Linear envelope detection for pulse NMR

JOURNAL

OF MAGNETIC

RESONANCE

17,344-349 (1975)

Linear Envelope Detection for Pulse NMR L. J. BURNETT

AND

C. R. WINTHER

Physics Department, San Diego State University, San Diego, Califovnia 92182 Received October 3,1974 A linear envelope detector, suitable for operation at frequencies commonly used in pulse NMR experiments, is described. The detector exhibits 0.5 ‘A linearity over the range O-7 V output and operates with rf inputs of 100 mV or less. An active six-pole Butterworth filter with a wide range of selectable cutoff frequencies is included for signal-to-noise ratio optimization. Critical portions of the circuit utilize inexpensive commercially available modules, thus minimizing potential difficulties in construction. INTRODUCTION

A common problem in pulse NMR relaxation measurementsoccurs when a linear phase-coherentdetection systemis used in conjunction with a current regulated magnet system. Small drifts in the DC magnetic field, H,, cause changesin the NMR carrier frequency, o. = yH,, and produce beats in the free induction decay, FID, when detected.The frequency of thesebeats,6 = (o - oo), where o is the transmitter oscillator frequency, changeswith tim e making a measurementof the m a g n itude of FID difficult and offsetting somewhat the convenienceof the phasedetector’s linearity. As relaxation times and self-diffusion coefficients are commonly determined from measurementsof FID m a g n itude, these small drifts in Ho can turn an essentially simple measurement into a time-consuming chore. This occurred in our laboratory while performing routine measurementsusing an NMR SpecialtiesPS-60coupled with a Varian M o d e l V-4012A high-resolution magnet system. Several methods have traditionally been used to eliminate this difficulty, the most common being to install a diode detector in place of the phase detection system (Z-3). Diode detectors are nonlinear, however, and their use requires a calibration equation (2) or a seriesof careful calibrations that take into account the m a g n itude of the noise voltage into the detector (3). This is necessarybecausethe diode detector’s linearity dependsstrongly upon the bias level, due to noise, when no signal is present.In passing, it should be noted that commercial AM radio systemswhich e m p loy diode detection m inimize the linearity problem by utilizing a m o d u lation level of 80 % or less. This, of course, is not possible in pulse NMR applications. A second method (4) of overcoming the effects of nonlinearity is to use a diode detector and install a calibrated variable attenuator in the rf a m p lifier section of the receiver. The variable attenuator is used to keep constant the signal voltage into the diode. Though convenient, this method also suffersfrom changesin the level of the noise bias at the detector and is suitable only for measurementsinvolving relatively high signal-to-noise ratios. Copyright0

1975 by Academic Press. Inc. in any form reserved.

All rights of reproduction Printed in Great Britain

344

LINEAR

ENVELOPE

345

DETECTION

One solution to both these difficulties is to construct a linear envelope detector, thus eliminating the problem of beats from the phase detector and the problem of linearity in the diode detector. This solution has not been widely used in the past due, in large part, to the difficulty of designing and constructing a circuit useful in the frequency range of pulse NMR experiments. The requirements for a practical device include: (a) a wide linear range; (b) high frequency operation, up to 100 MHz and beyond; (c) sufficient gain to allow use with the great majority of rf amplifiers in pulse NMR systems; (d) a variable bandwidth filter system for signal-to-noise ratio optimization ; and, (e) building of the sophisticated portions of the circuit from readily available commercial modules, thus minimizing construction difficulties. The unit described below fulfills all the above requirements. DESCRIPTION

Although the design of linear envelope detectors is well documented (5, 6), difficult problems of component selection, matching, and placement arise at frequencies greater than about 50 kHz. As the bulk of pulse NMR experimentsare performed above 10 MHz, we chose to employ a commercially available low-frequency absolute value module as the detector unit and couple this to a versatile double superheterodyne mixer system constructed from inexpensive kits. 60 MHl

NMR +

SIG

10.7 MHZ

MIXER1

>

MlXER

II

IN

450

BUFFER

KHZ ’

DETECTOR

h

.a

Y osc

I

49 3 MHZ

osc II IO 25 MHZ

LOW PASS FILTER

l OUTPUT

FIG. 1. Block diagram of the linear detection system.

A block diagram of the detector used with our 60 MHz system is shown in Fig. 1. The mixers and oscillators, which convert the incoming signal down to 450 kHz prior to detection, were mounted in a shielded cabinet. Crossed diodes, two IN373 1, were placed from the input signal line to ground in order to limit the detector input voltage to safe levels. Two International Crystal Type OX oscillators and two International Crystal Type MXX-I rf mixers’ were used without modification and these devices should be suitable for applications up to 170 MHz. The circuit is readily adaptable to NMR frequencies other than 60 MHz by selecting the correct oscillator frequencies. That is, for 100 MHz operation the frequency of the first oscillator could be changed to 44.65 MHz and the second harmonic used for injection into the mixer. In an alternative scheme,the first oscillator frequency could be 60 MHz and the second oscillator frequency, 39.55 MHz. The buffer and detector schematic is shown in Fig. 2. A gain control and monitor are included in the buffer, which drives the detector and acts as a filter for the high-frequency ’ Available from International Crystal Mfg. Co., 10 No. Lee, Oklahoma City, OK 73102; Type OX, $690 with crystal; Type MXX-1, $3.50.

;

.

L

47

MONITOR

10K

-15v

t15v

.

FIG. 2. Schematic of the buffer-detector. In this circuit, all resistance values are in ohms, all capacitance values less than one a.re in If, and all capacitance values greater than one are in pf.

2 20KI

347

LINEAR ENVELOPE DETECTION

components of the mixer output. The zero control is used to set the DC output of the buffer to zero. The heart of the detector is an Optical Electronics Model 9004 Absolute Value Module.z This device is useful at input frequencies up to 3 MHz and performs with good linearity, as discussed in the following section. The output slew rate of 0.1 V/psec potentially limits its performance in certain applications but is not an imponant factor for FID’s with Tf 2 500 psec. A high impedance load for the OEI 9004 is provided by the LM 3 18 voltage follower that is used as the output stage for this section

FIG. 3. Schematic of the low pass filter. In this circuit, all resistance values are in ohms, all capacitance values less than one are in pf, and all capacitance values greater than one are in pf.

The low pass filter schematic is shown in Fig. 3. This six-pole Butterworth design was chosen for its sharp rolloff and incorporates a wide range of cutoff frequencies. Cutoff frequencies between 100 Hz and 100 kHz can be selected in a l-3-10 sequenceallowing TABLE

G

G

G

0.150 0.050 0.015 5000 1500 500 150

0.015 5000 1500 500 150 50 15

0.066 0.022 6600 2200 660 220 66

1

c5

-_-----100 300

Ik 3k 10 k 30 k 1OOk

0.033 0.012 3300 1200 330 120 33

0.047 0.015 4100 1500 470 150 41

0.047 0.015 4700 1500 470 150 47

a The cutoff frequency fe is in Hz, and all capacitance values less than one are in pf, .a11capacitance values greater than one are in pf.

the minimum acceptable bandwidth to be used. This, of course, optimizes the signal-tonoise ratio with respect to bandwidth. Component values used in the filter are shown in Table 1. z Available from Optical Electronics Inc., P.O. Box 11140, Tucson, AZ 85734; $33 plus socket.

348

BURNETT AND WINTHER

Although we used a sophisticated filter design in this final section, it is possible that a simple filtering scheme would be adequate in many applications. A two-pole active filter (7), with or without switchable cutoff frequencies, may provide adequate rolloff with reduced complexity. In fact, it is possible that a simple passive RC filter connected to the output of the LM 318 voltage follower could serve, although the general advantages of the active filter configuration would then be lost. OPERATION

The detector has sufficient gain to convert an input signal of about 100 mV into an output in excess of 10 V. The linearity of the device depends upon output level and is illustrated in Fig. 4 for outputs between zero and 7.5 V. This curve was obtained by driving the input of the detector with a calibrated signal generator and measuring the outputs of both the signal generator and detector with a high-frequency oscilloscope. + AV (mv)

v)

FIG. 4. Plot of the output voltage error A V= V, - V., where V, is the value expected for a perfectly linear device and V, is the experimental value versus the output voltage, Vo.

Though the claimed linearity of the absolute value module is approximately 0.1 %, we found that the entire detector is linear to within 0.5 % in the range O-7 V output (8) and linear to within 5 % of the full scale output voltage over the range O-9 V output. It should be noted that a linearity of 0.5 % or so compares favorably to that obtainable using phase detection, especially in caseswhere the phase difference between the signal and reference voltages approaches 7c/2(9). The advantage of phase detection in signalto-noise ratio enhancement applications, of course, still applies (3). The recovery time of the detector depends, as expected, upon the bandwidth selected for the low pass filter and has a minimum value of about 400 ,~secin the 100 kHz setting.

LINEAR ENVELOPE DETECTION

349

This lim iting value is a result of the rather slow slew rate of the OEI 9004 and can only be improved by the substitution of a faster device.3 We have not yet encountered a situation in which a shorter recovery time was required and, hence, no reduction has been attempted. ACKNOWLEDGMENTS

Acknowledgment is made to the donors of the Petroleum Research Fund, adm inistered by the American Chemical Society, for partial support of this research. In addition, Dr. J. F. Harmon of Idaho State University has constructed a similar detector, based upon our design, and provided us with a number of comments and suggestions,along with an independent evaluation of the device. We thank Dr. Harmon for his interest and assistance. REFERENCES 1. E. L. HAHN, Phys. Rev. SO, 580 (1950). 2. E. 0. STEJSKAL,Rev. Sci. Instrum. 34,971 (1963). 3. J. REICHERT AND J. TOWNSEND,Rev. Sci. Instrum. 35,1692 (1964). 4. J. F. HARMON AND B. H. MULLER, Phys. Rev. 182,400 (1969). 5. J. G. GRAEME, G. E. TOBEY, AND L. P. HUELSMAN, Eds., “Operational

Amplifiers, Design and New York, 1971. D. BLOYET, P. PIWUS, E. VAROQUAUX, AND 0. AVENEL, Rev. Sci. Znstrum. 44,383 (1973). J. G. GRAEME, G. E. TOBEY, AND L. P. HUELSMAN, Eds., “Operational Amplifiers, Design and Applications,” Chapter 8, McGraw-Hill, New York, 1971. G. L. SAMUEL~~N AND D. C. &LION, Rev, Sci. Znstrum. 40,676 (1969). W. N. HARDY, Ph.D. Thesis, University of British Columbia, 1964 (unpublished).

Applications,” Chapter 7, McGraw-Hill, 6. 7. 8. 9.

3 To the authors’ knowledge, the only commercially available device with a faster slew rate (50 Vjpsec) is the OEI Model 9014. This device, with proper design, could provide recovery times as short as a few microseconds.