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10– NMR Hardware

In this lecture, we will begin to familiarise ourselves

with the more practical aspects of NMR - i.e. major

components of a spectrometer, with probeheads, and

with the definition of signal-to-noise.

10.1 The spectrometer

A spectrometer consists of the following components:

superconducting coil

shim coil

probehead

filter

shim power supply

receiver

computer

1H amplifier

13C amplifier

1H frequency

13C frequency

HX

pulse programmer

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i) The magnet

The magnet, which provides the ~B0 field needed for

precession to take place, is a superconducting

magnet. This means it is made out of

superconducting material (e.g. Bi-Sr-Ca-Cu-O based

superconductors) that has a minimal resistance at

0K (-273.15 oC). These temperatures can be

achieved by immersing the superconducting material

in liquid helium.

The superconducting coil is made out of wire which

is several miles long and wound into a multi-turn

solenoid. The wire itself is made out of different

materials, arranged as illustrated below. The reason

for this arrangement is to minimize the chances of a

quench if there should be material failure in the coil.

Superconducting Material

Insulating Material

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To keep the coil cold, it is immersed in a dewar

containing liquid helium and kept at 4.2 K. Some

magnets have a pump built-in so that the helium can

be supercooled. This is used to reduce the resistance

in the coil further, allowing higher B0 fields to be

achieved.

In order to slow down the evaporation of helium, the

dewar is surrounded by dewars of nitrogen, as shown

in the diagram below:

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Used with permission, JEOL USA, Inc.

Used with permission, JEOL USA, Inc.

ref: http://www.cis.rit.edu/htbooks/nmr/chap-7/chap-7.htm

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The outer vacuum region is filled with many layers of

reflextive mylar film, which serves to insulate the

magnet by diminishing the amount of heat which can

enter the helium region.

ii) The shim coils

The shim coils, which are situated inside the bore of

the magnet, provide compensatory magnetic fields,

such that the net ~B0 field is spatially homogeneous.

Inhomogeneities in the ~B0 field arise from the way in

which the magnet is designed, from materials in the

probe (e.g. metallic objects in proximity to the RF

coil in the probe), from the sample tube, from

sample permeability, and from ferromagnetic

materials around the magnet.

As a result of the inhomogeneities, a field gradient

may exist across the sample, e.g.

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The shim coils consist of wire through which current

is passed so that small magnetic fields are generated.

These coils have particular shapes which correspond

to particular functional forms. Some typical shim

coils and their corresponding functional forms are:

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Z0

Z1

Z2

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X

XZ

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Y

Y Z

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XZ3

ref: http://www.cis.rit.edu/htbooks/nmr/chap-7/chap-7.htm

Shimming consists thus in finding the optimal

current settings such that the ~B0 field is

homogeneous. This can be determined by either

maximizing the lock signal (see below) or by

maximizing the size of the free induction decay

(FID) of, for example, water.

Because the linewidths observed in the solid state are

typically broader than in solution state, it is not

necessary to shim very precisely. This is often why

most people only optimize the lower order shims (Z0,

Z1, Z2, X, XZ, Y , and Y Z) and do not modify the

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higher order shims (e.g. Z4,Z5,XZ2,XZ3,...).

iii) The lock

The lock is needed to compensate for external drifts

in the magnetic field (e.g. from a tram, metallic

trolleys). In solution state, it is very common and

works by using the signals arising from deuterated

solvents (in the sample) which are then monitored by

the computer. The signal is “locked” on to the

frequency of something like D2O and monitored

constantly during the course of the experiment.

Small changes are compensated for by a coil in the

shim stack.

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In solid state, the lock isn’t as commonly used, but

can be useful, as illustrated here for a 13C line of

adamantane, spinning at 4 kHz. For some solids

probe assemblies, the lock is situated in the duct

used to eject the MAS rotors. The deuterium

sample, in this case, sits close to the RF coil but is

not surrounded by it.

iv) The probehead

The probehead contains an RF coil which produces

the ~B1(t) magnetic field needed to perturb the spins

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away from equilibrium. The major component

within the probe is a resonance circuit, built from

inductors and capacitors which allow the probe to be

tuned and matched to a particular frequency

(Larmor frequency of the nuclei to be observed

and/or excited).

We saw in Chapter 2, that a probe consists of a

slightly more complex version of an LC circuit. In

our circuit, we said last time that the inductor L is

the coil where the sample is placed. There are a

number of different coil geometries which are used.

In solution, standard coils are the saddle coil:

and Helmholtz coils

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whereas, in solids, a solenoid or flat coil is used. The

choice on geometry depends on power applied to the

coil, filling factor, and homogeneity.

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v) The frequency generator

The frequency generator, also known as the

synthesizer, generates a sinusoidal modulation, which

has a frequency close to the Larmor frequency of the

nucleus to be excited/perturbed. The base frequency

generated is called the carrier frequency or reference

frequency, such that the synthesizer output is defined

as

s ≈ cos(ωref t + φ(t)) (10.1)

where φ(t) is the phase of the radiofrequency

modulation.

vi) The pulse programmer

The pulse programmer “interprets” the pulse

program that the user writes. It controls how long a

pulse is on for (i.e. gating), the phase of the pulse

and the shape of the pulse (e.g. rectangular,

Gaussian,...).

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M.H. Levitt’s book, p. 74-75

vii) The amplifiers

The amplifiers increase the amplitude of the output

of the frequency generator so that the final

amplitude of the RF pulses ranges from milliwatts

(no amplification) to kilowatts.

The output of an amplifier is characterised by its

peak-to-peak voltage (Vpp) or power in Watts (P), i.e.

P =Vpp

2

400∗ 10

dB

10 (10.2)

where Vpp is the voltage measured on the oscilloscope

and dB is the attenuation used.

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Just as a probehead can be tuned to a specific

frequency, so can an amplifier. To tune an amplifier,

the following procedure can be used:

1. Connect the output of the amplifier into an

attenuator (e.g. 40dB). The output of that can

now be connected to an oscilloscope for

observation.

2. Start pulsing using a single pulse, with an easy

to observe pulse width (e.g. 1-2ms). Use a power

level setting which is in the middle of the

available range.

WARNING!: Beware of connecting high

power outputs directly to the oscilloscope!

3. Most amplifiers have a button for ”tuning” and

one for the ”amplifier load”. Change the tuning

and load so that the maximum amplitude

(largest Vpp) value is achieved.

vii) Filters

Although the probehead behaves as a filter for a

particular frequency that is to be excited and/or

observed, there are often spurious frequencies still

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present in the lines leading up to the receiver. To

eliminate these unwanted frequencies a number of

filters can be used, namely low-pass filters, high-pass

filters, band-pass filters, or band-stop filters. A

low-pass filter allows low-frequency signals to be

transmitted, while attenuating higher frequencies. A

high-pass filter behaves in an opposite manner in

that it lets through high frequencies, while

attenuating low frequencies. A band-pass or

band-stop do not attenuate or attenuate a range of

frequencies, respectively. Schematically,

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ref: R. Ludwig and P. Bretchko, RF Circuit Design: Theory and

Applications, Prentice Hall, NJ, 2000.

A low-pass filter consists of a circuit containing a

resistor R and a capacitor C. A high-pass filter

consists of a circuit containing a resistor R and an

inductor L. And a bandpass filter consists of an RLC

circuit.

For NMR purposes, the best is always to use a

bandpass filter since only the frequencies to be

excited/observed are let through. These filters are

more expensive though and so are often replaced by

a low-frequency filter or a high-frequency filter.

viii) The receiver

As with a radio, a NMR spectrometer is equipped

with a receiver to detect the RF (or magnetization)

coming from the sample in the probehead. Typically

it consists of a quadrature detector, which is a device

which separates the Mx component of the

magnetization from the My component.

Electronically, this is done with a doubly balanced

mixer. For more details cf. R. Ludwig and P.

Bretchko, RF Circuit Design: Theory and

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Applications, Prentice Hall, NJ, 2000.

ix) Co-axial cables

Connecting all the different components of a

spectrometer are co-axial cables. These cables

consist of:

1. an inner cylindrical conductor of radius a,

2. surrounded by a dielectric material, such as

polystyrene, polyethylene or teflon,

3. an outer conductor, which is grounded to

minimize radiation loss and field interference

4. and an outer insulator.

To avoid losses between the different components of

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the spectrometer, it is important to use good quality

co-axial cable (usually the thicker kind).

x) The computer

The computer controls most of the components listed

above and acts as an interface between the user and

the hardware.

10.2 Signal-to-Noise Ratio

When we discussed probes in Chapter 2, we

introduced the concept of the sensitivity of the

probehead. A measure of this sensitivity in terms of

the electronics is given by the quality factor, Q.

There is another measure of sensitivity, known as the

signal-to-noise ratio, given in terms of the observed

magnetization.

In a NMR experiment, the signal is given by

S ∝ ω0,xMxtot (10.3)

where ω0,x is the Larmor frequency and Mxtot is the

magnetization detected in the receiver.

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The noise, known as thermal or Johnson noise,

coming from the electronics, is

N ∝ keff,x√

ω0,x (10.4)

with keff,x is a proportionality constant which takes

into account the Q of the circuit and other electronic

parameters of the detection devices.

Therefore the signal-to-noise ratio is given by

S

N= keff,x

√ω0,xMxT2,x (10.5)

where T2,x is the transverse relaxation time.

Using Curie’s law for the magnetization for a spin

1/2,

Mx =Nxγx

2h2B0

4(2π)2kT, (10.6)

the signal-to-noise ratio can be rewritten as

S

N=

keff,xNxγx5/2h2B0T2,x

4(2π)2kT. (10.7)

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This latter equation shows that one can expect

improved sensitivity if:

1. the probe has a high Q (keff,x is high);

2. there is a lot of sample (Nx large);

3. the spins observed have a high γ value;

4. the magnetic field is large (e.g. 800 MHz vs 400

MHz);

5. the temperature at which the experiment is

carried out is low.