LECTURE 4
Pulse: frequency
B0: 9T-27T
1H: 400 MHz-1200 MHz 13C: 100 MHz-300 MHz 15N: 40 MHz-120 MHz
Pulse: phase
first pulse:
convention: 180° for 7 > 0 convention:     0° for 7 < 0
other pulses:
0° x 90° y 180° -x
270° -y
Pulse: phase modulation
0 cycle per pulse 100/is pulse: +0 kHz
Pulse: phase modulation
1 cycle per pulse 100 /xs pulse: +10 kHz
Pulse: phase modulation
2 cycles per pulse 100 /xs pulse: +20 kHz
Pulse: phase modulation
4 cycles per pulse 100 /xs pulse: +40 kHz
Pulse: power / amplitude
field strength power
attenuation
P ocBl 10log10gf
kHz W
dB
20 logic
B\\2 B\ l
lOlogio
Bi Bi
2 2
2 1
10 logic
P2 Pi
typical: P< 1000W, cjx < 50 kHz limit: sample/coil heating
Pulse: length
calibrate so that a
Co
where a = 90°, 180°,.
OFFSET EFFECTS
Pulse: amplitude modulation
calibrate/calculate power so that a = \wi\tp
where a = 90°, 180°,...
O
Offset effects / selectivity
Offset effects / selectivity
Q^O    off resonance
Offset effects / selectivity
Offset effects / selectivity
Offset effects / selectivity
Offset effects / selectivity
Offset effects / selectivity
Offset effects / selectivity
t M
Q/^15;    ujeff = VI + 15oji
Quadrature detection / frequency discrimination
COS(u;o^) —>
^cos(ujQt) —> ^cos(ujQt) cos(—u;ra(jj0t) channel a ^cos(ujQt) —>• ^cos(o;o*) sin(—wraC|j0t) channels
icos(^0t) cos(-wradiot) : i cos(^0t) sin(-wradiot)
high Q low
J COS(Oo - wradio) t) + \ COS((w0 + <^radio) *)
: isin(O0 - wradi0)t) - Jsin((wo + ^Yadio)*)
^cos(Qt) channel a o = Acos(Qt) isin(Qt)     channel b     6 = Asin(Qt)
data storing option:
a,
a, ■6,
6 conventionally labeled
a -b
—o, a
x
y
—x
-y
Single channel, real Fourier transformation
Two channels, complex Fourier transformation
a + i&—y X + \Y
Complex signal in indirect dimension
1
H
or
1
5N
JL    JL y
4J | 4J |
x/y
I
ti
Repeat with y and y
Complex signal in indirect dimension
v\ = Aca = cos(Qc^i) cos(QH^2) channel a, pulse x r2 = Acb = cos(Qc^i) sin(^H^2) channels, pulse x r3 = Asa = sin(Qcti) cos(QH^2) channel a, pulse y r4 = As6 = sin(Qcti) sin(QHt2)   channels, pulse y
(Ac+iAs)(a+i6)
x/y	receiver		acquired as	stored as records r7-
-\-x	-\-x	a	: Acsin(QH*2)	ri,r2 = Acsin(QH^2)^cCOs(QH^2)
		b	: Accos(QH^2)	
+y	-\-x	a	: Assin(QH*2)	r3,r4 = Assin(QH^2)^sCOs(QH^2)
		b	: Ascos(QH^2)	
Complex signal in indirect dimension
(Ac + \As)(a + \b) —► (Ac + iAs)(X2 + \Y2) —>• (Xi + iYi)(X2 + \Y2) =
XiX2 - YXY2 + \{XXY2 + 11X2)
(Ac + Us)(a + 16) —>• (Ac + iAs)(X2 + \Y2) —► (Ac + iAs)X2 —>
(Xi + iYi)X2 = XiX2 + i^Xs
Phase cycling
1
1 y
1
H
4J I 4J
4>3
1
1
4J
1
3C or15N
4»i/4»i
I
d).
tl
(j>1 =X,-X,X,-X,X,-X,X,-X 4>2=X,X,-X,-X,X,X,-X,-X
4h =y-y.y-y.y-y.y-y <l>3=x>x>xlx-x-x-x-x
receiver phase: x,-x,-x,x,x,-x,-x,x
Pulsed-field gradients
Pulsed-field gradients
1						
cd		CD		cd		
				cd		CD
c3>		o		cd		<z>
		o		cd		O
C*>		o		cd		cd
CS>		o		cd		cd
G)		o		cd		cd
<3>		o		cd		cd
c3>				cd		cd
c3>		Cx>		cd		cd
<3>				cd		<^d
C5)		cd				cd
C3>		CD		o		cd
<3>		CgD		o		cd
		<^d				cd
						\C3/
Gradient echoes
a
Gradients in HSQC
1H
3C or15N
j_
4J
i / \i
a b G7 i
i y I ^ I
c d e
mm
ti
1
x/y
"I I
i
g h
7
	Ii		t2
1	Hl	(p	yu V/v vyyv>^—
	GARP		
Preservation of equivalent pathways
H
JL    JL y
| 4J | 4J |
1
3C or15N
•—4
j_    JL y JL JL
| 4J | 4J | 4J | 4J | |
^2 -x/x y
t2
t1
a b c d e
1  i I
f
GARP
g n
1 k
k_A
♦-
(|>i=x,-x,x,-x,x,-x,x,-x and receiver phase x,-x,-x,x,x,-x,-x,x for odd increments of ti §^=-x,x-x,x,-x,x-x,x and receiver phase -x,x,x,-x,-x,x,x,-x for even increments of ti (J)2=x,x,y,y,-x -x -y-y