Phase Cycling and Gradient Pulses - The James Keeler Group

magnetization from z onto –y, whereas the same pulse applied about the y-axis
rotates the magnetization onto the x-axis. The idea of the receiver phase is
slightly more complex and will be explored in this section.
The NMR signal – that is the free induction decay – which emerges from the
probe is a radiofrequency signal oscillating at close to the Larmor frequency
(usually hundreds of MHz). Within the spectrometer this signal is shifted down
to a much lower frequency in order that it can be digitized and then stored in
computer memory. The details of this down-shifting process can be quite
complex, but the overall result is simply that a fixed frequency, called the
receiver reference or carrier, is subtracted from the frequency of the incoming
NMR signal. Frequently, this receiver reference frequency is the same as the
transmitter frequency used to generate the pulses applied to the observed
nucleus. We shall assume that this is the case from now on.
The rotating frame which we use to visualise the effect of pulses is set at the
transmitter frequency, ω rf
, so that the field due to the radiofrequency pulse is
static. In this frame, a spin whose Larmor frequency is ω 0
precesses at (ω 0
–
ω rf
), called the offset Ω. In the spectrometer the incoming signal at ω 0
is downshifted
by subtracting the receiver reference which, as we have already decided,
will be equal to the frequency of the radiofrequency pulses. So, in effect, the
frequencies of the signals which are digitized in the spectrometer are the offset
frequencies at which the spins evolve in the rotating frame. Often this whole
process is summarised by saying that the "signal is detected in the rotating
frame".
9.2.1 Detector phase
The quantity which is actually detected in an NMR experiment is the transverse
magnetization. Ultimately, this appears at the probe as an oscillating voltage,
which we will write as
S = cosω FID 0t
where ω 0
is the Larmor frequency. The down-shifting process in the
spectrometer is achieved by an electronic device called a mixer; this effectively
multiplies the incoming signal by a locally generated reference signal, S ref
,
which we will assume is oscillating at ω rf
Sref
= cosω
rft
The output of the mixer is the product S FID
S ref
S S = Acosω
tcosω
t
9–2
FID ref rf 0
1
=
2
A[ cos( ωrf
+ ω0) t + cos( ωrf
−ω0)
t]
The first term is an oscillation at a high frequency (of the order of twice the
Larmor frequency as ω 0
≈ ω rf
) and is easily removed by a low-pass filter. The
second term is an oscillation at the offset frequency, Ω. This is in line with the
previous comment that this down-shifting process is equivalent to detecting the
precession in the rotating frame.