The Spectrometer

1
The Spectrometer

• The Hardware

2
The Challenge

• NMR is technically difficult
• NMR signals are very weak
• Individual nuclear magnetic moments are very
  small compared to those of electrons
• Very slight thermal imbalance (1 in 105)
• Extremely high accuracy in measurements (1 in 109)

3
The Overview

• An NMR Spectrometer consists of three main parts
• The magnet
• - producer
• The console
• - controller
• The probe
• - source and
• detector

4
The Magnet

• High magnetic fields
• Extremely high magnetic field homogeneity
  (independent of position) within one part per
  109, to avoid inhomogeneous linebroadening and
  resolve small differences in the Larmour
  frequency due to chemical shift, spin-spin
  coupling, or other interactions
• Large sample volumes ranging from many cubic
  centimeters to hundreds of cubic centimeters

5
Superconducting Magnets

• Once charged with a large amount of current,
  superconducting magnets run almost indefinitely
  providing an extremely stable magnetic field with
  no outside interferences
• Superconducting materials used in NMR are
  typically made from a Nb and Sn alloy surrounded
  with copper
• Superconducting materials must be kept at 4 K by
  a liquid He bath
• The liquid He bath is insulated by a liquid N2
  (at a temperature of 77 K) bath
• The baths are separated from each other and the
  outside environment by evacuated barriers
• Running through the center of the magnet is a
  hole, known as the bore, in which one places the
  probe
• The bore is isolated from the superconducting
  coil by cooled evacuated barriers allowing for
  the probe to operate at room temperature
• The magnetic coil is supported by two other sets
  of coils known as shims which are used to adjust
  the homogeneity
• The cryogenic shims are made of superconducting
  materials and immersed in the He bath
• The room temperature shims are supported on a
  tube which is inserted into the bore

6
The Super-Conducting Magnet
What we see
What it really is
7
The Magnet (Bore)
Liq He Vessel
20 K Rad Shield
Liq N Vessel
Out Vac Chamber
Quench Resistor Charging Plug
Liq He Baffle
Supercon Solenoid
Supercon Shims
http//www.jeol.com/nmr/mag_view/magnet_destructio
n.html
8
The Radio Frequency (RF) Unit
9
The Transmitter Section

• This section of the NMR spectrometer consists of
  several parts and produces the radiofrequency
  irradiation close to the Larmour frequencies of
  different isotopes.

10
The Synthesizer r.f. phase shifts

• This section produces an oscillating signal with
  an extremely well defined frequency via a number
  of frequency-conversion and electronic filtering
  steps.
• The end result is a radiofrequency wave which
  oscillates at the spectrometer reference
  frequency, denoted ?ref.
• The output wave can generally be described as
• ssynth cos (?ref t ?(t)) Eq. 2.1
• where ?(t) is the r.f. phase and t is the time
  coordinate.
• The phase, ?, of an oscillating wave indicates
  the position of an oscillation at the time t0
• In a large number of NMR experiments ? is jumped
  rapidly between values as dictated by the pulse
  programmer both in t and ?.

11
More on Phase

• The phase of an r.f. pulse is governed by the
  underlying function, and not by the timing of its
  appearance.
• r.f phase Jargon (NMR geek speak)

12
The r.f. amplifier (Transmitter)

• The role of the r.f. amplifier is to scale-up
  (amplify) the generated waveform and produce a
  large-amplitude r.f. pulse (a few W for liquids,
  up to kW for solids) for transmission to the
  probe

Possible Pulse Errors
13
The Real Layout Without the Preamplifiers
14
The Probe

• This section of the NMR spectrometer consists of
  several parts and is where the NMR signal
  generated and detected.

15
The Probe

• The probe is a very complex and can be viewed
  very roughly as the detector
• Modern NMR Probes
• Locate the sample in the homogenous region of the
  magnetic field
• Include r.f. electronic circuits for sample
  irradiating and detection of the subsequent r.f.
  emissions from the sample
• Rotate the sample (in some cases)
• Stabilize the samples temperature
• Contain additional coils which create magnetic
  fields with controlled spatial inhomogeneity for
  imaging and other applications
• The probe is by far the most specialized part of
  an NMR spectrometer and a large array of
  different probes are available e.g. liquid and
  solid state probes

16
The Probe
17
The r.f. Circuits of a Probe

• The probe has a very difficult job as it has to
  deal with extremes in r.f. signal amplitudes
• There are two very important capacitors within
  the probe.
• The matching capacitor which couples the external
  signals into the probe circuit with maximum
  efficiency
• The tuning capacitor which enhances the current
  in the coil by electronic resonance, and thus
  allows the probe to handle to the extremes that
  it must.
• The electric properties of the tune circuit are
  affected by the nature of the sample. It is
  therefore important to match and tune the probes
  circuit every time the sample is changed

18
Tuning and Matching and the Preamps
Match
Tune
19
The Receiver and Preamp Section

• This section of the NMR spectrometer consists of
  several parts and determines the immediate fate
  of the NMR signal.

20
The Signal Preamplifier

• The NMR signal first arrives at the duplexer
  (pinhole diode), which diverts it the wire
  (cable) to the signal preamplifier (preamp for
  short).
• The signal preamplifier is a low noise and
  distortion r.f. amplifier which scales up the
  tiny signal to a more conventional voltage level
  (as was/is needed with vinyl records).

21
The Quadrature Receiver

• The raw NMR signal oscillates at 100s of MHz
  which is simply too fast for current
  analog-to-digital converts, thus it must be down
  converted to be handled by the digital
  electronics down stream.
• The quadrature receiver accomplishes this by
  combining the NMR signals (which oscillates at
  the Larmour frequency ?0) with the reference
  signal (from the synthesizer which oscillates at
  a frequency of ? ref), to generate a new signal
  which oscillates at the the relative Larmour
  frequency
• ?0 (?0 - ?ref) Eq. 2.2
• A similar process is used in an ordinary radio
  receiver in which the modulating radio frequency
  traveling through space is transformed into
  mechanical oscillations known as music

22
Two signals rather than one

• The NMR signal (free-induction decay) sfid,
  including a damping
• factor with a rate constant of ?T2-1, has the
  following form
• Sfid(t) cos (?0 t) exp- ? t Eq. 2.3
• The down converted output can be represented as
• cos (? 0 t) exp- ? t Eq. 2.4
• However, there is a problem as spins which
  precess at a frequency of
• ?0 greater and less than ?ref can not be
  distinguished.
• We have seen this many times before, e.g. the
  square root of 2 and -2

23
An Example

• Assume we are acquiring a proton spectrum on a
  400 MHz NMR spectrometer (?ref/2?-400.000000
  MHz) in which we have two nuclear spin
  environments, one in a slightly stronger magnetic
  field and one in an equally weaker magnetic field
  such that the spin in the stronger field
  precesses at ?0/2? -400.001000 MHz while the one
  in the weaker field precesses at ?0/2?
  -399.999000 MHz, thus we will have ?0/2? -1.000
  kHz for the high field spin and ?0/2? 1.000 kHz
  for the low field spin.
• However, Eq. 2.4 cannot distinguish the signals
  arising from these two physically distinct
  situations, and hence our problem.

24
The Solution

• The receiver supplies two output signals with the
  following forms
• sA cos (? 0 t) exp- ? t Eq. 2.5
• sB sin (? 0 t) exp- ? t Eq. 2.6
• This looks like, and is a case, where we have a
  complex signal, s(t) which can be
• represented by a real and imaginary components
• sA(t) Res(t) Eq. 2.7
• sB(t) Ims(t) Eq. 2.8
• where
• s(t) sA(t) isB(t) exp (i ? 0 - ? )t Eq.
  2.9
• This double output allows one to keep all the
  information and distinguish between
• the two different states presented above, and is
  known as quadrature detection.
• The representation of the data as a complex
  function is very beneficial in terms of
• the mathematics of NMR.

25
Quadrature Detection Graphically
PH 0
B
F
B
w (B1)
F
PH 90
PH 0
F
B
PH 90
F
B
26
Analog to Digital Conversion (ADC)

• The analog NMR signal (voltage) is converted to a
  digital form (0s and 1s) by repeating the
  measurement at a set of time points and storing
  the information in the computer as a set of
  values.
• The time separation between the sampling points
  of the ADC is called the sampling interval, or
  the dwell time (DW, ?sample). The sampling
  bandwidth (a.k.a. spectral width, SW) sets the
  maximum range of frequencies which is represented
  accurately by the sampling process.
• The total time duration over which the signal is
  sampled is called the acquisition time (a.k.a.
  acquisition interval) and is given by
• ?acqnsample??sample Eq. 2.10
• The Nyquist Theorem States
• That one must sample at a
• Rate of at least 2 F if one
• desires to sample a signal
• with a frequency of F Hz
• i.e. DW1/2SW Eq 2.11

Sampled well
Sampled poorly
27
More NMR geek speak

• Jargon used for the number of digital sampling
  points

28
Even more phase

• Phase is extremely important in NMR as it allows
  one to distinguish real
• NMR signals from artifacts, and allows one to
  distinguish different types
• of NMR signals.
• We saw earlier that phase can be applied to the
  excitation pulse, however
• the phase of the NMR signal can be altered after
  it leaves the probe.
• Receiver Reference Phase the quadrature receiver
  compares the NMR signal with a reference wave
  from the synthesizer. If the phase of the
  synthesizer reference wave changes to some value,
  ?rec, during the entire acquisition period of
  signal detection, then this phase shift, ?rec, is
  transferred to the signal emerging from the
  receiver.
• Digitizer Phase the second method (and more
  modern) operates on the digitized signal emerging
  from the ADCs. The digitized complex signal is
  passed into a device called the post-digitization
  phase shifter which multiplies the complex signal
  by a factor exp-i?dig before it is passed on to
  the computer.

29
Take Home

• The NMR Spectrometer is a complex instrument
• The amplitude (extremes), frequency (small
  difference in large numbers), and phase are all
  important