A proton resonance magnetic field stabilizer using a quartz stabilized reference frequency

NUCLEAR

INSTRUMENTS

AND

84

METHODS

(I97O) 83-89;

©

NORTH-HOLLAND

PUBLISHING

CO.

A PROTON RESONANCE MAGNETIC FIELD STABILIZER USING A QUARTZ STABILIZED REFERENCE FREQUENCY P. BRI~ONCE and B. GRENNBERG* Bureau International des Poids et Mesures, Pavilion de Breteuil, F - 92 S~vres, France

Received 16 March 1970 An NMR stabilization for an electro-magnet has been built. The NMR frequency is held at a pilot frequency derived from a quartz oscillator. The unit is being used for fields between 0.7 and

1.0 T. Stability near the probe has been found as good as the quartz oscillator (±10-6). Hartree mean values for semicircular trajectories have been observed to keep within ~: 5 x 10--6 for days.

1. Introduction

means o f a f e e d b a c k system c o u p l e d to the magnetic field. A possible w a y o f doing this accurately is offered by nuclear m a g n e t i c resonance ( N M R ) . A b l o c k d i a g r a m o f the present a p p a r a t u s m a y be seen in fig. 1. The N M R p r o b e is p a r t o f a m a r g i n a l oscillator set at a f e e d b a c k level such t h a t it will n o t oscillate b y itself. It is forced into oscillation by a crystal stabilized oscillator. T h e magnetic field at the p r o b e is m o d u l a t e d by a small coil. A t times when the resulting varying field passes the value o f p r o t o n magnetic resonance, the p r o t o n s o f the p r o b e a b s o r b energy f r o m the rf field, thus decreasing the a m p l i t u d e

The present a p p a r a t u s has been constructed in o r d e r to stabilize the m a g n e t i c field in a semicircular a b s o l u t e a-energy spectrometer. Originally, the m a g n e t was p r o v i d e d with a c u r r e n t stabilization to better t h a n _ 2 x 10 -5. Since there are always variations in the m a g n e t i c susceptibility o f the m a g n e t due to t e m p e r a ture variations, it is n o t meaningful with the present m a g n e t to p u s h c u r r e n t stabilization m u c h further, a n d a n y i m p r o v e m e n t m u s t therefore be m a d e by * On leave from the Institute of Physics, Uppsala, Sweden.

P.as, H OC Voltag.I ~ " I Time II Amplifier I >

LF ~

Satecti~ta band Amplifier

Comparator

•

.~

t

Marginal Oscillator

Or+"

I

to°--

amplifier

~ ~ ~ ~ ~

I ++°°"',

a <

Modulationl I

Power

Preamplifier HF

I ° C " ....

1.1 c°°--'°r I

o+°i,,.,o.

Stabilization windings

+

[

Oscillator

Constant

1 Fig. 1. Block diagram of stabilization. 83

+

I

-

;I h

84

P. BRI~ONCE AND B. GRENNBERG

of oscillation in the probe circuit. This low frequency amplitude modulation in the marginal oscillator is detected, amplified and compared with the modulating frequency in a special network (phase sensitive detection). The procedure of comparison can be understood as that of measuring the first order sine Fourier coefficient of the signal, in terms of the modulation current phase. If the resonance falls symmetrically relative to the modulation, this coefficient will be zero. For a different value of the field, however, the signal will not arrive at the moment of zero current in the modulating coil but at some other value, and the output will be a signal proportional to the difference between the actual field and the value wanted. The error signal is amplified and fed back into the system by means of an extra winding on the magnet. However, a correction in this manner has a limit for two reasons. First, the maximum current of the corrector coils is necessarily limited and may not suffice to compensate for a slow but large setoff. Second, the amplification has to be kept within reasonable limits to assure stability. Therefore, a simple regulation working directly on the current generator has been added. Whenever the current in the corrector coils surpasses a certain limit, a relay is activated which acts on the current setting of the generator. Thus the field given at zero current in the corrector spools will be transferred to a more suitable value.

2. S o m e details on the electronics

2.1. THE FREQUENCY STANDARD This is the standard element to which the field is referred by means of the equation

v= B~'p/2~, where ~ is the gyromagnetic ratio of the proton (uncorrected for diamagnetism), B the magnetic induction and v the resonance frequency. In the present case, we use a commercial quartz oscillator with a nominal frequency of 4.3 M H z with a guaranteed stability of ~10 -6. This frequency is multiplied by an integer which can be varied from 6 to 10. This gives a selection of different fields which is sufficient for our purpose. 2.2. THE MARGINALOSCILLATOR After several trials we have adopted the design described in 1) (fig. 2). Some changes have been imposed by the use of a pilot frequency, necessitating the possibility to adjust the feedback to a level below self-oscillation. 2.3. THE PROBE The proton sample consists of about 1 cm 3 of an 0.1 N aqueous solution of MnSO4, kept in a sealed glass envelope. The concentration of paramagnetic ions has been selected in function of the modulation frequency. Although a lower concentration of

2mH

L

II -

- o .... p" D!

PROBE Pilot in ~

i

..~

Q

~

-w at.

1000p

2 N 83

0-9

0-9

0-9

Fig. 2. Marginal oscillator. Pilot signal forces it into oscillation. 5 kf~ variable resistor permits feedback adjustment.

PROTON RESONANCE MAGNETIC FIELD STABILIZER

+12 ~ 2oo~ _

2

85

470 ~NWk'-'-°+24

3oop ..33n N2219

±t

J

© i

~J

~0p

2

LF~out

470 ~-24

2200p

Fig. 3. Preamplifier.

47 -12

1•

lk /~

~ lO0~J 0 -24

i

) BCY40 I

a'°P wl

_

=~To oscilloscope

for increased

d I i

power

7 Fig. 4. Lf oscillator. Mn + + ions would give a narrower signal, the relaxation time would become too long and the second order echoes ("wiggles") would be too dominant. A lower modulation frequency could compensate this. However, at the same time the upper frequency limit of the whole system would be diminished. Thus, a compromise has been sought, permitting a modulation frequency slightly below 200 Hz. (Harmonics of the 50 Hz mains must be avoided.) The coaxial tube from the ampoule to the oscillator had to be given a fairly low capacitance. This means that the central wire can hardly be made self-supporting. It was made from a silvered copper wire. Some paper strips were glued to it to ensure mechanical damping, and it was given suitable stress.

2.4. THE PREAMPLIFIER This amplifier (fig. 3) gives an output signal of about 0.5 V. It consists of an integrated circuit (Texas Instruments 709) coupled to give an amplification of about 2 000 with an upper frequency limit of 3 kHz. The output noise is about 10 mV peak to peak. 2.5. L o w FREQUENCYOSCILLATOR Another Texas Instruments 709 integrated circuit is used, with a circuit in double tee (fig. 4). The frequency is about 200 Hz, adjusted to have no factor in common with the 50 Hz mains. The 1 kE2 thermistor serves to stabilize the output level. It has a dissipation of 0.1 m W / K and a negative temperature coefficient of 2 300 K - 1.

86

P. BRI~ONCE A N D B. G R E N N B E R G

470 2.2k Fro~mp. . . . pli~lo;

=--i10p

~B

0--24

47

CY40

4,

--

t-12

To ~ase

comparator

68k

68k

°i~'r

iP

I

i s

470

0+24

Fig. 5. Selective amplifier. T h e frequency is adjusted by m e a n s o f the two 47 k ~ resistors. T h e variable 100 k ~ resistor permits band-width adjustment.

2.6. SELECTIVE AMPLIFIER

By means of a double tee circuit, a 709 integrated circuit is transformed into an amplifier adjusted to the same frequency as the oscillator and with a narrow band ( ~ 6 Hz). The selective amplifier (fig. 5) gives an output signal which is proportional to the deviation of the magnetic field from its ideal value. This can be seen from fig. 6. It is clear that the sign of the deviation is given by its phase as compared to that of the modulating field. 2.7. PHASE SENSITIVEDRIVER AND DETECTORUNITS These units are practically copied from ref. 2, figs. 8 and 9. It thus serves no purpose to describe them here at length. The general idea is to multiply the 200 Hz sinusoidal from the selective amplifier with the 200 Hz modulating signal. As can be inferred from fig. 6, the two will be either in phase or 180 ° out of phase depending on the sign of the field's deviation from the ideal. The output after such a multiplication will be a set of positive or negative pulses. The mean value, however, will be proportional to the field deviation (see appendix). In the process a substantial amount of irrelevant noise is eliminated. In order to obtain a dc signal suitable for feedback purpose, it is now sufficient to introduce a filter such that the discrete character of the signal vanishes.

output current in either direction. It is clear that a good stability of the zero is necessary. In order to obtain this, a thermoresistor has been included in the part Bmod.

,...:.o b-.

~V~ .

.

/~V/~.

.

Slgna, from p.... plifier -'-t NO2 0 0 H z component

f

output from P t No selective amplifier

Bm°d

@

I

'i

[v v

V

I Av

I

i

I

I

,

'V-

I

I I A_A_

] ~ ~

.,

S*.ne,,.omp.... p.,,..

- =' Fromselective

amplifier

Brood,

l / i

2.8. CURRENT POWER AMPLIFIER The output from this unit (fig. 7) should be zero in the case of zero error signal and be able to supply an

~ V ~ . .

.

i

l

I

~

~

~

~

v

~

I

/~1~ v

I

I

~

~

~

~t Signalfrom p.... plifier --t F. . . . .

lecti . . . .

plifier

Fig. 6. D i a g r a m s to explain h o w the p r o t o n resonance signal is converted into a n error message. See text a n d appendix.

PROTON

RESONANCE

MAGNETIC

of the network which is kept in a block of aluminum to ensure thermal uniformity. 2.9. SECURITY DEVICE The magnet current being stable to + 2 x 10 -5, the

FIELD

87

STABILIZER

stabilizing unit described should be sufficient to cope with remaining instabilities. However, this is not quite the case. First, the magnetic field may change slowly because of a change in temperature inducing a change in the magnetization. Such changes, although slow, Meter

=To.o°r.,~'

P:~p~ r|art°or~

i~

i ÷')q~-I q ~

/~¢~0"~


i 709 ~

ity

E2

a

n

t

I, ~

I

~

+(~ L.~ F0

I

I

~--~3-'~~3~To

I

_:o

_stabilizing

+:' -6 <

-6

~0 -6

Fig. 7. C u r r e n t power amplifier. T h e Si a n d Ge diode pairs protect the meter.

Fig. 8. Security device.

88

P. B R F . O N C E A N D B. G R E N N B E R G

may necessitate very large currents in the compensating coils to offset. Second, there is always the risk of rapid changes in the mains voltage which are incompletely guarded against. Even if the current will rapidly return to its original value, the field will not, due to the hysteresis of the curve of magnetization. Fig. 8 shows schematically the network designed to cope with these difficulties. Whenever the current to the compensating coils exceeds 200 mA in either direction, one of the relays R l , R2 will be actuated. This will start the motor of the regulating potentiometer in the magnet current generator, thus resetting it to a more appropriate value. The signal from the preamplifier is felt at E3, and if it vanishes, the relay R3 will be agitated. The contact R31 will then short a resistor in the If oscillator, thus augmenting the modulation amplitude. In most cases, when the field has suddenly been lost, a signal will be found which actuates one of the relays R1, R2. In this way, the stabilization will work itself into ideal conditions again. N o t until the error has become reasonably small, however, will the augmented modulation be switched off, since a signal of a certain size at E2 will maintain the relay R3 actuated. As long as the relay R3 is actuated, a mild warning sound is heard. However, if R3 is actuated and simultaneously none of the relays R1, R2 is working, this means that the signal is entirely lost. Then a strong alarm signal is given since a rapid intervention might be needed to save the experiment. It is planned to add another feature which will, by pneumatic means, temporarily block the ray in the spectrometer whenever the field is not properly stabilized. This will permit unwatched operation and very long exposure times.

3. Gain properties of the feedback system A precise measurement of the frequency characteristics of the whole system has not been made and would be difficult to execute. However, a few particularities may be noted. The time constant imposed after the phase sensitive detector is 1 s. The amplification of the whole system is between 20 and 30, as judged from the degree of adjustment against an error introduced into the field. No oscillation has been detected, at least not beyond the level of the 50 Hz and 300 Hz ripples in the magnet current. This ripple component is about 2 x 10 -7 of the field and is present whether the stabilization is in function or not.

4. Stability In principle, a drift in one of the amplifiers should stabilize itself by means of the main feedback loop. However, this effect is impaired by the low amplification of the system, and therefore, it is advisable to have well compensated electronics. In our case, using integrated operational amplifiers, the general drift gives rise to a zero drift in the output at zero input of less t h a n 10 - 2 A. This is equivalent to a change in the field of 10-7. (This performance is obtained in a room which is conditioned to 1 °C.) There is a slight pickup of parasitic signals with the modulation frequency. Since this can hardly be avoided altogether, the marginal oscillator being extremely sensitive to pickup, the only realistic remedy would be to inject a counter-signal with the appropriate amplitude and phase, in order to compensate for the disturbance. Due to the apparent stability of this spurious pickup, it creates no further problem.

5. Performance The commercial quartz oscillator being guaranteed to _+10-6 only, a much better stability cannot be expected. Direct measurements of this frequency have shown a period of about 2 min, synchronous with the barely audible click of the bimetal switch of the crystal oven, and with an amplitude of about one in 106. A measurement with an independent N M R apparatus shows fluctuations of the field with the same period and amplitude. Long time drift has not been observed and should be less than 5 x l 0 - 7 at points near the stabilizing probe. It is clear that the present unit will stabilize the field at one point only, and changing thermal gradients in the magnetic poles would impair its validity at points distant from the probe. However, it is interesting to note that the Hartree mean values for several semicircular trajectories, as measured point by point, have stayed constant within better than ___5 x 10 - 6 for several days, once a thermal equilibrium attained. The radii were comprised between 370 and 420 m m in a semicircular geometry. The location of the probe at near 90 ° in the trajectory and "inside" it might have helped, so that the chosen point is very representative. It might be added that deviations at points remote from the probe show field deviations up to five times greater than that of the mean Hartree mean. Thus, the importance of the choice of the point to stabilize is demonstrated.

PROTON

RESONANCE MAGNETIC

The authors want to express their sincere gratitude to Dr. A. Rytz for his constant support and encouragement of this work. They are also indebted to Mr. D. Carnet for stimulating discussions. Further, one of us (B.G.) wants to express his thanks to Dr. J. Terrien, Director of the B.I.P.M., and Prof. K. Siegbahn, Uppsala, for having made possible his stay at the B.I.P.M.

FIELD STABILIZER

89

If the two otherwise identical signals have a difference in phase of n + 6, the total output will be

• Ak [sin (kcot) + sin (k~ot + n + 6)] = k=l

= ~ 2 Ak sin (kcot + n/2 + 6/2) cos (n/2 + 6/2). k=l

References 1) A. Faulkner and B, H o l m a n , J. Sci. Instr. 44 (1967) 391. 2) C. Olsen, Nucl. Instr. and Meth. 31 (1964) 237.

Appendix THE EXTRACTIONOF THE ERROR SIGNAL I f we regard the resonance signals at rising and falling modulation field respectively, we find that each of them has the same periodicity as the modulating field. Each can be described as

• k=l

A k sin

(kcot).

The amplitude for the component at frequency co, as resulting from a selective amplifier, will be proportional to cos (n/2 + 6/2) = - s i n 6/2. The output from the selective amplifier will thus be proportional to sin 6/2 • cos (cot+6~2). Now, in the phase comparator we multiply by sin cot. The ac output of this multiplication will be proportional to sin 6/2" sin z cot, which after the integrating time constant will leave only a voltage proportional to sin 6/2. But sin 6/2 is proportional to AB/Bmoe (see fig. 6), which means that the error signal is proportional to the field deviation.