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Bas
ic B
iom
olec
ular
Tra
inin
g C
ours
e
Exp
erim
enta
l Bio
mol
ecul
ar N
MR
Tra
inin
g C
ours
e
Day
1
S
pect
rom
eter
Bas
ics:
mag
net,
prob
e, c
onfig
urat
ion,
tuni
ng, l
ocki
ng, s
him
min
g,
gr
adie
nt s
him
min
g.
Day
1,2
1D s
pect
ra: d
eter
min
ing
H2O
line
shap
e, c
alib
ratin
g 1 H
pul
se w
idth
s, a
cqui
ring
H2O
pre
satu
ratio
n sp
ectra
.
W
ater
sup
pres
sion
: cal
ibra
ting
wat
er fl
ip b
ack
puls
es, a
cqui
ring
flipb
ack-
wat
erga
te
1D s
pect
ra.
Day
2,3
Hom
onuc
lear
2D
: Flip
back
, wat
erga
ted
NO
ES
Y sp
ectra
.
Het
eron
ucle
ar 2
D: W
ater
gate
d an
d S
ensi
tivity
-Enh
ance
d H
-N H
SQ
C.
Con
stan
t-Tim
e, H
-C H
SQ
C.
Day
4
Het
eron
ucle
ar 3
D: N
OE
SY-
HS
QC
, HN
CA
B 0
xy
z
n↑n↓ ν 0 =
γ B 0
2 π
xy
z
xy
z
⇒
n↓n↑
≡
ν 0
Meq
A su
perc
ondu
ctin
g so
leno
idis
use
d to
gen
erat
e a
hom
ogen
eous
mag
netic
fie
ld B
0 al
ong
the
vert
ical
(z
) axi
s. A
sam
ple
cont
aini
ngN
MR
activ
e nu
clei
(e.g
. 1H
,13
C) i
s pla
ced
in th
e ce
nter
of th
e fie
ld.
The
nucl
ear s
pins
in
tera
ct w
ith B
0 an
d,
base
d on
thei
r spi
n st
ates
,di
stri
bute
d in
to
ener
gy le
vels
whi
ch a
rese
para
ted
by th
e La
rmor
fr
eque
ncy
ν 0, p
ropo
rtio
nal
to B
0 an
d nu
clea
r gy
rom
agne
tic ra
tio (γ
) (fo
r 1H
, B0
= 1
1.7
T ⇒
ν0
= 5
00 M
Hz)
. For
+ve
γ, t
he lo
wer
ene
rgy
"up"
spin
s are
in sl
ight
ex
cess
ove
r "do
wn"
spin
s, at
equ
ilibr
ium
.
Equi
vale
ntly
, the
spin
sm
ay b
e re
gard
ed a
spr
eces
sing
aro
und
B 0w
ith a
freq
uenc
y ν 0
, with
the
n↑ a
nd n
↓ sp
ins
poin
ting
in o
ppos
itedi
rect
ions
alo
ng th
e z a
xis,
and
the
xy
com
pone
nts d
istr
ibut
edra
ndom
ly.
At e
quili
briu
m, t
his
resu
lts in
the
deve
lopm
ent o
f a b
ulk
nucl
ear m
agne
tizat
ion
(Meq
) alo
ng th
e z a
xis (
para
llel t
o B 0
), pr
opor
tiona
l to
the
exce
ss o
f low
er e
nerg
ysp
ins. M
eq ∝
(n↑
− n↓
)
Bas
ic N
MR
Spe
ctro
scop
y: th
e M
agne
t
xy
zB 0
B 1 c
os (2
πν0t
)
n↑n↓
xy
zM
eq
B 1
B 1
M0
xy
z
Mt
≡
A tr
ansm
itter
gen
erat
esa
radi
o fre
quen
cy (r
f) fie
ld o
scill
atin
g at
the
Larm
or ("
reso
nanc
e")
frequ
ency
in rf
coi
ls
surr
ound
ing
the
sam
ple
in th
e pr
obe.
The
dire
ctio
n of
the
asso
ciat
ed o
scill
atin
g m
agne
tic fi
eld
B 1 is
pe
rpen
dicu
lar t
o B 0
.
The
rf fi
eld
indu
ces
tran
sitio
ns b
etw
een
the
nucl
ear s
pin
ener
gy le
vels
.
This
is e
quiv
alen
t to
aro
tatio
n of
the
bulk
nuc
lear
m
agne
tizat
ion
Meq
from
the
z axi
s tow
ard
the
xy p
lane
.C
ompl
ete
satu
ratio
n of
spin
pop
ulat
ions
cor
resp
onds
to a
900
rota
tion.
The
tran
smitt
er is
turn
ed o
ff,an
d th
e m
agne
tizat
ion
vect
orpr
eces
ses f
reel
y in
the
xypl
ane
at a
n an
gula
r fre
quen
cyv 0
. A B
1 fie
ld w
hich
indu
ces
a 90
0 ro
tatio
n is
cal
led
a 90
0
puls
e.
B 0
Bas
ic N
MR
Spe
ctro
scop
y: th
e Tr
ansm
itter
x
y
x
y
z
The
freel
y pr
eces
sing
mag
netiz
atio
n ve
ctor
M0
trac
es a
spir
al tr
ajec
tory
as i
t exp
erie
nces
"fr
ictio
n"
in th
e fo
rm o
f rel
axat
ion
proc
esse
s (T 1
,T2)
whi
ch
retu
rn it
to e
quili
briu
m (M
xy d
ecay
s to
zero
, M
z gro
ws t
o M
eq ).
In
the
xy p
lane
, the
foot
prin
t of t
he p
rece
ssin
gm
agne
tizat
ion
indu
ces e
xpon
entia
lly d
ecay
ing
sinu
soid
al v
olta
ges i
n th
e rf
coi
l, al
ong
the
x an
d y
axes
: Fre
e In
duct
ion
Dec
ay (F
ID)
M0Mt
Mz(
∞) =
Meq
Mxy
(∞) =
0si
n (2
πν0t
) e− t
/T2
cos (2πν0t) e−t/T2
Bas
ic N
MR
Spe
ctro
scop
y: th
e R
ecei
ver
My(
t) =
A c
os (2
πν0t
) e− t
/T2
Mx(
t) =
A si
n (2
πν0t
) e−t
/T2
AD
C1
AD
C2
Com
pute
r
Rea
l
Imag
inar
y
The
NM
R si
gnal
com
pris
ing
of tw
o FI
Ds r
epre
sent
ing
x an
d y
com
pone
nts o
f the
pre
cess
ing
mag
netiz
atio
nis
fed
into
two
Anal
og to
Dig
ital C
onve
rter
s (AD
Cs)
, whe
re th
ey a
re sa
mpl
ed a
t equ
al ti
me
inte
rval
s.
The
digi
tized
dat
a is
tran
sfer
red
to a
com
pute
r and
stor
ed a
s the
"re
al"
and
"im
agin
ary"
com
pone
nts o
f a
com
plex
tim
e do
mai
n si
gnal
.
The
com
bine
d da
ta is
subj
ecte
d to
a c
ompl
ex F
ouri
er T
rans
form
(FT)
to y
ield
a fr
eque
ncy
dom
ain
spec
trum
.
FT
Mxy
(t) =
My(
t) +
i Mx(
t) =
A e
−i( 2
πν0t
) e−t
/T2
Re
ImR
e (A
bsor
ptiv
e)Im
(Dis
pers
ive)
ν 0
ν 0
Bas
ic N
MR
Spe
ctro
scop
y: th
e D
igiti
zer &
Com
pute
r
B 0
xy
z
RF
Tran
smitt
er+
Puls
e Pr
ogra
mm
er
Rec
eive
r+
Dig
itize
r
Com
pute
r
Mag
net
Prob
e +
Sam
ple
Bas
ic E
lem
ents
of a
n N
MR
Spe
ctro
met
er
Prea
mpl
ifier
Set
the
tem
pera
ture
Tune
the
prob
e
Lock
the
field
Shi
m -
man
ual +
gra
dien
t
Ana
lyze
H2O
or H
DO
line
shap
e
Det
erm
ine
1 H 9
00 p
ulse
wid
th
Det
erm
ine
H2O
/HD
O fr
eque
ncy
Acq
uire
a 1
H 1
D s
pect
rum
inte
rcha
ngea
ble
repe
at u
ntil
lines
hape
's
OK
Bas
ic S
tartu
p Pr
otoc
ol
ensu
res
rf p
ulse
sar
e op
tim
ally
abs
orbe
dby
the
sam
ple
corr
ects
for
mag
neti
cfi
eld
drif
t ov
er t
ime
ensu
res
unif
orm
m
agne
tic
fiel
d ov
ersa
mpl
e vo
lum
e
Fiel
d-Fr
eque
ncy
Lock
ing
The
spec
trom
eter
mon
itors
the
2 H si
gnal
from
the
deut
erat
ed so
lven
t to
(a).
Ach
ieve
spat
ial
hom
ogen
eity
of t
he B
0 fie
ld o
ver t
he sa
mpl
e vo
lum
e (s
him
min
g).
(b).
Smoo
then
out
tim
e-va
ryin
g flu
ctua
tions
in th
e B
0 fie
ld (l
ocki
ng).
x
yM
0
M0
sin
(2πν
0t) e
−t/T
2
M0 cos (2πν0t) e−t/T2
Mt
Re
(Abs
orpt
ive)
Im (D
ispe
rsiv
e)
ν 0
ν 0
mon
itore
d fo
r shi
mm
ing
mon
itore
d fo
r loc
king
A d
edic
ated
par
t of t
he sp
ectro
met
er c
ontin
uous
lym
onito
rs th
e a
bsor
ptiv
e an
d di
sper
sive
line
shap
esof
the
2 H si
gnal
.
B =
B0
− ∆
B
ν 0
VV
+∆V
B =
B0
+ ∆
B
−∆V
ν 0
Posi
tive
err
or v
olta
ge +
∆V
at
lock
res
onan
cefr
eque
ncy:
neg
ativ
e fi
eld
drif
t: i
ncre
ase
curr
ent
to c
ompe
nsat
e B
by
+∆B
Neg
ativ
e er
ror
volt
age
−∆V
at
lock
res
onan
cefr
eque
ncy:
pos
itiv
e fi
eld
drif
t: d
ecre
ase
curr
ent
to c
ompe
nsat
e B
by
−∆B
Fiel
d D
rift C
orre
ctio
n by
Fee
dbac
k Lo
op
Lock
freq
uenc
yva
riatio
n
Fiel
d C
orre
ctio
n
B0(
t)
t
Tx
Rx
V
B0
∆B
The
err
or v
olta
ge i
s no
tco
mpu
ted
inst
anta
neou
sly,
but
afte
r in
tegr
atin
g th
e lo
ck s
igna
l ov
er a
per
iod
of t
ime
(> 1
s).
Prop
er lo
ckin
g (a
nd sh
imm
ing)
requ
ires t
he lo
ck p
hase
to b
e pr
oper
ly a
djus
ted
so th
at th
e re
sona
nce
freq
uenc
y of
the
disp
ersi
on m
ode
sign
al a
nd th
e pe
ak h
eigh
t of
the
abso
rptio
n m
ode
sign
al -
for s
him
min
g- a
re re
gist
ered
cor
rect
ly.
mis
adju
sted
lock
pha
se
The
Lock
ing
Proc
edur
e
lock
off
fiel
d no
t at
res
onan
ceos
cilla
tion
s re
duce
as
we a
ppro
ach
reso
nanc
e
adju
st z
0
lock
sig
nal l
evel
s ou
t at
res
onan
ce
turn
lock
on
NM
R P
robe
From
: Pro
tein
NM
R S
pect
rosc
opy,
P
rinci
ples
and
Pra
ctic
e,
J. C
avan
agh,
W.J.
Fai
rbro
ther
,
A.G
. Pal
mer
III,
N.J.
Ske
lton,
A
ssoc
iate
d Pr
ess,
San
Die
go, 1
996,
pag
e 98
.
Sche
mat
ic o
f an
NM
R P
robe
tuni
ng ro
dm
atch
ing
rod
Prob
e B
ase
coax
ially
m
ount
ed
obse
rve
coil
deco
uplin
gco
il
C
hara
cter
istic
s of a
n N
MR
pro
be (t
uned
LC
circ
uit)
:
freq
uenc
y
ω =
1/√
LC
L
= in
duct
ance
, qu
ality
fact
or Q
= ω
L/R
C =
cap
acita
nce,
im
peda
nce
Z =
R +
i[ ω
L −
1/(ω
C)]
R
= re
sist
ance
The
prob
e is
an
LC c
ircui
t whi
ch m
ust b
e tu
ned
to th
e re
sona
nce
freq
uenc
y of
the
nucl
eus b
eing
stud
ied
(impe
danc
e =
R w
hen
ω =
1/√
LC) a
nd,
The
impe
danc
e of
the
rf c
oil +
sam
ple
mus
t be
mat
ched
to th
at o
f the
sour
ce
(spe
ctro
met
er) e
lect
roni
cs.
Thes
e ar
e ad
just
ed u
sing
var
iabl
e ca
paci
tors
− tu
ning
and
mat
chin
g:
Coi
l Len
gth
rela
ted
to (
a). l
engt
h of
hom
ogen
eous
regi
on o
f B0.
(b)
. len
gth
of R
T sh
ims a
ctiv
e re
gion
. (
c). R
F ho
mog
enei
ty.
Coi
l Fill
ing
Fact
or η
(inc
reas
es w
ith η
).Pr
obe
Q (i
ncre
ases
with
Q).
Die
lect
ric c
onst
ant o
f sam
ple
(dec
reas
es w
ith
incr
easi
ng d
iele
ctric
- re
duce
s Q, t
unin
g/m
atch
ing
is d
iffic
ult).
Prob
e Se
nsiti
vity
V2 R
coil
(Rco
il +
Rso
urce
)2P c
oil =
Ctu
neCm
atch
L
Tuni
ng u
sing
a D
irect
iona
l Cou
pler Tr
ansm
itter
Ctu
neCm
atch
LD
.C.
Pow
er M
eter
Thes
e ad
just
men
ts a
re u
sual
ly in
depe
nden
t if y
ou a
re c
lose
to o
ptim
al tu
ning
/mat
chin
g. O
ther
wis
e,th
ey a
re li
kely
to in
tera
ct w
ith e
ach
othe
r.
or
exte
nt o
f mat
chin
g(m
axim
ize
dip)
ext
ent o
f tun
ing
(min
imiz
e se
para
tion)
tuni
ngfr
eque
ncy
Gra
phic
alD
ispl
ay
Adj
ust t
unin
g an
d m
atch
ing
capa
cito
rs
to m
inim
ize
refle
cted
pow
er in
the
pow
er m
eter
.
Reflected Power
Freq
uenc
y
Hig
h Q
, Low
RLo
w Q
, Hig
h R
Q =
ωR
/∆ω
Inse
nsiti
ve to
cha
nges
in sa
mpl
e co
nditi
ons,
or c
hang
es in
cen
ter f
requ
ency
.Lo
w ω
, or l
ossy
sam
ples
: R =
hea
t, du
e to
high
salt/
cond
uctin
g co
nditi
ons
Hig
h se
nsiti
vity
aro
und
cent
er fr
eque
ncy
and
chan
ges i
n sa
mpl
e co
nditi
ons,
e.g.
diel
ectri
c co
nsta
nt. ω
R∆ωV
VR
∆ω =
wid
th c
orre
spon
ding
to
V=
VR
/√2
ωR
= re
sona
nce
freq
uenc
y
xmtr
prob
e
outp
ut tu
neou
tput
prob
e
From
Tx
(cha
n 1) To
Rx
To
Pro
be
1H/1
9Fpr
eam
p
B
Pro
beH
1
filte
ra b
A
C13 N15
From
Tx
(dec
2,
cha
n 3)
From
Tx
(dec
1,
cha
n 2)
15N filter
13C filter
xmtr
prob
e
outp
ut tu
neou
tput
prob
e
From
Tx
(cha
n 1)
To R
x
To
Pro
be
Pro
beH
1fil
ter
C13 N15
From
Tx
(dec
2,
cha
n 3)
From
Tx
(dec
1,
cha
n 2)
15N filter
1H filter
1/4
wav
ele
ngth
ca
ble
BB
pre
amp
Con
figur
atio
n fo
r 1H
Obs
erve
13C
,15N
(or X
) Dec
oupl
e
Con
figur
atio
n fo
r 13C
(or X
) Obs
erve
, 1H
Dec
oupl
e
xmtr
xmtr
outp
ut
prob
e
outp
utfilte
r
tune
outp
ut
prob
e
50
From
Tx
From
Tx
To R
xTo
Rx
1/4
wav
ele
ngth
cab
le
To
Pro
be
1H/1
9Fpr
eam
p40
-400
MH
zB
B p
ream
p
xmtr
xmtr
outp
ut
prob
e
outp
ut tu
neou
tput
prob
e
50
From
Tx
From
Tx
To R
xTo
Rx
1/4
wav
ele
ngth
cab
le
To
Pro
be
1H/1
9Fpr
eam
p40
-400
MH
zB
B p
ream
p
prob
epr
obe
atte
nch
anat
ten
chan
filte
r
Prea
mpl
ifier
Hou
sing
Con
figur
atio
n
H1
or F
19 O
bser
veX
Nuc
leus
Obs
erve
Dis
conn
ect c
able
from
A(f
ilter
) and
con
nect
it to
a
(por
t lab
eled
pro
be)
on th
e tu
ning
inte
rfac
e.
Pro
be
To
Pro
beH
1xm
tr
prob
e
outp
ut tu
neou
tput
prob
eFrom
Tx To
Rx
1H/1
9Fpr
eam
p
B
filte
ra b
Pro
be
Axm
tr
prob
e
outp
ut tu
neou
tput
prob
eFrom
Tx To
Rx
To
Pro
be
1H/1
9Fpr
eam
p
B
Pro
be
H1
filte
ra b
A
Cab
le c
onne
ctio
ns fo
rH
1 ob
serv
e op
erat
ions
To
Pro
beP
robe
H1
xmtr
prob
e
outp
ut tu
neou
tput
prob
eFrom
Tx To
Rx
1H/1
9Fpr
eam
p
B
filte
ra b
AD
isco
nnec
t cab
le fr
om B
on H
1 pr
eam
p (la
bele
d ou
tput
) an
d co
nnec
t it
to b
on
tuni
ng in
terf
ace
(labe
led
tune
out
put)
.
Tuni
ng C
onfig
urat
ion
for H
1
1
2
xmtr
prob
e
outp
ut tu
neou
tput
prob
eFrom
Tx
To R
x
1H/1
9Fpr
eam
p
B
a b
c h a n
a t t e n
- +0
- +9
prob
e To P
robe
a
LED
c h a n
a t t e n
- +0
- +9
prob
ea
LED
c h a n
a t t e n
- +1
- +9
prob
e To P
robe
a
LED
100
c h a n
a t t e n
- +1
- +9
prob
e To P
robe
a
LED
001
c h a n
a t t e n
- +0
- +9
prob
ea
LED
xmtr
prob
e
outp
ut tu
neou
tput
prob
eFrom
Tx To
RxTo
P
robe
1H/1
9Fpr
eam
p
B
filte
ra b
A
Ensu
re a
ttenu
atio
n is
8 o
r 9 a
ndch
anne
l sel
ectio
n is
0. T
he d
ispl
ay
is d
ark
and
LED
is fl
ashi
ng re
d.
Pres
s the
+ k
ey to
sele
ctch
anne
l 1. T
he d
ispl
ay tu
rns o
nan
d di
spla
ys re
flect
ed p
ower
(arb
itrar
y un
its).
Pres
s the
(−) k
ey to
sele
ctch
anne
l 0. T
he d
ispl
ay tu
rns o
ffbu
t LED
con
tinue
s to
blin
k.
Dis
conn
ect c
able
(LED
stop
sfla
shin
g) a
nd re
conn
ect t
ofil
ter.
Adj
ust m
atch
ing
and
tuni
ngca
paci
tors
to m
inim
ize
refle
cted
pow
er (<
10)
. DO
NO
T FO
RC
ET
UN
E/M
ATC
H R
OD
S IF
T
HE
Y A
RE
PE
GG
ED
OU
T !!
Dis
conn
ect t
une
out c
able
from
b a
nd re
conn
ect t
o H
1 pr
eam
p ou
tput
(B).
Proc
edur
e fo
r Tun
ing
H1/
F19
Spat
ial
Mag
neti
c Fi
eld
Inho
mog
enei
ty
B(z) B0
ν 0 z
B(z) B0
ν 0 z
ν(z)
= γ
B(z
)/(2
π)
Inho
mog
enei
ty o
f th
e st
atic
fiel
d al
ong
the
z axi
s, B
(z).
Diff
eren
t par
ts o
f the
sam
ple
reso
nate
ove
ra
rang
e of
freq
uenc
ies
(∆ν)
due
to th
e fie
ld
inho
mog
enei
ty:
The
spec
trum
co
nsis
ts o
f con
tribu
tions
from
eac
h of
thes
esp
in is
ochr
omat
s
The
reso
nanc
e is
bro
ader
th
an th
e in
trins
ic li
ne-w
idth
line
λ, a
nd th
e lin
e-sh
ape
refle
cts t
he fi
eld
inho
mog
enei
ty p
rofil
e
Shim
min
g
Idea
lized
, per
fect
lyho
mog
eneo
us st
atic
fiel
d pr
ofile
alo
ng th
e z
axis
:
B(z
) = B
0
Ever
y pa
rt of
the
sam
ple
reso
nate
s at t
he sa
me
freq
uenc
y:
ν(z)
= γ
B0/
(2π)
The
linew
idth
(λ) o
f eac
h re
sona
nce
is d
icta
ted
sole
ly b
y ph
ysic
o-ch
emic
al p
rope
rties
of t
he m
olec
ule
(rel
axat
ion,
exc
hang
e, e
tc)
The
sign
al h
eigh
t is t
hesu
m o
f all
thes
e co
ntrib
utio
ns.
If λ
is sm
all,
the
peak
is in
tens
ean
d na
rrow
.
∆v
λ
shor
t,bro
ad, d
isto
rted
inte
nse,
narr
ow, s
ymm
etric
B(z
) = B
0 +
b 1 z
+ b
2 z2
+ b
3 z3
+ …
B'(z
) = −
b1
z −
b 2 z
2 −
b 3 z
3 −
…
B(z
) − B
'(z) =
B0
The
field
inho
mog
enei
ty is
exp
ress
edas
a p
olyn
omia
l in
z (ac
tual
ly
sphe
rica
l har
mon
ics,
or a
ngul
arpa
rts o
f ato
mic
orb
itals
).
The
user
(or s
oftw
are)
man
ipul
ates
curr
ent i
n sh
im c
oils
surr
ound
ing
the
sam
ple
to g
ener
ate
a co
unte
ract
ing
mag
netic
fiel
d B
'(z).
Adj
ustin
g a
shim
z2, f
or e
xam
ple,
mod
ulat
es th
e b 2
z2 te
rm.
Idea
lly, a
per
fect
B'(z
) fie
ld w
ill c
ompl
etel
yca
ncel
the
field
inho
mog
enei
ty a
nd
yiel
d a
perf
ectly
hom
ogen
eous
fiel
d, B
0.
z2 z4 z6
z z3 z5
Impr
ovem
ent i
n fie
ld h
omog
enei
ty is
ass
esse
d by
obs
ervi
ng
an in
crea
se in
the
heig
ht o
f the
abs
orpt
ion
mod
e di
spla
y lo
ck si
gnal
(loc
k le
vel)
duri
ng th
e sh
imm
ing
proc
edur
e
Shim
min
g
Fiel
d in
hom
ogen
eitie
s alo
ng x
and
y d
irect
ions
als
o ne
edto
be
shim
med
out
. Ind
ivid
ual s
him
s are
not
inde
pend
ent
and
inte
ract
with
one
ano
ther
. Hig
her o
rder
z sh
ims a
re
"con
tam
inat
ed"
by lo
wer
ord
er sh
ims.
B(x
,y,z)
= B
(z) +
c1
x +
c 2 y
+ c
3 xz
+ c
4 yz
+ c
5 xy
+ …
Th
ere
are
28 sh
ims o
n ou
r 500
MH
z sp
ectro
met
er
(type
dgs
in v
nmr)
.
Shim
min
g is
a c
ompl
ex a
nd o
ften
tedi
ous p
roce
ss, b
ut is
key
to o
btai
ning
goo
d sp
ectr
a.
Shim
min
g
lock level
z2 z4z z3
Low
er o
rder
z sh
ims (
z, z2
) affe
ct th
e ce
ntra
l par
t of t
he sa
mpl
e; h
ighe
r ord
er sh
ims (
z3−z
6 ) a
ffect
the
edge
s of t
he sa
mpl
e.
Odd
ord
er sh
ims d
isto
rt th
e lin
esha
pe sy
mm
etri
cally
; Eve
n or
der s
him
s dis
tort
the
lines
hape
asy
mm
etri
cally
B0
+b z3
−b z3
ν 0 =
γB
0ν +
= γb
z3ν −
= −γ
b z3
B0
+b z4
ν 0 =
γB
0ν +
= γb
z4ν +
= γb
z4
z3z4
ν −ν 0
ν +ν 0
ν +
b <
0b
> 0
b >
0, b
< 0
Shim
min
g
Man
ual S
him
min
g adju
st s
him
s to
m
axim
ize
lock
leve
l
Puls
ed F
ield
Gra
dien
ts
B0
G z
−G z
ν(0
) = γ
B0
ν(+z
)= γ
G z
ν(−z
) = −
γ G
z
z
ν(−z
)ν(
0)ν(
+z)
A g
radi
ent i
s a li
near
var
iatio
n of
the
stat
ic fi
eld
impo
sed
on th
e sa
mpl
e, th
roug
h gr
adie
nt c
oils
in th
e pr
obe,
an
d st
rictly
und
er u
ser c
ontro
l, as
opp
osed
to v
aria
tions
in B
0 fie
ld d
ue to
fiel
d in
hom
ogen
eity
.
A fi
eld
grad
ient
is d
efin
ed th
roug
h it'
s slo
pe a
s a fu
nctio
n of
dis
tanc
e. A
z-gr
adie
nt (G
z) is
def
ined
as:
B
(z) =
Gz z
As
a re
sult,
eac
h pa
rt of
the
sam
ple
tube
reso
nate
s at a
diff
eren
t fre
quen
cy d
epen
ding
upo
n it'
s pos
ition
alo
ng
the
z axi
s (le
ngth
of t
he tu
be):
B(z
)
ν(z)
= γ
G z
A sp
ectru
m m
easu
red
in th
e pr
esen
ce o
f a fi
eld
grad
ient
est
ablis
hes a
cor
rela
tion
betw
een
freq
uenc
y an
d po
sitio
n
∆ν ∝
L (l
engt
h of
sam
ple)
A g
radi
ent i
n B
o in
the
Z di
rect
ion
is a
chie
ved
with
an
antih
elm
holtz
type
of c
oil.
Cur
rent
in th
e tw
o co
ils fl
ow in
op
posi
te d
irect
ions
cre
atin
g a
mag
netic
fiel
d gr
adie
nt
betw
een
the
two
coils
. The
B fi
eld
at th
e ce
nter
of o
ne c
oil a
dds t
o th
e B
o fie
ld, w
hile
the
B fi
eld
at th
e ce
nter
of t
he o
ther
coi
l sub
tract
s fro
m th
e B
o fie
ld.
From
: The
Bas
ics o
f NM
R, J
. Hor
nak
http
://w
ww
.cis
.rit.e
du/h
tboo
ks/n
mr/
Puls
ed F
ield
Gra
dien
t (PF
G):
A li
near
gra
dien
t G a
pplie
d fo
r a b
rief p
erio
d of
tim
e (τ
)
B 0G
zB 0
Gz
B 0G
zB 0
B 0
Gz
τ
The
max
imum
gra
dien
t stre
ngth
s are
~ G
= 6
0−70
Gau
ss/c
m. M
ost g
radi
ent p
robe
s are
z-ax
is o
nly.
The
rapi
d tu
rnin
g on
and
off
of th
e gr
adie
nts l
ead
to e
ddy
curr
ents
in th
e pr
obe
and
mag
net
bor
e tu
be. T
hese
dis
turb
ance
s tak
e se
vera
l mill
isec
onds
to su
bsid
e, d
urin
g w
hich
obs
erva
tion
of sp
ectra
is im
poss
ible
. G
radi
ent p
robe
s con
tain
act
ivel
y sh
ield
ed g
radi
ent c
oils
whi
ch d
o no
t pro
duce
sign
ifica
nt e
ddy
curr
ent o
utsi
de th
e sa
mpl
e vo
lum
e, a
nd th
e gr
adie
nt st
abili
zatio
n tim
e is
typi
cally
50−
250
µs.
Usi
ng sp
ecia
l pul
se se
quen
ces,
PFG
s can
be
used
to m
ap th
e m
agne
tic fi
eld
inho
mog
enei
ty a
long
the
z axi
s i.e
., de
term
ine
the
coef
ficie
nts b
n in
B(z
) = B
0 +
b 1 z
+ b 2
z2 +
b3
z3 +
… in
a sh
ort p
erio
d of
tim
e (f
ew m
inut
es).
The
inho
mog
enei
ty c
an th
en b
e re
mov
ed b
y su
btra
ctin
g a
coun
tera
ctin
g fie
ld B
'(z) =
B0
− b 1
z −
b 2 z2
− b
3 z3
+ …
A st
rong
sign
al (u
sual
ly so
lven
t) is
requ
ired
for g
rad
shim
min
g: 1 H
for H
2O so
lven
t, 2 H
for D
2O so
lven
t.
This
form
s the
bas
is fo
r Gra
dien
t Shi
mm
ing.
Bas
ic P
rinci
ples
of G
radi
ent S
him
min
g
B 0
Gz
z
B(z)
B 0
Gz
z
B(z)
Rec
ord
spec
tra in
pre
senc
e of
stro
ng, u
ser c
ontro
lled
grad
ient
Gz,
to a
mpl
ify e
ffect
s of
rel
ativ
ely
wea
k st
atic
fiel
d in
hom
ogen
eity
B(z
).
wea
k
stro
ng
B 0
Gz
z
B(z)
B 0
Gz =
0
z
B(z)
= 0
B 0
Gz
z
B(z)
B 0
Gz =
0
z
B(z)
perfe
ctly
hom
ogen
eous
line
wid
th, i
n ab
senc
e of
any
field
gra
dien
tsbr
oade
ned
line,
in p
rese
nce
of s
tatic
fiel
d ho
mog
enei
ty, l
inew
idth
is te
ns o
f Hz.
B 0
Gz
z
B(z)
B 0
Gz
z
stro
ng
broa
dene
d lin
e, in
pre
senc
e of
a s
trong
z-g
radi
ent a
ndno
sta
tic fi
eld
hom
ogen
eity
, lin
ewid
th is
sev
eral
kH
z.in
pre
senc
e of
a s
trong
z-g
radi
ent a
nd s
tatic
fiel
d ho
mog
enei
ty,
effe
ct o
f B0
inho
mog
enei
ty is
am
plifi
ed.
10-5
0 H
z
~ 10
kH
z
B 0
Gz
z
B(z)
B 0
Gz
z
B(z)
wea
k
stro
ng
Step
1G
radi
ent S
him
min
g B
asic
s
Step
1: o
btai
n a
grad
ient
pro
file
poin
ts t
o re
mem
ber
grad
ient
s no
t on
(pfg
on='
nnn'
)
tpwr
too
hig
hpw
too
long
gain
too
hig
h
tpwr
too
low
pw t
oo s
hort
gain
too
low
The
effe
ct o
f var
ying
diff
eren
t shi
ms
(z1,
z2,
etc
) on
thes
e gr
adie
nt p
rofil
es g
ener
ate
info
rmat
ion
rega
rdin
g th
eco
ntrib
utio
n of
diff
eren
t shi
ms
to B
(z).
This
is c
alle
d a
shim
map
:
This
shi
m m
ap s
how
s th
at th
ere
is a
larg
e z2
, z4
and
z5 c
ontri
butio
n to
B(z
) and
rela
tivel
y m
inor
z1,
z3
and
z6 c
ontri
butio
ns
Bas
ed o
n th
ese
shim
map
s, th
e gr
adie
nt s
him
min
g pr
ogra
m c
an c
alcu
late
how
muc
h to
alte
r diff
eren
t shi
ms
in o
rder
tore
mov
e th
eir c
ontri
butio
ns fr
om B
(z).
This
is u
sual
ly a
qui
ck, i
tera
tive
proc
edur
e.
z1
sam
ple
leng
th
fieldz2
z6z5
z4
z3
Step
2: o
btai
n a
shim
map
ω(z
) ∝ z
φ(z)/τ ∝ Β(z)
Firs
t It
erat
ion
Fin
al I
tera
tion
whit
e: f
ield
pro
file
ove
r sa
mpl
e le
ngth
red:
bes
t fi
t
mag
neti
c fi
eld
shou
ld b
e as
"fla
t" o
ver
the
sam
ple
leng
th
as p
ossi
ble
Step
3: c
arry
out
iter
ativ
e gr
adie
nt s
him
min
g
Acq
uiri
ng S
pect
ra
Set
the
tem
pera
ture
Tune
the
prob
e
Lock
the
field
Shi
m -
man
ual +
gra
dien
t
Ana
lyze
H2O
or H
DO
line
shap
e
Det
erm
ine
1 H 9
00 p
ulse
wid
th
Det
erm
ine
H2O
/HD
O fr
eque
ncy
Acq
uire
a 1
H 1
D s
pect
rum
inte
rcha
ngea
ble
repe
at u
ntil
lines
hape
's
OK
Bas
ic S
tartu
p Pr
otoc
ol
ensu
res
rf p
ulse
sar
e op
tim
ally
abs
orbe
dby
the
sam
ple
corr
ects
for
mag
neti
cfi
eld
drif
t ov
er t
ime
ensu
res
unif
orm
m
agne
tic
fiel
d ov
ersa
mpl
e vo
lum
e
A ra
dio
freq
uenc
y pu
lse
at a
tran
smitt
er fr
eque
ncy
ν T a
nd a
mpl
itude
(rf f
ield
stre
ngth
) B1
may
be
repr
esen
ted
as a
vec
tor o
f le
ngth
B1
in a
refe
renc
e fr
ame
rota
ting
at ν
T.
The
phas
e of
the
B 1 fi
eld
coin
cide
s with
the
x ax
is o
f the
rota
ting
fram
e.
The
B 1 fi
eld
act
s on
the
mag
netiz
atio
n ve
ctor
(M0)
of n
ucle
ar sp
ins w
ith re
sona
nce
freq
uenc
y ν 0
.
If th
e tra
nsm
itter
freq
uenc
y is
on
reso
nanc
e, i.
e. ν
T =
ν 0, M
0 "s
ees"
B1
as t
he o
nly
effe
ctiv
e m
agne
tic fi
eld
for
the
dura
tion
of th
e pu
lse
(τP)
(M0 d
oes n
ot h
ave
to b
e al
igne
d al
ong
the
z axi
s).ν T
= tr
ansm
itter
freq
uenc
y (e
.g. s
frq,
dfr
q)
=
freq
uenc
y of
rota
ting
fram
e
B 1 =
am
plitu
de o
f rf p
ulse
(rf p
ower
∝ B
12 )
x ≡
phas
e of
rf p
ulse
(axi
s of a
lignm
ent o
f B1
v
ecto
r in
rota
ting
fram
e)
M0
= m
agne
tizat
ion
vect
or fo
r a p
eak
o
n re
sona
nce
(ν0
= ν T
)
τ P =
dur
atio
n of
the
rf p
ulse
(pul
se−w
idth
)
x
y
z
B 1
ν 0 =
νT
M0
B 1
ν T
M0
The
RF
Puls
e B 1 (p
w)
(sfr
q)
(tpw
r)
τ P
x
y
z
B 1
M0
θ
τ P =
τ90
θ=π/2
x
y
z
B 1
M0
x
y
z
B 1
M0
θτ P
pw90
ω1=γB1
θ=ω1τP
The
RF
puls
e ro
tate
s th
e nu
clea
r mag
netiz
atio
n fr
om th
e z a
xis
tow
ards
the
xy p
lane
A 9
00 p
ulse
(pw
90) r
otat
es M
0 int
o th
e xy
pla
ne, g
ivin
g ris
e to
max
imum
sign
al.
A 3
600 p
ulse
(pw
360)
rota
tes
M0 b
ack
to th
e z a
xis,
yie
ldin
g m
inim
um si
gnal
.
H2O
Lin
esha
pe, 1
H 9
00 P
ulse
-Wid
th, H
2O F
requ
ency
ar
e de
term
ined
usi
ng v
aria
tions
of t
he s
ame
puls
e se
quen
ce(t2
pul o
n Va
rian,
zg
on B
ruke
r)
pw
acqu
isiti
on ti
me
recy
cle
dela
y (d
1)
H2O
Lin
esha
pe
1 H 9
00 P
ulse
-Wid
th
H2O
Fre
quen
cy
1 H c
arrie
r aw
ay fr
om H
2O.
shor
t pw
(1-2
µs)
, low
pow
er.
long
acq
uisi
tion
time
(1-2
s).
no w
indo
w fu
nctio
ns b
efor
e FT
.
shor
t rec
ycle
del
ay (d
1) 1
-2 s
.
low
rece
iver
gai
n in
H2O
.
1 H c
arrie
r on
H2O
.
vary
(arr
ay) p
w.
shor
t acq
uisi
tion
time
(0.2
5-0.
5 s)
.
win
dow
func
tion
befo
re F
T.
long
d1
for D
2O s
ampl
es (5
s).
low
rece
iver
gai
n in
H2O
.
vary
H2O
pre
satu
ratio
n fre
quen
cy.
pw c
lose
to p
w90
.
shor
t acq
uisi
tion
time
(0.2
5-0.
5 s)
.
win
dow
func
tion
befo
re F
T. sh
ort r
ecyc
le d
elay
(d1)
1-2
s.
high
rece
iver
gai
n.
1 H P
ulse
Wid
th D
eter
min
atio
n
Load
par
amet
ers
Set
1H
car
rier t
o H
2O fr
eque
ncy
Set
pow
er le
vel
Arr
ay th
e pu
lsew
idth
(pw
) to
dete
rmin
e a
null
(zer
o si
gnal
)
Bes
t: de
term
ine
a 36
00 p
ulse
: no
radi
atio
n da
mpi
ng, s
hort
recy
cle
dela
ys. H
owev
er, i
s af
fect
ed b
y rf
inho
mog
enei
ty.
- nu
lls a
re e
asie
r to
det
ect
than
max
ima.
A 1
800
pw is
the
fir
st n
ull b
ut r
esul
ts in
sig
nal d
isto
rtio
n a
nd A
DC
over
flow
bec
ause
of
radi
atio
n da
mpi
ng in
H2O
sam
ples
.
- A
180
0 pu
lse
requ
ires
long
rec
ycle
(d1)
del
ays
betw
een
puls
ewid
ths.
signal intensity
puls
e-w
idth
9018
0
270
360
10
radi
atio
n da
mpi
ng, s
igna
l dis
tort
ion,
long
d1
mea
sure
men
t wi
ndow
1st n
ull
2nd
nullpw
atd1
360
null
Det
erm
inin
g th
e H
2O F
requ
ency
In H
2O s
ampl
es, t
he H
2O li
ne is
too
broa
d (>
30
Hz)
to a
llow
pro
per p
eak
iden
tific
atio
n us
ing
the
curs
or
A be
tter w
ay is
to p
resa
tura
te th
e H
2O s
igna
l prio
r to
dete
ctio
n an
d ar
ray
the
satu
ratio
n fre
quen
cy.
The
H2O
freq
uenc
y co
rres
pond
s to
a m
inim
um in
the
H2O
sig
nal i
nten
sity
(max
imum
sat
urat
ion)
.
pres
at fr
eque
ncy
intensity
choo
se t
his
one
pres
at
pw90
at
1−1.
5 s
End