_{x}pulse, the magnetization resides on the -y axis. The real FID (along the -y axis) starts at a maximum (cosine) and the imaginary FID (along the x axis) starts at zero (sine) and increases as the magnetization vector rotates anti-clockwise. The Fourier transform of the complex FID produces a real spectrum (typically the one displayed to the user) and an imaginary spectrum (typically not displayed to the user). Note that the degree of absorption vs. dispersion character in the spectrum depends on the phase of the FID signals. If an NMR spectrum is not in phase, perhaps due to a receiver dead time problem, it can be corrected after the collection of the data by calculating the phase angles needed to put the real spectrum enitirely in absorption mode and the imaginary spectrum entirely in dispersion mode.

## Thursday, November 18, 2010

### The Phase of an NMR Spectrum

Most students know that the phase of an NMR spectrum has to do with the
degree to which the NMR resonances are above or below the baseline of
the spectrum (i.e. the amount of absorption and dispersion character).
Most students have also learned that the phase of a periodic time domain
function depends only on the value of the function at time zero. Thus,
the only difference between a cosine and a sine function is where the
function starts at time zero. A sine is said to be 90° out of phase with
respect to a cosine. Many students do not understand the connection
between the phase of their NMR spectrum and the phase of the periodic
time domain function giving rise to their spectrum by way of a Fourier
transform. The figure below is an attempt to make the connection.
The left-hand portion of the figure shows equilibrium magnetization
vectors being rotated by radio frequency pulses. 90° pulses along the x,
y, -x and -y axes rotate the z magnetization vector to the -y, x, y and
-x axes of the rotating frame, respectively according to the right-hand
screw rule. After the pulse, the magnetization vector rotates in the
rotating frame of reference at a frequency equal to the difference
between the transmitter frequency and the frequency of the NMR
resonance. In the figure, the magnetization is assumed to be rotating
anti-clockwise representing an NMR resonance with a positive frequency
with respect to the transmitter frequency. The NMR spectrometer measures
the time dependent voltages on two of the four orthogonal axes of the
rotating frame separated by 90° (quadrature detection).
The time dependent voltages are proportional to the amount of
magnetization on the axis as a function of time. One of the two time
dependent voltages is called the "real" signal and the other is called
the "imaginary" signal. Together these two signals make up the complex
free induction decay (FID) which is Fourier transformed to produce the
NMR spectrum. In the figure, the -y(t) voltage is the real FID and the
x(t) voltage is the imaginary FID. The figure shows representations of
the real and imaginary FIDs after the delivery of pulses along each of
the orthogonal axes. Note that the phases of the real and imaginary FIDs
depend on the pulse delivered. For example, after a 90°

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## 1 comment:

The figure in this post was corrected on March 17, 2016 after an error was pointed out by Huldrych Egli. Thank you Huldrych.

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