NMR Techniques at Liquid Helium Temperatures - Low ...

2.2 Basics of NMR 10
temperature of the wire. To achieve homogeneity and stability of H over space and
time, shim coils and field locks can be used, respectively [29].
Inside the NMR magnet, the NMR sample is surrounded by the RF and detection
coils which are needed for excitation and signal detection. RF coils can
be shaped in many different ways, e.g. as a solenoid coil, saddle coil or wave
coil [30]. The excitation coil has to resonate at the NMR frequency, so there must
be capacitive elements present in addition to the inductive coil. The resonance
frequency of this kind of LC resonator can be calculated, but it must be noticed
that the conductivity and the dielectric constant of the sample inside the RF coil
also affect it in addition to the values of the coil and the capacitor. In the twocoil
configuration the RF and detection coils are in an orthogonal arrangement,
to reduce inductive coupling between the coils. In pulsed NMR imaging measurements
one coil is sending a pulse into the sample and another is monitoring
the voltage induced by the relaxing transverse magnetization after the pulse. It
is also possible to have only one coil both generating the oscillating Hrf field and
measuring the absorbed RF energy. This is often the setup used in cw-NMR measurements
although the two-coil arrangement is possible reducing the excitation
voltage leaking into the signal amplifier chain. Requirements for the Hrf field are
the perpendicularity to the H field and the homogeneity over the volume of the
sample. Otherwise the amount of magnetization would be different in the different
parts of the sample and the measured spectra would deform.
Depending on the required setup, the sample probe can also contain a sample
spinner for rotating the sample, temperature controlling circuitry, and gradient
coils producing gradients in H.
Our NMR magnet configuration inside the cryostat is presented in Sec. 5.1.1.
2.2.4 Q-factor
Figure 2.2 shows a generalized response curve of a band-pass filter, such as our
LC resonator. The filter passes frequencies within a certain range and rejects
frequencies outside that range. The bandwidth is defined as the difference between
the frequencies at which the energy is half of its peak value, fl and fh. In terms of
the oscillation amplitude this means that at these frequencies the voltage is
V∆ f = Vmax
√2 . (2.19)
The quality factor (Q-factor) of a band-pass filter is defined as the ratio of the
resonance frequency to the bandwidth:
Q = f0
fh − fl
= f0
. (2.20)
∆ f