Pulses and Decoupling

Scuola nazionale GIDRM‐ Corso BaseTorino 25/09/13

Mo

z

x

yBo

NMR excitation (detecting NMR)

• An ensemble of spins (of a single type and I = 1/2) generates an average magnetization, Mo, upon interaction with an external magnetic field, Bo:

• This magnetization is proportional to the population difference of spins in the low and high energy levels, and that it is precessing at a frequency o, the Larmor frequency of the particular observed spin at a particular Bo

• So far, nothing happened. We need to do something to the system to observe any kind of signal. What we do is take it away from this condition and observe how it goes back to equilibrium. This means affecting the populations...

y

x

z

Bo

Mo

z

x

i

B1 = C * cos (ot)

B1

Transmitter coil (y)

yBo

NMR excitation (continued)

• We need the system to absorb energy. The energy source is an oscillating electromagnetic radiation generated by an alternating current:

NMR excitation (continued)

• How is that something that has a linear variation can be thought as circular field? A linear variation in y is the linear combination of two counter-rotating circular fields:

+=

+=

+=

•Only the one vector that rotates at o(in the same direction

of the precession of Mo) interacts with the bulk magnetization

= +

RF Coil: Transmitting B1 Field

The effect of the tiny B1 isto cause M to spiral awayfrom the direction of thestatic B0 field

B110–4 Tesla If B1 frequency is not close toresonance, B1 has no effect

RF pulse

B1 field perpendicular to B0 Mxy

Mz

Classical Description

• Observe NMR Signal Need to perturb system from equilibrium.

B1 field (radio frequency pulse) with Bo/2 frequency Net magnetization (Mo) now precesses about Bo and B1

MX and MY are non-zero Mx and MY rotate at Larmor frequency System absorbs energy with transitions between aligned and unaligned states

Precession about B1stops when B1 is turned off

z

x y

z

x y

z

x y

PULSED MAGNETIC FIELDS

= 2  B1 z

x y

B1=1/(8

B1=1/(4

Polarization distribution after a pulse

Transverse magnetization

Polarization distribution at thermal equilibrium

PULSED MAGNETIC FIELDS

z

x y

90° Pulse

= 2  B1

• Once the pulse is turned off, the spins resume their precessional motion.

• The individual spins precess on their individual cones.• On a macroscopic scale, the bulk magnetization moment also

precesses, rotating in the xy-plane, perpendicular to the main magnetic field.

z

x y

90° Pulse90° Pulse

The NMR signal

* =

1

Radiofrequency pulses

FT

Frequencies that are excited by the pulseB1

Pulse Generator & Receiver Systema) RF pulse width determines band-width of excitation

Null, no effect

Invert signal, 180o pulse

Maximum effect at

1

1

FT

Frequencies that are excited by the pulse

FT

SW

B1

Hard Pulse

1H 10s 90o pulse ±100000 Hz ±166.7 ppm at 600 MHz(total SW 12 ppm)

±1/PW Hz

= +

z

x’ y’

The rotating frame

z

x y

Larmor precession in the rotating frame

Laboratory frame

Bo

z

x' y'

Rotating frame at 0

=-B=0 B=0!!

0 = -B0

z

x' y'

B1 is the only magnetic field “experienced” by the spin system

Mxy

Mz

+

Larmor precession in the rotating frame

z

x'

y'

Larmor precession in the rotating frame

Bo

z

x' y'

Rotating frame at 0

z

x' y'

B1 is the only magnetic field “experienced” by the spin system

=-B=0 B=0!!

This is the key to how the very weak RF field can affect the magnetization in the presence of the much stronger B0 field. In the rotating frame this field along the z axis appears to shrink, and under the right conditions can become small enough that the RF field is dominant.

A Mechanical Analogy: A Swingset

• A person sitting on a swing at rest is “aligned” with externally imposed force field (gravity)

• To get the person up high, you could simply supply enough force to overcome gravity and lift him (and the swing) up– Analogous to forcing M over by turning on a huge static B1

• The other way is to push back and forth with a tiny force, synchronously with the natural oscillations of the swing– Analogous to using the tiny RF B1 to slowly flip M over

On‐resonance pulses

= 2 B1z

x’ y’

=0

z

x’ y’

=/4

z

x’ y’

=/2z

x’ y’

=

z

x’ y’

=3

z

x’ y’

=2

DETERMINING A 90° PULSE

= tp

DETERMINING A 90° PULSE

In Hz:

Larmor precession in the rotating frame

z

x' y'

Rotating frame at rf = 0

z

x' y'

=-B=0 B=0!!

Rotating frame at rf ≠ 0

=-B= 0 -rf

0 is in the MHz orderis in the kHz order

The effective field

z

x' y'

Rotating frame at rf ≠ 0

=-B= 0 -rf

The effective field in frequency units

Off‐resonance effects

Off‐resonance effects

Laboratory and rotating framesrf rf rf

0 Hz3600 Hz -3600 Hz

1H 10s 90o pulse

cycle in 10 us cycle in 40 us1=1/21/4*10-5=Hz1=*2 rad/sec=3600*2 rad/sec

=arctan(1/°

The effective field

90°

-80°

80°

1H 10s 90o pulseB1 of 25 kHz

0,988

0,99

0,992

0,994

0,996

0,998

1

-3000 -2000 -1000 0 1000 2000 3000

Mxy/Mz0

The effective field

13C 12s 90o pulseB1 of 20.8 kHz

Mxy/Mz0

0,8

0,85

0,9

0,95

1

-100 -50 0 50 100

ppm @ 150 MHz

-40

-30

-20

-10

0

10

20

30

40

-100 -50 0 50 100

PULSED MAGNETIC FIELDS

=

z

x’ y’

z

x’ y’

z

x’ y’

z

x’ y’

PULSED MAGNETIC FIELDS

= 2 B1z

x’ y’

z

x’ y’

z

x’ y’

z

x’ y’

Pulses of different phases

The phase of a pulse

x

y

B1

B1-

B1+

x

y

x'

y'

An x pulse

The phase of a pulse

x

y

B1

B1-

B1+

x

y

x'

y'

An -y pulse

y

Maximum affect: width of excitation:±1/(4PW) Hz

The longer the pulseThe more selective it is

Selective pulse

1H 1ms 90o pulse ±250 Hz ±0.4 ppm at 600 MHzUsed for pulses exciting only H2O magnetization

Shaped RF pulses

Rectangular pulse

Fourier pairs

Fourier pairs

To get a perfectly rectangular excitation profile we will need an infinitely long sinc pulse which is, naturally, impractical, so the waveform has to be truncated

Some commonly used RF shapes

Excitation bandwidth

Decoupling techniques

J (Hz)

13C

13C

1H

1H

1H

13C

1H

13C

1H 1H

Proton-decoupled 13C-NMR

B2/2>2JHC

Homonuclear decoupling

Main problems:• Selective irradiation is

not always feasible• Bloch-Siegert shift:

Heteronuclear Decoupling

• The frequency difference 2-1 lies in the MHz range. The second field B2 is produced by a separate transmitter.

• A curly bracket is used to indicate which nucleus is being decoupled during the experiment, e.g. 13C1H indicates a 13C spectrum acquired with 1H decoupling.

Heteronuclear DecouplingBroadband decouplingUsing the spin flip experiment (MLEV, Malcolm Levitt):

x

y

x

y

J / 2

J / 2

x

y

°

J / 2

J / 2

x

y

Heteronuclear DecouplingA train of pulses will be susceptible to the errors due to pulse length inaccuracy, since they will accumulate. The non-ideal pulse can be replaced with a composite pulse.

Heteronuclear Decoupling