M. Henner, P. Levoir and B. Ancian lnstitut de Toooloaie et de Dvnamiaue des . Systemes de I'UniversiteParis VII Paris, France
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An NMR Spectrometer-Computer Experiment Demonstrating how signal averaging influences signal-to-noise ratios
It is well-known that, in nmr spectrometry, signal averaging can serve to enhance the signal-to-noise ratio, SIN, by a factor of .\/;;where n is the numher of accumulations ( I ) ;however, the instrument used often lacks stability when the signals are accumulated over a long period of time. In order to avoid spectrometer drift and, more importantly, to demonstrate the exact manner in which signal averaging can influence signalto-noise ratios in nmr spectracopy, we have conceived an nmr spectrometer-computer interface experiment in digital acquisition of spectroscopic data, intended for students nearing the end of a master's degree in physical chemistry. Interface A simple interface system (block diagram, Fig. 1) between an nmr spectrometer (Jeol-C-60-HL) and a PDP-8 computer (Dieital Eauinment Corn.) , " . . . is described. Its desien is such that it can be adapted to any kind of nmr spectrometer (provided it incor~oratesa dieital recorder to monitor maanetic field sweep) and to any i i n d of microprocessor (a ma$ point in its favor eiven the low cost and readv availability of the latter). The command unit (Fig. 2) has two decimal counter chains (2) (7 X SN 74190); the first one counts the pulses required
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NMR JEOL C60-HL
NMR
interface analog
signal
Ampourput
,,nit
jLmPmTy 2
interface: command unit
8 bits
"lock 5
Figure 1. Interface block diagram
684 / Journal of Chemical Education
computer
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per scan, and the second one (commanded hv three-decade thumbwheel switches (0 < n < 1000)) counts-the number of accumulated signals up t o n . This unit synchronizes recorder scan and computer scan, selects n, orders the quick return (15s) of the recorder carriage by means of a 555 monostable after each scan. and halts sienal accumulation after n scans. The analog unit (Fig. 3) has an RC low-pass filter (2 Hz cutoff freauencv) which minimizes hieh freouencv noise from the nmr signid in urcordance with sample thrurern ( B ) , therehy nermittioe sienal amolificarion in a 0-10 V ranee comnatible kith the ~ ~ ~ c o n v e rvia i otwo r operational amplifie;s. The digital recorder (Fig. I), whose stepping motor is driven by a built-in clock whose signal is the time base for the interface, simultaneously moves the pen carriage and scans, via a potentiometer, the magnetic field. Memory capacity is respected by taking only one reading per five pulses, thereby reducing the numher of steps along the X-axis to 1120 and setting the interval between each pulse at 0.5 Hz, i.e.. 0.01 m . .m , a dieital restrlution generally sutficient for ruutine nrnr rneasurern~nu. At each pulse the nmr signal is dixitnlized with X - t i t accu. racv. All interface components are provided in the laboratory. I t is left to the student to make the annronriate .. . connections. select the proper conditions for operation, and verify that the interface functions properly.
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Figure 2. Command unit
signal 9 KO
amplified NMR signal totheA/D merter
1 KO
INPUT AMPLIFIERS 3 W"
OUTPUT ATTENUATOR
output 0.+1omv into the recorder Figure 3. Analag unit
&0 Trigger
THRESHOLD
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Figure 5. 100 Averaged spectra of 1% ethylbenzene in CCI, (a) with driA correction (upper): (b) without drift correction (lower).
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Figure 4. Flow diagram: Acquisition and dataprocessing routines(fen)and data reduction routine (right).
Software
The experimenters' program, which should respect the flow-chart (Fig. 4), must include the following considerations: (1)the rate at which the numher n of spectra are to he timeaveraged, (2) data storage, (3) drift correction, and (4) data reduction. For the PDP-8, we recommend writing a 700 word program for a system of 4K core memory words; 1120 data points should be used as a buffer for data acquisition, with 2240 available for double precision averaging. At the start of the experiment, the operator defines n and inputs it into the computer via the teletype and triggers the acquisition. The data prorrssing routine should be designrd to perform spectrometer drift currection w d double precihion addition (which dramatically enhances the dynamic range of nrcurnulations to 2"'in the wesent mse), thereby allowinr the automatic plot of the averaged spectra. The data reduction routine should be designed to perform MNOISE and RMS
Figure 6. Plot 01 SINfor aromatic protons versus &for CClr.
1% ethylbenzene in
Noise calculations and integration of the data points of each peak. Data output should include the peak index (1 for the first low field peak), its memory index, its maximum intensity and its area. Spectrometer Drift Correction
We suggest correcting spectrometer drift by (a) seeking the maximum intensity peak of the first incoming spectrum and recording its position in the memory; and (h) seeking the maximum peak of each following spectrum and shifting its Volume 56, Number 10, October 1979 / 685
Signal-to-Noise Ratio S/N at the aromatic protons of 1% ethylbenzene in CCI,
Number of experiments
Number of Accumulation n
Signal Amplitude
position to coincide with that of the first spectrum before its storage in the ~reviousreference memory. (Cf. Fiz. . 5 as example of drift effects).
RMS Noise
We suggest analyzing the dependence of the SIN ratio for aromatic protons upon n (\/;; = 1,2,. . . ,101 by using a 1% ethylbenzene solution in CCI4 as a spectrometer sensitivity test, as this is used by mast manufacturers. Experimental conditions could he, for example, RF power = -60 dh, RF gain = 4, modulation index = 4-10, and AF amplitude = 4 X 1.It should, however, be noted that any samplecan he used to test the \/;;rule, and that experimental conditions depend on the chosen sample and on the spectrometer. Mean Noise
The simplest way to determine signal magnitude, S , is t o employ a mean noise threshold ( 4 ) ,MNOISE, beyond which all dataare assumed to he peaks (rise or fall). . .
where Piand Pi-,are adjacent points, and N is the accumulated number of noise points. S is thus determined after integration by addition of the data points of each peak. R M S Noise
RMS Noise voltage is calculated from the noise power ( I ) , PN,
Standard deviation
in which N(u) is the noise a t variahle frequency v , and A"is the mean value of N(v) in the frequency interval from "1 to vn. I t is suggested that repetitive measurements of background signal a t an appropriate frequency he taken and that the standard deviation he n m p u t c d i n urdrr tc, o h ~ n l nI h e nc.1.e \.due h ~ 1r , ~ $inrlt h r u n and nrrrngr >Irr
