ELECTRICAL MEASUREMENTS

D E T E R M I N A T I O N OF THE G Y R O M A G N E T I C R A T I O OF PROTONS

G. K, Y a g o l a , V, t. Z i n g e r m a n and V, N. S e p e t y i *

Translated from Izmeritel 'naya Tekhnika, No, 5, pp. 24-29, May, 1962

Accurate evaluation of the gyromagnetic ratio of a proton provides means of raising the precision of atomic reference units in electrical and magnetic measurements, since it becomes possible to calculate accurately magnet- ic induction by means of a simple relationship.

oJ = ~, B (1 )

where w is the Larmar precession of atom nuclei of a substance placed in a magnetic field; B is the magnetic in- duction; 7 is the gyromagnetic ratio of atomic nuclei.

A proton is the best-known of all the atomic nuclei. In a number of instances a proton can serve as a "ref- erence ~ nucleus for determining the gyromagnetic ratio of other nuclei [1].

Work for determining the gyromagnetic ratio of a proton has been carried out in the last ten years in physical and metrological laboratories of a number of countries. However, the results obtained by various investigators differ by amounts greater than the evaluated errors [2-6]. These discrepancies are due, it would appear, to unaccounted systematic errors in different methods and means of measurements, and to discrepancies in state standards.

The gyromagnetic ratio can be estimated by measuring the precession frequency of protons in a sample placed in a magnetic field and by evaluating the magnetic induction of that field.

The frequency can easily be measured by radiotechnical means, b y using the effect of nuclear magnetic reso- nance absorption. It is more difficult to evaluate magnetic induction with the required accuracy. For this purpose the KhGIMIP (Khar'kov State Institute of Measures and Measuring Instruments) used magnetic balances which meas- ured the interacting force between a current-carrying conductor and the magnetic field in an electromagnet air gap which contained the substance with the resonating nuclei.

The measuring equipment (see Figure) consists of an electromagnet which produces in a given volume a uni- form magnetic field stabilized by a proton magnetic resonance, and of magnetic batances which measure magnetic induction in units of mass, length, time and current.

Magnetic balances. The electromagnetic interaction force of a magnetic field and a current-carrying circuit is related to magnetic induction by the well-known formula

~t:=] f [ d l " ~ . (2) L

Induction B ~ in a given point of the field can be calculated from the geometrical dimemions of circuit L, the 0 distribution along the circuit of the relative values of the magnetic induction vector B/B, current I in the circuit

and the vertical component Fy of the force acting upon the circuit.

A computing parameter X ~ is introduced for the convenience of calculations and is henceforth called "effec- tive width of a turn"

* A. A. Vetvinskii and E. E. Bogatyrev participated in certain stages of this work.

387

where j is the ver t ica l axis vector.

Induction B ~ is de termined from the equal i ty

B ~ Fy 7x7"

(4)

In de te rmin ing the gyromagnet ic rat io of a proton by means of magnet ic balances i t is possible to find the

va lue of B ~ which satisfies re la t ion B ~ - 2~tf0 for a given value of frequency f0 , The current -carrying c i rcui t

of the KhGIMIP magnet ic balances comis~ of rectangular turns with ver t ica l sides. The lower horizontal sides are p laced in the air gap of an e lec t romagne t which produces a magnet ic field with an induction differing but l i t t l e from the va lue of 13 ~ The upper hor izonta l sides are p laced in a field whose induction approaches zero.

Coils with a large number of turns were used in the previously described magne t ic balances [2, 5]. A large

number of turns fac i l i ta tes the measurement of the force interact ing with the magnet ic field; however, i t impedes an accura te eva lua t ion of the ef fec t ive width. We used a c i rcui t with a smal l number of turns (one or two), morn- over, in order to raise the accuracy of de te rmining the ef fec t ive width of these turns our design provides a separate measurement of each turn. We made two coils on glass formers with a smal l l inear temperature coeff icient . Each co i l has a width of about 100 m m and a length of 500 ram. The first coi l has one turn wound over the edges of a glass p la te 2.8 m m thick, and the second has two turns on a glass plate 8 m m thick. The current -car ry ing turns are

made of a c h e m i c a l l y pure 0.8 m m copper conductor.

1) Compensat ing coi l ; 2) main current coi l ; 3) control coils; 4) control unit; 5) 350 cps modulator; 6) 50 cps modula tor and biasing current; 7) s tab i l izer transducer II; 8) measuring transducer I; 9) phase shifter; 10) out- put stage; 11) 10 and 20 Mc frequency unit; 12) osc i l -

loscope.

The d iamete r of the wire and the distance between the external sides of the wires in a coi l were measured by a contac t comparison method with block gauges; moreover, measurements along the la te ra l sides were made at in ter - vals of 0 . 5 , 1 or 5 cm according to the requirements of ca lcula t ions . Random measurement errors of the distances between the conductor axes (turn width) amounted for coi l No. 1 to 1.1/~ and for coi l No. 2 to 0.33 p . Thepos- sible unaccounted-for systematic errors of measurement

did not exceed 0.6 V.

These measurement results were used for ca l cu l a -

ting the ef fec t ive width X ~ of turns; moreover, formula (3) was replaced by an approximate equal i ty

X0= ~ k dx, (5) L

Bz is the coef f ic ien t of the magne t ic in- where/~= B-- ~-

duction dis t r ibut ion equal to the rat io of the induction vector B component B z para l l e l to the induction vector in the lower part of the turn and the value of B ~

Relationship (5) was integrated numer ica l ly by means of the trapezoid formula separa te ly for the lower, upper and l a te ra l sides of the turn.

n--1 Xo~-X'-~ ~ aiq-(Zl~'l-- dxl"t-

2 ~=o (6)

p-1 k; "~- Z m--I kt_t_ki+l 2 dxi'~- ~ ~ k / + l 2 dxl'

i=p l~n

388

where X' is a basic dimension arbi t rar i ly selected to approximate the width of a turn; cq = k i -1.

The first two terms of (6) represent a summation along the lower side of the turn, and the third term along

the upper side. The length of segmenls dx i are chosen so that

n--1 rn--1

(7) f = 0 i=p

The fourth term of (6) represents a summation along the l a te ra l sides of the turn, and i t is assumed that dx i = X i+ 1

-Xi, where X i is the width of the turn at point ~.

Dimension X ~ determined from (6) is subjected to a temperature correct ion accounting for the devia t ion of the coi l t empe ra tu r e from 20"C during theopera t ion of the equipment .

The errors in de termining the ef fec t ive turn width X ~ are main ly due to errors in l inear measurements and errors in account ing for the distr ibution of induction along the c i rcui t of the turn (see Table) .

Calcula t ions from (6) are based on the assumption that the coi l plane is perpendicular to the magne t ic induc-

t ion vec tor in the lower part of the turn. This condi t ion is compl ied with by a free suspension of the coi l . The rod on which the coi l is suspended from the ba lance beam has an agate thrust bearing with a spher ical cup, and the coi l is provided with a cone-shaped pivot made of fused quartz. The coi l is connected by means of conductors inside the rod to highly f lexible and l ight gold l ead -ou t wires. The posit ion of the coi l is checked by means of a l ight beam ref lec ted from a mirror fixed to the coi l .

The weighing of the current -car ry ing coi l in the magne t ic field is made by means of equa l - a rm balances with a h igh-grade aged bronze beam which has a distance of 200 m m between the middle fulcrum l ine and the stirrup suspension l ine, and is provided with an agate kn i f e -edge and a block.

The current is supplied to the frame through gold fibres 5 - 7 ~ thick, 0.2 m m wide and 200 mm long. The

c i rcu i t of each turn contains four current -car ry ing fibres connected in para l le l pairs. The sagging of these conduc- tors is adjusted in such a manner as to reduce their ef fec t on the accuracy of the balances. The sensi t ivi ty of the

ba lances with the l e a d - o u t conductors amounts approximate ly to 0.02 rag / division. The position of the ba lance is read by means of an opt ica l syst6m with a l ight beam 3.5 m long.

In order to obtain the required s tabi l i ty of readings the balances are not arrested comple t e ly during measure-

ments. The ba lance is supported, when weights are being changed, by means of long f ia t phosphor-bronze tapes which are smoothly approached from below. The tapes are not rigid and on touching them the ba lance beam does not ex- per ience any no t i ceab le shocks. This system provides a constant equi l ibr ium position of the balances with an error not exceed ing 10 -5 of the smal les t force which had to be measured, and amounting to approximate ly 10 -8 of the full load, which indicates high s tabi l i ty in the operat ion of the balances.

The ba lance beam and the stand are surrounded with a j a c k e t of copper sheets in order to reduce the t empera - ture gradient along the beam. The ba lance in its j acke t is p laced inside a transparent plast ic cab ine t whose internal surface is covered by a copper grid connected e l e c t r i c a l l y to a l l the me ta l components of the beam and intended for e l imina t ing e lec t ros ta t ic interact ion of the ba lance moving system with the stat ionary parts of the equipment . The ba lance is p laced into a second casing resting on a frame mounted on a substantial wall .

The measures thus adopted could not c o m p l e t e l y e I imina te variat ions in the position of equi l ibr ium produced

by changes in the air temperature of the premises. The drift in the positiOn of equi l ibr ium of the magne t ic balances is de te rmined for each measurement by checking i t pe r iod ica l ly when the current is made to flow in opposite d i rec - tions through the coi l . The equi l ibr ium positions thus de termined were used to plot two curves each of which cor- responded to the variat ions in its position with t ime for one of the directions of the current flow through the coi l . The mean di f ference between readings on the two curves obtained at the same instant was taken as a measure of changes in the posit ion of equi l ibr ium due to the reversal of the current through the coi l . Each posit ion of equ i l i - br ium was evalua ted for 7 elongations read with an error equal to 0.1 scale divisions. Numerous exper iments have shown that the random fluctuations in the osciaUation of the beam due to air currents, vibrations of the building, and smal l bursts of current are sat isfactor i ly averaged out in ca lcu la t ing the equi l ibr ium positions, and do not lead, in plot t ing ei ther ze ro-dr i f t curve with respect to t ime from 6 points, t o errors exceed ing one scale division (0.02 mg)

389

Limit ing Relative Errors in a Single Determinat ion of the Gyromagnetic Ratio of a Proton

Error components

In the ef fec t ive width of a turn:

in l inear dimensions of the c o i l

in distribution coefficients of the magnet ic induction

in computat ion methods

in the position of the coi l with respect to the magnet ic

field.

in the direct ion of the magnet ic induction vector in the

lower part of the turn with respect to the horizontal

plane. . .o .... in the temperature correc t ion

in the instabil i ty of co i l dimensions;

Total error of the ef fec t ive width of a turn

In the e lec t romagnet ic interact ion force:

in determining the equil ibr ium of b a l a n c e s ,

in the sensitivity of balances

in the ef fec t of the l ead- in conductors.

in the mass of the balancing weights

in the correct ion for the displaced air

in the value of acce lera t ion due to gravity . . . . . . . . . . .

Total error of the e lec t romagne t ic interact ion force

In the value of currents:

in comparing standard ceffs with a reference vo l t .

in comparing the resistance coi l with a standard ohm . . .

in compensating the vol tage drop across the resistance

coi l by the e m f of a standard c e l l .

in temperature corrections of reference measures

Total error in current values

Effect of measuring device components on the magnet ic

induction,

Frequency errors . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Random for

the series

Resulting error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.6" 10 -~

0.5" i 0 -6

2 . 1 0 -6

6 . 1 0 -6

20.10 -6

2- 10 -6

2" 10 -6

20" 10 "s

2" 10 -6

2" 10 -6

3 . 1 0 -6

constant ....

for a

turn

Systematic for the series

none l imi-

nated

systematic

7 .10 -6

2 . 1 0 -6

2 .10 -6

8- 10 -6

5 . 1 0 "6

5" 10 -a

constant

for a

coi l

1 .7 .10 -6

3.10 -6

1" 10 "6

2" 10 -6

2 . 1 0 -6

4" 10 -6

2 . 1 0 -6

2" 10 -6

4.5" 10 -6 Total error in evaluations 21 .10 -6 9 .10 -8

Resulting error without accounting for the possible non-

e l imina ted systematic errors . . . . . . . . . . . . . . . . . . . . 23" 10 -6

25- 10 -6

1 .6 .10 -6

6 .10 -6

2" 10 -6

7 .10 -6

2 ' 10 -~ 2" 10 -6

3 . 1 0 .6

1" 10 -6

3 �9 10 -6

2 . 1 0 -6

4" 10 -6

2 .10 "6

1 �9 10 "6

9" 10 -6

in determining the mean difference between readings taken from two curves. The measured force is balanced by

weights placed on the same rod from which the coi l is suspended. The weights are made of plat inum and their mass

is determined with an error not exceeding 0.002 rag. The weights are selected in such a manner that a variat ion in

the equil ibr ium position of the balance due to a reversal of current in the coi l does not, as a rule, exceed 15 scale divisions. Moreover, the error due to an inaccurate determinat ion of sensitivity does not exceed 0.0015 mg.

390

The acce le ra t ion g due to the force of gravity in the p lace where the equipment was loca ted was determined

by grav imet r ica l communica t ion with the nearest reference point which is d i rec t ly connected to Potsdam and the

basic points in the USSR. A correct ion of 11 mgl based on [7] and recommended by the XI General Assembly of the

Internat ional Geodet ic and Geophysical Union was appl ied to the Potsdam System.

The force operat ing on the ba lance with the current flowing through the l e a d - i n wires was also taken into account, since the magne t ic field in the region of these wires was not compensated in the balances. This correct ion was determined by disconnect ing the l e a d - i n wires at the coi l , shorting them and measuring the d i sp lacement in the ba lance equi l ibr ium with a reversal of the current through the wires. This correct ion amounted to 0.013 t o0 .046mg for different combinat ions of the l e a d - i n wires.

The current in the co i l ( ~ 0.2 a m p ) was measured by a compensat ion method with an accuracy equivalent

to reference measurements . The vo l tage drop produced by the measured current across the reference resistance coi l of 5 ohm was compensated by the emf of a standard ce l l . The reference resistor and standard c e i l s were compared d i rec t ly with state standards of an ohm and a volt .

Electromasnet . The gyromagnet ie rat io of a proton was measured in fields with a magne t i c induction in the range of 0.2 to 0.5 w e b e r / m z.

The required magnet ic fields are produced by an e l ec t romagne t with a double yoke, c0ne-shaped po le -p i eces and an effect ive air gap 40 m m long. In order to obtain a uniform magne t ic field along the lower part of the coi l , the magne t is provided with po le -p ieces 250 m m in d iamete r whose surfaces are made fiat to a high degree of ac - curacy (within l imi ts of 0.2 p ) and are p laced para l le l to each other (deviations not exceeding 1.5/*). The upper part of the po le -p ieces is provided at a dis tance of 100 m m from the center with a horizontal cut, which is required in order to reduce errors due to possible deviat ions of the l a te ra l sides of the coi l from the ver t i ca l position. The above-men t ioned values of magne t ic induction in the air gap are obtained with a smal l power (not exceeding 120 w) dissipated in the main windings of the e lec t romagnet . Owing to the large cooling surface the hea t ing -up of the coils is so smal l (less than l ' C ) that no forced cool ing is required. These thermal conditions reduce to a min imum air cur- rents which have an unfavorable effect on the operat ion of the ba lance mounted i m m e d i a t e l y above the magnet ,

The magnet is mounted on a car r iage which is displaced hor izonta l ly along a guide. The magne t can be with- drawn from the ba lance by means of this system in order to study the distr ibution of a magne t ic field in the space occupied by the coi l in normal operation.

The distr ibution of the f ield between the poles was studied in de ta i l by means of nuclear magne t ic resonance. I t becomes possible by means of the se lec ted measuring c i rcui t to de te rmine coeff icients a= (B - 13~ ~ which are

required for ca lcu la t ing the ef fec t ive width of the ba lance coi l , by passing a d i rec t current through a coi l surrounding the ampoule of a nuclear resonance de tec tor probe supplied with a frequency of f0- The d i rec t current is adjusted until nuclear magne t i c resonance is obtained, with the va lue of current I then meet ing the condit ion of I = ( B - B ~ where C is a constant of the probe coi l .

The field distribution measurements may be affected by the components of the measuring probe. Moreover, the distribution of the f ie ld is also af fec ted by the p lac ing in the air gap of the coi l with its casing. Calcula t ions have shown that the error produced by neglec t ing these effects does not exceed 2 . 1 0 -6.

The magne t ic field gradient near the coi l in a direct ion perpendicular to the surface of the poles is ex t r eme ly small , which indicates that in this region the magne t ic l ines of force are perpendicular to the pole surfaces.

The po l e -p i ece s are fixed with a devia t ion from the ve r t i ca l not exceeding 0.001 radians, hence, the dev ia - tion of the lines of force from the horizontal does not exceed a quant i ty of the same order.

The induction is measured in an area 65 to 320 cm away from the pole center , where the nonuniformity of the field precludes the use of the nuclear magne t ic resonance method, by means of set IMI-3 which uses the Hall effect [8]. The instrument 's transducer is then p laced in a posit ion to measure the magnet ic induction component which is para l le l to the lines of force in the lower part of the magnet ic ba lance coi l .

The e l ec t romagne t ' s stray field is compensated at the leve l of the upper side of the coi l by means of f lex ib le coils with ben t -ou t sides. I t becomes possible by shaping these coils and adjusting their position to reduce the hori- zonta l component of the e lec t romagne t ' s stray field along the entire length of the upper edge of the coi l to values not exceed ing 10 -6 webe r /m z. The hor izonta l component of the residual field is evaluated by means of a test

391

generator and a phase-sensi t ive vol tmeter . The same method is used for measuring the field in the area between 320 cm from the center and the upper edge of the coi l .

The s tab i l i ty of the magne t ic induction in the operat ing gap of the e lec t romagne t during the entire t ime used for measurements (about 3 hr for a s ingle- turn coi l , and about 7 hr for a double- turn coil) is ensured by s tabi l iz ing

the field in the air gap by means of the nuclear magne t i c resonance method. The s tabi l izer ' s transducer is supplied

with a high frequency from the source used for studying the field distr ibution along the lower edge of the coi l .

The source of the h igh-f requency vol tage consists of a generator whose frequency is s tabi l ized by means of a quartz crystal p laced in a thermostat. Frequency variat ions during measurements were less than 5 .10 -7. This source

provides vol tages with nominal frequencies of 10 and 20 Me. The ac tua l values of these frequencies are de termined by compar ing them with the frequency standard whose error is less than 5 . 1 0 -7 .

The magne t i c field s tab i l i ze r has a s tab i l iza t ion coef f ic ien t of 3000 to 15000 (depending on the operat ion con- ditions). The variat ions in the mean value of induction along the lower edge of the coi l during the series of measure- ments of the gyromagnet ic rat io did not exceed 10 "6.

Measurements and the evalua t ion of their error. The gyromagnet ic rat io of a proton in an aqueous solution of NiSO a" 7H90 (in a concentra t ion of 0.1 mole) was evalua ted by means of the above apparatus. I t was established

expe r imen ta l l y that there were no shifts exceed ing the l imi ts of 1" 10 -6 in the resonance frequency of protons in this solution as compared with the resonance in minera l oi l which has been thoroughly studied by many investigators.

The possible errors can be divided into three groups according to the nature of the ef fec t o n the de te rmina t ion of the gyromagnet ie rat io. The first group consists of random errors whose va lue may change for every repeated

measurement on the magne t ic ba lance . These errors were reduced by carrying out a t leas t 12 series of measurements involving each turn. A series included 10 evaluat ions on the ba lance of variat ions in the e lec t romagne t i c in teract ion

force when the current was switched in the coi l . Several conditions were changed from measurement to measurement in order to account more fully for the random errors. Thus, for instance, the ba lancing weights were changed, the

nature of the residual f ield distr ibution at the upper end of the coi l was also changed, the magnet ic field s tab i l izer probe was displaced, and the temperature of the equipment varied. Measurements were made for two values of mag-

net ic induction B ~ (about 0.24 and 0.47 weber/rag). The random error component was smaUer than the sys temat ic component for the chosen number of measurement series.

The second group includes errors which can change only when the coi l is changed. In double- turn coils a part of these errors may also change when transferring from one turn to the other, or to a matched connect ion of both

turns. These errors were reduced by measuring with two separate coils, one of which has two independent turns.

The third group consists of the possible une l imina ted sys temat ic errors which are fully included in the result i r respect ive of the number of determinat ions of the gyromagnet ie rat io of aproton made on this equipment.

The va lue of the errors on the basis of ana lyz ing a single measurement (for a single turn of the coi l and 13 =

0.24 w e b e r / m ~) is shown in the table above.

The expe r imen ta l ly obtained errors of a series of measurements were found to approach very closely the values

given in the table .

The gyromagnet ic ratios of a proton (without a d iamagne t i c correct ion) for various connections of the coi l are

as follows: Coi l No. 1 2.67500" 10 s (weber /m2)- lsec - l

Coi l No. 2, Turn A 2.67508" 108 " Turn B 2.67506.108 "

Matched connect ion of Turns A and B 2.67508- 108 "

Mean) ' = 2 .67505.10 s

The l imi t ing measurement error amounts to -~ 0.00005.10 s (weber /mZ) "1 see "1. The gyromagnet ie rat io of

a proton thus obtained is expressed in units reproducible from USSR state standards.

392

1, 2. 3. 4. 5. 6.

7, 8.

L I T E R A T U R E C I T E D G. K. Yagola, and E. E. Bogatir'ov. Ukrainskii fizichnii zhumal, 1962, No. 2. H. A. Thomas, R. L. Driscoll, and L A. Hippie. Journ. Res. NBS, 1950, 44, 569. P. I. Bender and R. L. Driscoll. IRE Trans. on Instruments, 1958, 1 - 7, No. 3-4, 179. W. Wilhelmy. Armalen der Physik, 1957, 19, 329. H. Capptuller. Zeirschrift fur Instrumentenkunde, 1961, 6..99; p. 133-140, 191-198 . N. V. Studentsov, and B. M. Yanovskii. Transactions of the Institutes of the Commit tee of Standards, Measures and Measuring Instruments attached to the USSR Council of Ministers, 1961, v. 54 (114). P. N. Agaletskii and K. N. Egorov. Izmer i te l 'naya tekhnika, 1956, No. 6. D. D. Voeikov. Design of High-Precision Gaussmeters on the Basis of the Hall Effect. Dissertation, Leningrad, 1960.

T R A N S I S T O R I Z E D D E C O D I N G C O N V E R T E R

N. A. S m i r n o v , V. B. S m o l o v , V. S.

Translated from Izmer i te l 'naya Tekhnika, No. 5, pp, 29-32, May, 1962

F o m i c h e v , a n d E. A. C h e r n y a v s k i i

The application of digital electronic computers and their elements for data processing and production control is closely connected with decoding operations, that is,the conversion of a digital code N into a d c or ac equivalent voltage U

U=m u N, (1)

where m U = const is the conversion scale.

Linear decoding coverters (LDC) which reproduce relationship (1) form basic units of a number of modern auto- matic devices, for instance, digital measuring instruments, e lect romechanical and electronic tracking systems, nu- clear physics instruments, controlling digital machines, etc.

The accuracy, speed of operation and reliability of automatic digital devices which contain an LDC are nor- mal ly determined by similar characteristics of the converters. Below we describe one possible method of designing a transistorized LDC operating as "digital parallel code to dc voltage" converter, and provide the results obtained in experimental testing of a laboratory model of such a converter, developed by the authors in the V. I. U1 ~ (Lenin) LETI (Leningrad Electrotechnical Institute) in 1960-1961.

Desisn of the decodin~ network. The basic method for converting any digital code N into a proportional out- put voltage U consists in using ohmic resistance decoding networks.

The converted digital code is used for controlling switching elements which provide the required currents or voltages in units of the decoding network whose structure must ensure a relationship of the form (1).

Various structures of decoding networks are described in [1, 2].

In selecting an opt imum structure for the network it is necessary to take into account according to the specific operating conditions of an LDC the following basic factors: the effect of the switching e lement characteristics on the decoding error, the required decoding scale, the value and stability of the input and output resistances of the network, the range of nominal, ohmic resistances of the network, and the effect of the ambient medium on the accuracy of de- coding.

The above factors applied to the choice of the network structure for transistorized LDC circuits, which provide min imum dimensions and weight and high reliability, lead to the following considerations:

393