt–microvolt level to the 1–10 V level without introducing significant noise. The most important component in the receiver circuit was the 25-dB preamplifier, because it determined the noise level of the entire circuit. Crossed diodes to ground were placed before the preamplifier to protect it from high power pulses. After the preamplifier, a switch was used to protect the rest of the receiver circuit from the signal generated during the high-power pulse. The 60-MHz signal was filtered with a 60-MHz-bandpass filter and then mixed with the signal from the frequency synthesizer (40 MHz), and the resulting 20-MHz signal was amplified twice and filtered. At this point the signal was at the 10–100-mV level. The NMR signal was split into two components for quadrature detection, with one line representing the sine component and the other the cosine component. The signals passed through phase detectors, which mixed the signal down into the audio frequency range (0–100 kHz). Audio Filters High-frequency noise was strongly attenuated from the audio frequency signal of each channel with two 6-pole Butterworth low-pass filters. The filters were computercontrolled with a cutoff frequency variable discretely from 100 Hz to 25.6 kHz in 100-Hz increments. Pulse Generation/Data Acquisition The incoming signal was digitized using two digitizers in the Aries unit, both capable of operating at 1 µs/point. They were 12-bit digitizers, which meant that they could determine the amplitude of a signal within 1 in 212, or 4096 levels. The logic signals used to turn the switches on and off were provided by a pulse programmer, also located within the Aries unit. The timing resolution of the pulse programmer was 0.1 µs. Frequency control of the synthesizer was also provided via the Aries unit.
Procedures Undergraduate Course Students were instructed to examine the spectrometer circuit using the flow diagram (Fig. 3) as a guide. A basic overview of the system software (MacNMR 5.2), which controlled the Aries unit, was provided and a previously recorded free induction decay (FID) was made available so the students could practice signal processing. Operations such as baseline correction and Fourier transform of a FID were conducted to increase student familiarity with the software. Several other operations were conducted as well, including phasing, peak picking, determining signal-to-noise ratios, setting a reference frequency, and integration on a processed spectrum. The students tended to appreciate the latter parts of the experiment more if they took some time at the beginning to become familiar with the program. The importance of shimming (increasing the homogeneity of the static field of the permanent magnet) was stressed by having the students note the difference in line widths for water with the Golay shim controls turned off and then on. The students then adjusted the shims to further increase resolution. The controls were initially set to values close to the correct values (for maximum homogeneity) before the students arrived in lab, to decrease the amount of time spent shimming the magnetic field. One problem faced by the students was magnetic field drift due to temperature fluctuation. This caused changes in spectral line width over a short periods of time, making it more difficult to signal-average effectively. The goal set for the students was to achieve a symmetric peak shape with a full width at half-maximum (FWHM) of 8 Hz and a baseline width of no more than 40 Hz for the water resonance. One planned future project for the graduate level course is the construction of a deuterium lock system that can be used to eliminate the field drift problem. Given how the lock systems worked on the older CW instruments, it is unlikely that a lock built for a CW spectrometer will work on an FT instrument. A description of a lock channel modeled on a pulsed NMR spectrometer is describe in a paper by Hoult, Richards, and Styles (3). We intend to build a lock channel for our spectrometer based upon the information presented in this paper. We anticipate that it will cost an additional $3,000–$5,000 to add a lock channel, depending upon how the channel is designed. This lock channel should be suitable for both permanent magnet and electromagnet systems. After shimming the sample the students began studying the effect of modifying the acquisition parameters. The parameters examined were the observed frequency, spectral width, number of complex data points, and number of transients averaged. Examination of these parameters demonstrated the importance of proper setting of these values to optimize the resolution and the signal-to-noise ratio of the acquired spectrum. Next, the students modified the spectrometer circuit, using the same water sample to compare the effects of each change. They were asked to describe the effects of the changes made on the signal, explaining why the effect was observed. Several aspects of the spectrometer circuit and NMR principles were examined, including: amplification, filtering, quadrature detection, phase cycling, and the quarter-wavelength cable. Amplification. The signal-to-noise ratio (SNR) of the transformed FID of water was determined and recorded. The
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25-dB preamplifier located in the receiver section of the circuit was bypassed. This was done by disconnecting the input and output of the amplifier and connecting the two cables with a barrel connector. The circuit was reconnected to its original configuration. A 6-dB attenuator was added to the output of the 35-dB amplifier in the transmitter section of the circuit. The SNR was determined and compared to the SNR of the first acquisition. The circuit was reconnected to the original configuration. Filtering. The cutoff frequency of the audio filters was increased to 5, 10, and 25 kHz from 2.5 kHz without changing the spectral width and the change in the SNR was observed. The audio filters were set back to 2.5 kHz. The 21.4MHz bandpass filter located on the output of the frequency mixer in the receiver section (it is between the receiver gate and the 25-dB amplifier) was removed from the circuit. A spectrum was acquired and the SNR was compared to the original SNR. The 21.4-MHz bandpass filter was put back in the circuit. The 60-MHz bandpass filter on the same frequency mixer was removed. A spectrum was acquired and the SNR was compared to the original SNR. The 60-MHz filter was put back in the circuit. Quadrature Detection. The integral for the water peak was determined. The students were asked to notice a small peak on the opposite frequency side of the spectra at exactly the same frequency offset from the carrier frequency as the intense water absorption. This peak, called a quadrature image, was due to imperfect quadrature detection. Next, the imaginary portion of the complex data was viewed along with the real. A region of the FID was expanded until the oscillations of the signal were clearly visible. The students were asked to notice that the real and imaginary FIDs were 90° out of phase with one another, which is a necessary condition of quadrature detection. The 90° phase shift was created by the different cable output lengths on the power splitter/combiner before the phase detectors. The cable connected to the input of one of the phase detectors was disconnected. A 4-foot section of cable was added to the disconnected cable and the new cable was connected. After acquiring a new FID, the difference in phase of the real and imaginary FIDs was observed. The FID was transformed and the integral of the water peak was determined and compared to the original integral. The circuit was reconnected to the original configuration. The output on one of the phase detectors was disconnected. A FID was acquired. The FID was transformed and the students were asked to describe the effect of the change on the signal. The circuit was reconnected to the original configuration. Phase Cycling. The dc offset was misadjusted for either the real or imaginary channel and one scan was acquired. The students were asked to notice that the FID for either the imaginary or the real channel was not centered about zero. Next, the FID was transformed. The students were asked to notice the peak in the center of the spectrum. This peak, called a center glitch, arises from a dc offset in one or both channels. Next, two scans were acquired with the transmitter and receiver in the second scan 180o out of phase compared to the first scan. The FID was now centered about zero for both channels, and no center glitch in the transformed spectrum was observed. The gain of either the real or imaginary channel was altered so that the two channels had different amplitudes, and one scan was acquired. The students were asked to notice two peaks, the center glitch and the quadrature image. 1012
Four scans were acquired using 0, 90, 180, and 270° phase shifts, which corresponds to CYCLOPS phase cycling. The resulting spectrum had neither a center glitch nor a quadrature image. Finally, the logic lines for the 0/90 and 0/180 phase shifts were reversed, and four scans were averaged. The amplitude of the FID was noted after each scan. The students were required to diagram a switching scheme that creates pulses along the x, ᎑x, y, and ᎑y axes using the components found in the spectrometer circuit, and explain the effect of reversing the logic lines for the 0/90 and 0/180 phase shifts. Signal Averaging. The SNR was determined for 4 acquisitions and compared to the SNR for 1 acquisition. The results were compared to the theoretical SNR change, which is the square root of the number of acquisitions. Quarter-Wavelength (λ/4) Cable. The λ/4 wavelength cable, which was nominally 30 inches (see calculation of length of λ/4 cables in Probe and Matching Network section), was replaced by a cable that was significantly longer (48 inches) than the proper λ/4 length, but significantly shorter than λ/2. The students were required to comment on the difference in signal intensity. The consequence of changing the cable length is that part of the transmitter power is being routed through the diodes to ground and less is going to the probe. The preamplifier is unaffected by this change because the diodes limit the power seen by the preamplifier to a few volts, regardless of the input voltage. The original cable was put back into the circuit. Quantitative Determination of the Amount of Ethanol in a Liquor Sample. The students received an unknown sample that contained ethanol and water. It was their responsibility to develop an experimental procedure for determining the amount of ethanol in the sample. They were required to think about the problems encountered when analyzing a mixture of this type, including what peaks and multiplets would be seen for the different resonances. A spectrum of a 50:50 v/v ethanol–water solution is shown in Figure 4. It was particularly important to stress the need to wait a period of 5T1 (the spin-lattice relaxation time) between pulses to ensure full relaxation of the spins and quantitative results. An ethanol-to-
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ppm Figure 4. Representative 1H FTNMR spectrum for a 50:50 ethanol– water solution. Eight transients were averaged.
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water ratio of 49.5:50.5 was determined from integration of the hydroxyl and methyl resonances of the spectrum. Further work is being conducted to eliminate the noise and spinning sideband problems seen in Figure 4. An internal reference standard is necessary to properly determine the chemical shift of the resonances. The chemical shift is strongly dependent upon the χEtOH of the unknown mixtures (4 ). Although an internal standard was not used, one that is common to ethanol– water solutions is sodium 2,2-dimethyl-2-silapentane-5sulphonate (5).
Graduate Course The ultimate goal in this course was to construct a working spectrometer in two weeks from the individual components (mixers, amplifiers, cables, etc.) provided. By dividing the spectrometer into five sections the amount of work required by each student or group of students was consistent with the time allotted. Each group worked separately on their section and then tested each section before constructing the spectrometer. There were a few additional differences between this experiment and the undergraduate experiment. The group that was assigned to the audio filter section was required to build the low-pass filters that eliminate the high-frequency noise above the Nyquist frequency. The students were advised that the filter should have a sharp cutoff, linear phase response across the entire spectral width, and constant amplitude. The group assigned to the probe matching network was required to build the series diodes and diodes to ground, as well as make a quarter-wavelength cable. A phase-cycled signal from water was required for successful completion of the experiment. We have used this experiment as the final project in the graduate level analog instrumentation course for two years, and have found it to be very successful.
Conclusion The experiments described provided undergraduate and graduate students with an opportunity to examine the internal components of a working NMR spectrometer and to use the spectrometer to understand the basic principles of NMR. The accessibility of these components is a major advantage of this spectrometer. Many of the common techniques and principles used in NMR spectroscopy can be demonstrated by changing the configuration of the spectrometer. The students learned about data acquisition parameters and spectral analysis techniques that are common to all NMR instruments. The undergraduate students also had the opportunity to solve a chemical problem with NMR by determining the amount of ethanol in an unknown sample. The graduate-level course allowed the students to gain a deeper understanding of the electronics associated with an NMR spectrometer through the construction of the spectrometer. Acknowledgments We would like to thank Peter Carr for helpful discussions, Mark Zell for help revising the manuscript, and the University of Minnesota for generous support. Literature Cited 1. Job, C.; Pearson, R. M.; Brown, M. F. Rev. Sci. Instrum. 1994, 65, 3354–3362. 2. Fukushima, E.; Roeder S. B. W. Experimental Pulse NMR: A Nuts and Bolts Approach; Addison-Wesley: Reading, MA, 1981. 3. Hoult, D. I.; Richards, R. E.; Styles, P. J. Magn. Reson. 1978, 30, 351–365. 4. Mizuno, M.; Miyashita, Y.; Shindo, Y.; Ogawa, H. J. Phys. Chem. 1995, 99, 3225–3228. 5. Harris, R. K. Nuclear Magnetic Resonance Spectroscopy; Longman: New York, 1986.
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