Western Michigan University Western Michigan University ScholarWorks at WMU ScholarWorks at WMU Master's Theses Graduate College 12-1978 NMR Instrumentation with Solid State Devices NMR Instrumentation with Solid State Devices Syed M. Ahmed Follow this and additional works at: https://scholarworks.wmich.edu/masters_theses Part of the Physics Commons Recommended Citation Recommended Citation Ahmed, Syed M., "NMR Instrumentation with Solid State Devices" (1978). Master's Theses. 2075. https://scholarworks.wmich.edu/masters_theses/2075 This Masters Thesis-Open Access is brought to you for free and open access by the Graduate College at ScholarWorks at WMU. It has been accepted for inclusion in Master's Theses by an authorized administrator of ScholarWorks at WMU. For more information, please contact [email protected].
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Western Michigan University Western Michigan University
ScholarWorks at WMU ScholarWorks at WMU
Master's Theses Graduate College
12-1978
NMR Instrumentation with Solid State Devices NMR Instrumentation with Solid State Devices
Syed M. Ahmed
Follow this and additional works at: https://scholarworks.wmich.edu/masters_theses
Part of the Physics Commons
Recommended Citation Recommended Citation Ahmed, Syed M., "NMR Instrumentation with Solid State Devices" (1978). Master's Theses. 2075. https://scholarworks.wmich.edu/masters_theses/2075
This Masters Thesis-Open Access is brought to you for free and open access by the Graduate College at ScholarWorks at WMU. It has been accepted for inclusion in Master's Theses by an authorized administrator of ScholarWorks at WMU. For more information, please contact [email protected].
Faculty o f The Graduate College in p a r t ia l f u l f i l l m e n t
o f theDegree o f Master o f Arts
Western Michigan U n iv e rs ity Kalamazoo, Michigan
December 1978
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PREFACE
Since i t s development in the e a r ly f o r t i e s , NMR or Nuclear Mag
n e t ic Resonance has been a popular means o f probing in to the micro
scopic aspects o f m a tte r . The work described in th is th es is is an
e f f o r t towards construct in g two pieces o f apparatus which demonstrate
continuous wave (CW) and Pulsed NMR. The emphasis in th is p ro je c t
is on ins trum entation and in p a r t i c u la r , the problems encountered in
such a venture and how these various problems may be solved. How
e ve r , the re la te d theory has been included where necessary. The pre
sent work a lso shows how modern elements o f e le c t ro n ic s - fo r example,
in teg ra ted c i r c u i t s (o r ICs) can be u t i l i z e d to s im p l i fy the whole
p ro je c t tremendously.
Nuclei in a sample a t e q u i l ib r iu m possess both spin up and spin
down s ta te s . The corresponding magnetic quantum number m can assume
values ± i . In a steady magnetic f i e l d H0 the system's m agnetization
vec to r Mz w i l l po in t in the d i r e c t io n o f Hq and the to ta l magnetic
moment y w i l l precess around H0 w ith Larmor frequency cog- I f th is
system is e xc ite d e x t e r n a l ly by a ro ta t in g r f f i e l d Hj a t cog, the
spins o f the nuc le i w i l l f l i p to a h igher energy leve l m = - £ . As a
re s u l t y wi 11 t i p and energy w i l l be absorbed by the system. This is
c a l le d NMR absorp tion . George Pake (1 9 5 0 ) , Abragham (1961 ).
Two d is s ip a t io n mechanisms c a l le d the s p i n - l a t t i c e and sp in -sp in
in te ra c t io n s along w ith magnetic f i e l d inhomogeneity res to re the sys
tem to e q u i l ib r iu m over times ch ara c te r ize d by lo n g itu d in a l and
i i
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transverse re la x a t io n times Tj and T2 . In l iq u id s the d i f fu s io n o f
nuclei due to temperature is responsible fo r re la x a t io n in both
transverse and lo n g itu d in a l d i r e c t io n s , hence T2 g ives the combined
e f f e c t o f both (above) processes. Contrary to t h is , so lid s have
d i f f e r e n t T j and T2 as nuclei are bound in a l a t t i c e s t ru c tu re . The
d is s ip a t io n mechanisms make continuous absorption p o ss ib le . The ab
sorption s ignal w idth (gaussian shape) is inverse ly proportiona l to
time T2 , which can be determined from the s ignal d i r e c t l y .
Another method o f study o f re la x a t io n times is by pulsed e x c i
ta t io n o f the above system. An intense r f burst a t Larmore frequency
is app lied and the dura tion o f the burst is adjusted to pu ll down
the m agnetization vector Mz in to the plane o f H i . In the plane o f
H i, Mz breaks up in to i t s components which s c a t te r a l l around Hq in
a c i r c l e . Over time T2 1 u n t i l th is s c a tte r in g is complete, the
system rad ia tes energy Cat wq) which is detected as an exponentia l
decay c a l le d Free Induction Decay CFID), The decay time T2 ’
includes the e f f e c t o f T j , T2 and magnetic f i e l d inhomogeneity.
The th i rd method o f determining re la x a t io n time is the sp in -
echo method in which two consecutive pulses o f 90° and 180° a t t d is
tance a p art are a p p l ie d . The 180° pulse f l i p s the sca ttered compo
nents o f Ji from the 90° pu lse , through l 80° . The components th a t
are s t i l l in the plane o f Hi then regroup a f t e r a time x from the
180° pu lse, as a re s u l t o f reversal o f the order o f the system. At
the po in t o f regrouping a signal c a l le d "spin-echo" ( re v iv a l o f
phase memory - Bloch, 19^*6) is e m it te d . The am plitude o f spin echo
i i i
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is a decaying exponentia l function o f 2 t . The decay time o f the en
velope is the re la x a t io n time T2 ( in c lu s iv e o f T j ) independent o f
magnetic f i e l d inhomogeneity.
For th is p ro je c t CW NMR and pulsed NMR spectrometers were b u i l t
using s o l id s ta te devices. So lid s ta te devices have an advantage
over vacuum tubes in the areas o f response, working vo ltag es , de
coupling in the c i r c u i t r y , s iz e , and cost. However, s o l id s ta te
devices have only small s ignal handling c a p a b i l i t y and th e re fo re
s a tu ra te qu icker than vacuum tubes.
In th is p ro je c t FET's and IC *s were used fo r large impedance,
low n o is e , high gain and broad band a p p l ic a t io n s . The use o f wide
band v ideo a m p l i f ie r 1C (NE592K) in conjunction w ith FET's fo r the
f ro n t end in the re c e iv e r , s im p l i f ie s the design and takes care o f
the high impedance, low noise requirements w h ile the 1C provides
fa s t recovery from s a tu ra t io n .
Low e x c i ta t io n (10 to 12V pp) seemed to be the only problem in
the present apparatus. New products l i k e VMPA, VMOS FET tra n s is to rs
( S i l ic o n ix Incorporated) which have large power handling c a p a b i l i t ie s
a t high v o ltag e , o f f e r so lu tions to low amplitude e x c i ta t io n . Also
the re c e iv e r gain may prove to be low fo r some experiments (not per
formed here) in which case another id e n t ic a l a m p l i f ie r stage (minus
FET stage) can be added to the e x is t in g system.
Results fo r re la x a t io n time obtained from the CW NMR spectro
meter a re not r e l i a b le due to large sample s iz e : more magnetic f i e l d
inhomogeneity gets included. Also the method in i t s e l f is not very
iv
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accura te . The apparatus works w ell and d isp lays the resonance e f f e c t
c le a r ly .
Results from pulsed NMR spectrometer are good e s p e c ia l ly fo r
g ly c e r in e and l ig h t machine o i l . The o th er two samples (CuSo^.S^O
and w ater) seem to l i e on the upper and lower l im i ts o f the apparatus
c a p a b i l i t y , which again depends s tro n g ly upon magnetic f i e l d homo
g en e ity .
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ACKNOWLEDGEMENTS
I f in d i t d i f f i c u l t to exclude anyone who knows me personally
from being mentioned here. They have a l l contr ibuted d i r e c t l y or in
d i r e c t l y toward r e a l i z a t io n o f th is p ro je c t ; th e re fo re , I extend my
g ra t i tu d e to a l l my fr ie n d s and acquaintances.
My very special regards and thanks are due my adv isor,
Dr. K. Kameswara Rao; w ithout h is guidance and help th is work would
d e f i n i t e ly have not been possib le .
I would a lso thank Professor A. Spence o f the Department o f
Physics a t Michigan S ta te U n iv e rs i ty , Lansing, Michigan, fo r va luab le
discussions and a llow ing me the o pportu n ity to spend some time in his
NMR lab o ra to ry .
A lso , I would l ik e to acknowledge the h e lp , both f in a n c ia l and
academic, extended by the Physics Department a t Western Michigan
U n iv e rs ity and Vid-e-Com Engineering, Kalamazoo, Michigan fo r sparing
various components used in th is p ro je c t .
F in a l ly , I would l i k e to thank the members o f the Graduate Com
m itte e fo r t h e i r time reviewing th is work. A lso , A ,J . and G.G. fo r
typing the rough and f in a l d r a f ts .
Syed M. Ahmed
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UniversityMicrofilms
International300 N. ZEEB R O A D . AN N ARBOR. Ml 48106 18 B EDFO RD ROW. LO NDON WC1R 4EJ. E N G LA N D
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1312613
AHMED* SYED M.NMR INSTRUMENTATION KITH SOLID STATE DEVICES.
WESTERN MICHIGAN U N IV E R S IT Y , M . A . , 1978
UniversityMicrofilms
International 300 n ze e b r o a d , a n n a r b o r , mi «8 io6
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DEDICATION
To my fa th e r
vi i
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TABLE OF CONTENTS
CHAPTER PAGE
I INTRODUCTION .......................................................................................... 1
I I CONTINUOUS WAVE TECHNIQUES OF OBSERVING NMR . . . . 4
D escrip tion o f the Techniques ........................................ 4
D escrip tion o f the Apparatus ............................................. 5
Marginal O s c i l la to r ............................................................. 5
A m p l i f ie r .................................................................................... 7
Results and Discussion ............................................................. 9
I I I PULSED TECHNIQUES OF OBSERVING N M R ............................................ 14
D escrip tion o f the T e c h n iq u e ...................................................14
D escrip tion o f the A p p a r a tu s ...................................................18
O s c i l l a t o r .......................................................................................... 18
Gate and the Gate D r i v e r ......................................................... 21
B uffer A m p l i f ie r ...................................................................... 23
Tank Coil and Probe A s s em b ly ................................................25
R e c e i v e r .............................................................................................. 27
The Spin-Echo Attachment fo r Pulse Generator . . 28
Generator T r ig g e r Source ................................................... 31
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TABLES
TABLE PAGE
2.1 F ie ld Modulation AH vs. Linewidth fo rG l y c e r i n e ...........................................................................................11
2 .2 Relaxation Times & Linewidths fo r a l l Samples . . . . 13
3.1 FID Envelope fo r G l y c e r i n e ............................................................. 36
3 .2 FID Envelope fo r W a t e r ...................................................................... 38
3 .3 FID Envelope fo r CuSOi* 5H2O (IN) ....................................................39
3 . A FID Envelope fo r L ight Machine O il (LMO) ............................AO
3 .5 Spin-Echo Amplitude fo r G lycerine ........................................... A3
3 .6 Spin-Echo Engelope fo r L igh t Machine Oil (LMO) . . . A5
3 .7 Relaxation Times fo r A l l Samples Using PulsedT e c h n i q u e s ......................................................................................A 7
ix
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FIGURES
FIGURE PAGE
2.1 Marginal O s c i l la to r ....................................................................... 6
2 .2 Frequency Monitor ........................................................................... 8
2 .3 NMR Absorption Signal fo r G l y c e r i n e ....................................... 10
3.1 Various Phases o f FID S Spin-Echo Formation . . . . 16
3 .2 Block D ia g ra m ...........................................................................................19
3 .3 O s c i l la to r S B u f f e r ............................................................................ 20
3 . A Diode Gate & Gate D r i v e r .............................................................. 22
3 .5 B uffer A m p l i f i e r ........................................................................... 2A
3 .6 Sketch o f NMR Probe w ith Tank Coil S Diodes . . . . 26
3 .7 Receiver A m p li f ie r ....................................................................... 29
3 .8 Gen. Attachment fo r 180° P u l s e s ................................................ 30
3 .9 T r ig g e r Source fo r Pulse Generator .............................. 32
3 .1 0 FID Signal fo r G l y c e r i n e .......................... ....... .......................3A
3.11 FID P lo t fo r G l y c e r i n e ................................................................... 37
3 .12 Spin-Echo fo r G lycerine a t D i f f e r e n t t ................................A2
3 .13 Spin-Echo Amplitude P lo t fo r G lycerine ........................ kk
x
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I . INTRODUCTION
The roots o f NMR can be traced as f a r back as 1924, to P a u l i 's
explanation o f hyperf in e s p l i t t i n g o f o p t ic a l spectra using nuclear
magnetic moments. The f i r s t successful NMR experiments were per
formed independently by P u r c e l l , Torrey and Pound (1946 ), and by
Bloch, Hansen and Packard (1946 ). These were extended by Bloembergen
(1948 ). Hahn (1950) used pulse techniques in determining the re la x a
t io n time in l iq u id s and developed spin-echo techniques which over
come the problem o f magnetic f i e l d inhomogeneity. Pulse techniques
are c o n t in u a lly undergoing changes as newer s o l id s ta te devices are
becoming a v a i la b le .
The nucleus studied in th is in v e s t ig a t io n is proton, and has
nuclear spin quantum number I = 2 . The magnitude o f the nuclear1
angular momentum vector is [ l ( I + 1) ] J fi and the magnetic quantum
number m can take the values + i and - £ . When such a substance is
placed in a steady magnetic f i e l d H0 , the m = +£ s ta te , in which the
spin vector is along the d ire c t io n o f H0 , w i l l have a lower energy
than the m = -2 s ta te , in which the spin vector is in the opposite
d ir e c t io n . Each in d iv id u a l magnetic moment vector ( in the same
d ire c t io n as spin vec tor) precesses around H0 w ith a c h a r a c te r is t ic
frequency c a l le d the Larmor frequency, ojq. The Larmor frequency and
H0 are re la te d by the fo l lo w in g expression
uj q = y H q ( 1 . 1 )
where y is the gyromagnetic r a t io o f proton. The d i f fe re n c e o f
1
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2energy in the two s ta te s is hojg. This frequency f o r protons is 21 .3
MHz in a f i e l d o f 5KGauss.
I f a t th is p o in t another magnetic f i e l d vector Hj ro ta t in g a t
Larmor frequency is brought a t 9 0 ° to Hg i t s c i r c u l a r ly p o la r ize d
component ro ta t in g in the same sense as the nuclear spins induces
t r a n s it io n s from the low energy s ta te (spin up) to the high energy
s ta te (spin down). For th is to happen the f i e l d Hg and the f r e
quency o f H1 have to s a t is f y eq. 1 .1 . This phenomenon is c a l le d
Nuclear Magnetic Resonance.
In the absence o f an r f f i e l d the nu c lea r spins are in e q u i l i
brium a t the temperature o f the substance and the population o f the
lower energy leve l exceeds th a t o f the upper level by the Boltzmann
f a c to r . Hence the net magnetic moment o f the substance w i l l have a
non-zero component along the d i re c t io n s o f H g . At resonance the r f
f i e l d Hj reduces the excess o f population in the lower energy s ta te
by f l ip p in g spin-up s ta te s to spin-down. One can observe a steady
NMR absorption s ignal in a macroscopic sample s ince the in te ra c t io n s
amongst the spins and the spin s y s te m - la t t ic e in te ra c t io n s tend to
re s to re the o r ig in a l p o p u la t ion .
Since the spin system is in thermal e q u i l ib r iu m w ith the l a t t i c e
some o f the excess energy in the spin system w i l l be d is s ip a te d to
the l a t t i c e . This process is exponentia l in n a tu re and has a charac
t e r i s t i c time T j c a l le d s p i n - l a t t i c e or thermal re la x a t io n tim e.
This is a lso the c h a r a c te r is t ic time in which the magnetic moment
component along the d i r e c t io n o f Hg is restored to i t s steady s ta te
value ( o f f resonance). Hence i t is c a l le d lo n g itu d in a l re la x a t io n
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3
re la x a t io n t im e.
Each nuclear spin f in d s i t s e l f not only in an ap p lied magnetic
f i e l d H0 , but a lso in a small local magnetic f i e l d produced by the
neighboring sp ins. This sp in -sp in in te ra c t io n makes the resonance
not p e r fe c t ly sharp as suggested in eq. 1 .1 . The resonance l in e w i l l
have a w idth comparable to the average local f i e l d . The l inew id th
o f the resonance is re la te d to a c h a r a c te r is t ic time T2 (sp in -sp in
re la x a t io n time) by the fo l lo w in g equation (Andrew, 1958).
AH, = - f - (1 .2 )2 yT2
The sp in -sp in in te ra c t io n time T2 is the time during which the
in d iv id u a l nuc lear spins precess around H0 in phase, inducing a non
zero magnetic f i e l d component along the d ire c t io n perpend icu lar to
H0 . Hence T2 is c a l le d transverse re la x a t io n tim e.
In d i l u t e l iq u id s the thermal a g i ta t io n causes both lo n g itu d i
nal and transverse components to reach e q u i l ib r iu m in comparable
tim es, hence T j = T2 .
There are b a s ic a l ly two techniques fo r studying NMR, the con
tinuous e x c i ta t io n method and the pulse e x c i ta t io n method. In the
f i r s t method the nuclei in the sample are e xc ited by a continuous
wave (CW) e le c t r o n ic o s c i l l a t o r (source o f Hj f i e l d ) a t Larmor f r e
quency. In the second method the e x c i ta t io n is in the form of
bursts o f r f f i e l d a t Larmor frequency.
The method, apparatus, and re s u lts fo r the CW technique are
covered in Chapter I I , and the pulsed technique is covered in
Chapter I I I .
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I I . CONTINUOUS WAVE TECHNIQUES OF OBSERVING NMR
A. Descrip tion o f the Technique
In the absorption mode d e tec t io n o f NMR, w ith continuous radio
frequency wave e x c i ta t io n , the energy supplied by the r f f i e l d to the
nucle i is monitored. The sample is put in a te s t tube and the te s t
tube is placed in the tank c i r c u i t o f an r f o s c i l l a t o r . This allows
a good coupling between the o s c i l l a t o r and sample fo r energy tra n s fe r
(Bloch, 1946). The tank c i r c u i t is b u i l t p h y s ic a lly separate from
the res t o f the o s c i l l a t o r c i r c u i t to keep the e le c t ro n ic c i r c u i t
away from the magnetic f i e l d H0 . The tank c i r c u i t conta in ing the
sample te s t tube is now placed in the magnetic f i e l d Hg such th a t the
tank c o i l ax is is a t 90° to the f i e l d H0 . At resonance the energy
supplied to the nuclei is more than a t o f f resonance. The r f o s c i l
l a t o r used in the method o s c i l l a t e s m arg ina lly or weakly. This is
accomplished w ith an a d ju s tab le feedback so th a t i t can be operated
a t a po in t where i t b a re ly o s c i l l a t e s . The current supplied to the
o s c i l l a t o r is monitored and the e x tra current drawn by the o s c i l l a
t o r a t resonance is a m p lif ie d and displayed on the o sc il lo sco p e .
The signal is Gaussian in shape and the lin ew id th is defined
as the w idth o f the signal a t h a l f maximum am plitude. Eq. 1 .2 which
gives the re la t io n between re la x a t io n time and the l in e width is
v a l id only fo r a p e r fe c t ly homogeneous Hq. In p ra c t ic e Hq is never
p e r fe c t ly homogeneous fo r a l l the nuclei throughout the volume o f
the sample. This is l i k e the l o c a l - f i e l d e f f e c t broadening the
resonance; hence the l in ew id th observed in the experiment is given
4
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5
by the fo l lo w in g equation:
AH = (2 .1 )
y m
T2* is the c o n tr ib u t io n from the magnetic f i e l d inhomogeneities
The resonance l in ew id th in an inhomogeneous magnetic f i e l d is
more than in a p e r fe c t ly homogeneous f i e l d by a fa c to r determined by
T2* .
The s ize o f the sample determines the s ig n a l - to -n o is e r a t io and
the w idth o f the s ig n a l . The la rg e r sample gives a b e t te r s ig n a l -
to -n o is e r a t i o , but the signal becomes broader owing to the magnetic
f i e l d inhomogeneities.
B. D escrip tion o f the Apparatus
1. Marginal O s c i l la to r
The c i r c u i t diagram o f the o s c i l l a t o r is shown in F ig . 2 .1 .
The o s c i l l a t o r is o f the C o lp i t ts type using 2N5^59 FET fo r low
d r i f t and noise on a copper s t r i p m atr ix -b o ard . I t operates margin
a l l y around 130 yA. The tank c i r c u i t c o i l consists o f 12 turns o f
18 swg enamel w ire , wound d i r e c t l y over the te s t tube conta in ing the
sample. The diameter o f the te s t tube is 1 cm. Since the c o i l is
r i g i d , i t a lso functions as a te s t tube h o ld er. The c o i l is mounted
a t the end o f 12", 3 /8 " diameter copper tub ing . One end o f the c o i l
is grounded to the tube w h ile the o th e r runs v ia a piece o f RG59U
cable through the tub ing . The o th er end o f the tubing is f ix e d w ith
an Amphenol connector ( to make the tank c i r c u i t detachable) to a
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6
- u — 1—lo (ft X r
i»
b.
in
o*
U U U L /
CM
CP•Hfa
P O -P (0 i—i i—I•HOmO
(0c•H&>PCOs
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7“ x 5" x 3“ aluminum box. The box then contains both the o s c i l l a
to r and a m p l i f ie r c i r c u i t boards.
A good ground is es tab lish ed w ith in the box by running a piece
o f copper w ire b ra id along the length o f the box. A l l ground con
nections are t ie d to the b ra id which in turn is t ie d to the box.
This arrangement reduces the noise tremendously.
The o s c i l l a t o r regeneration contro l (p o s i t iv e feedback) is pro
vided a t the broadside o f the box along w ith frequency contro l and
a m p l i f ie r n u ll c o n tro l . The frequency contro l is achieved by vary ing
the capacitance across the tank c o i l w ith a v a r ia b le cap ac ito r and
geared d r iv e . The frequency range thus obtained is k MHz, s ta r t in g
a t 12.8 MHz.
A separate wide-band a m p l i f ie r (F ig . 2 .2 ) a llows frequency
m onitoring . In th is experiment the frequency was only determined
a f t e r the measurements on s ignal were made, because o f a noisy f r e
quency counter. Some d e v ia t io n in frequency occurs when cables are
attached to the a m p l i f ie r but th is was measured to be less than
0.5%.
2 . A m p li f ie r
The a m p l i f ie r is b u i l t using a p7^1 op era t io n a l a m p l i f ie r . The
c i r c u i t diagram is shown in F ig . 2 .1 . The gain o f the a m p l i f ie r is
around 2000. An e x te rn a l contro l over o f f s e t n u ll is provided, be
cause w ith d i f f e r e n t samples d i f f e r e n t conditions o f m a rg in a l i ty are
e s ta b l is h e d . So a small change in input vo ltag e occurs which has to
be balanced o f f fo r optimum a m p l i f ie r o p e ra t io n . The a m p l i f ie r is
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8
CN
CM
-H
>
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d .c . connected to the point in the o s c i l l a t o r c i r c u i t which l ie s on
the branch carry ing the o s c i l l a t o r c u rre n t . Once the nu ll is es ta
b lished (zero d .c . leve l a t the output) the a m p l i f ie r picks up any
dev ia t io n s from the n u l l condition and a m p li f ie s them. The output
is connected to a scope or X-Y recorder d i r e c t l y .
C. Results and Discussion
The steady magnetic f i e l d H0 is modulated w ith 60 Hz by passing
60 Hz c u rren t through a p a ir o f yoke c o i ls wound around the Hg mag
net poles. The p r in c ip a l f i e l d Hg in the above case is passed twice
in one c yc le .
(H 0 - AH) Hg = = (H 0 + AH)
The e x te n t o f scan 2aH is important. This has to be determined
e x p e r im e n ta l ly . For a s u i ta b le value o f modulating current the s ig
nal is obta ined . L a ter the modulating current is adjusted to get a
region o f constant w idth o f the signal fo r v a r ia t io n s in the modula
t in g c u rre n t . Large modulating current d is to r ts the Hg f i e l d and
hence shortens the re la x a t io n time T2 ; correspondingly the signal
width increases.
The s ignal fo r g ly ce r in e is shown in F ig . 2 .3 - The s iz e o f the
sample used in the experiment was approximately 2 c .c . The l in e
w idth is measured fo r a number o f modulation se tt in g s and the data
is given in Table 2 .1 . A value o f the l in ew id th was chosen in an
area where the l in ew id th v a r ia t io n was f a i r l y constant. The value
o f T2 is c a lc u la te d from th is l inew id th to be 0 .38 msec. The un
c e r t a in ty in the value can be as high as 10% due to the inaccuracy
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Fig 2.3 NMR Absorption Signal
for Glycerine.(a) off resonance(b) at resonance
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