Excitation profile

What is an excitation profile?

Hard pulses

During a regular (non-selective) pulse-acquire experiment (e.g. a 1D ¹H experiment), the NMR sample is irradiated with an RF pulse. This pulse should excite all the frequencies within the entire spectral width. Such pulses should be short in length (e.g. around 10 µs for ¹H) and high in power and are referred to as hard pulses. This is the case when the offset of the peaks with respect to the carrier frequency (Ω in rad/s) is much smaller than the RF field strength (ω₁ in rad/s). For a simple rectangular pulse, the excitation profile varies accoring to the sinc(x) function, symmetrically decaying around the transmitter frequency (i.e. the middle of the spectrum, O1P). The excitation profile of a rectangular pulse follows the equation \[f(\nu) = {10^6 \over \pi \times \nu \times p} \times \sin \Big( { \pi \times \nu \over 10^6 } \times p \Big) \] \[f(\delta) = {10^6 \over \pi \times \delta \times SF \times p} \times \sin \Big( { \pi \times \delta \times SF \over 10^6 } \times p \Big) \] where \(\nu\) is the offset frequency of an observed signal (Hz), \(\delta\) is the chemical shift of this observed signal (ppm), \(SF\) is the spectrometer frequency (MHz) and \(p\) is the pulse length (µsec). Around O1P, there is a small frequency range where all the signals in the sample are more or less equally excited. In order to minimize distortion of the peaks at the edges of the spectrum, the excitation profile of the pulse should be uniform over the entire spectral range. The shape of the excitation profile depends both on the transmitter frequency and the pulse length. A broader excitation profile requires shorter pulses or a lower transmitter frequency. Usually, hard pulses are calibrated to be as short as possible to provide a uniform excitation bandwith as large as possible. As pulse length and pulse power go hand in hand, the minimal pulse length is limited by the maximum pulse power of the probe.

Soft pulses

In a selective experiment, the applied RF pulse should only excite a single frequency instead of the entire spectral width. For this type of experiments, pulses with a long duration (e.g. around 100-1000 µs for ¹H) and (very) low power are used, called soft pulses. This is the case when the offset of the irradiated peak with respect to the carrier frequency (Ω in rad/s) is close to the RF field strength (ω₁ in rad/s). The (uniorm) excitation bandwidth of such pulse becomes much smaller than for a hard pulse, allowing for the selective excitation of a peak lying around O1P.

Before analyzing and quantifying NMR spectra, make sure that the peaks of the spectrum lie within the uniform excitation range. For QNMR purposes, this should be investigated before executing of the experiment. For an excitation error < 1%, the quantified peaks should all lie within the 99% excitation range around O1P. Using the widget below, the excitation profile of rectangular pulses can be visualized.

Calculate your own excitation profile

The interactive widget below allows to calculate and display the excitation profile for a rectangular pulse.

Parameters

Spectrometer frequency (MHz)

E.g. 300.1300000 MHz for ¹H on the Bruker Avance 300 or 100.6228265 MHz for ¹³C on the Bruker Avance III HD 400.

Pulse length (µs)

E.g. 10.05 µs for ¹H 90° pulse on the Bruker Avance III HD 400. Remember to adjust the value according to the flip angle of your experiment.

Graph range (ppm)
This value determines the width of the graph window, but doesn't influence the calculation of the excitation profile. Defaults to 500 ppm.

The preview on the right is non-interactive. For an interactive graph, please scroll below.

Interactive excitation profile

The interactive graph below displays the blue excitation profile of the rectangluar pulse, described by the parameters above. The green horizontal line represents the 99 % peak intensity threshold that should be respected for broadband excitation. The orange horizontal line represents the the 99 % peak intensity threshold that should be respected for quantitative NMR (QNMR) with excitation errors < 1 %.