# NUTS Help

## Virtual Spectrometer Parameters

Maximum signal is obtained when the excitation pulse is turned on for exactly the length of time necessary to rotate the net magnetization vector 90 degrees, referred to as a 90-degree pulse. This rotates the magnetization from its initial position aligned along the magnetic field (designated as the z-axis) to a position perpendicular to the z-axis, in the x-y plane. The pulse length necessary to do this is dependent on the each instrument’s hardware, such as the transmitter power and the efficiency of the detector coil in the NMR probe. It must therefore be determined empirically and will vary slightly from day to day. Typical values are 5-15us.

The NMR operator must decide what fraction of the 90-degree pulse, commonly referred to as the "tip angle", will be used to generate the NMR signal. For a single-pulse experiment, as is used to acquire a basic spectrum, there is no value in exceeding a 90-degree pulse. So the choice for values of pulse width are from zero up to the 90-degree pulse.

The obvious question is: Why not always use a full 90-degree pulse? More is better, right? The answer is, not always. For a concentrated sample, a smaller pulse angle might be necessary to keep the signal from overloading the receiver, which leads to artifacts in the spectrum. In addition, some of the most valuable information which can be obtained from NMR is quantitative. For this data to be reliable, the spectrum must be obtained under conditions which result in peaks whose integrated area is proportional to the number of nuclei which each peak represents. The complication is that different nuclei relax at different rates. Any nuclei which have not fully relaxed by the time the next excitation pulse is applied will give a signal with somewhat reduced intensity. The result is a spectrum with distorted integration. Therefore, the factors which must be considered are the concentration of the sample and the relaxation time of the nuclei under observation. A relaxation delay and/or smaller pulse angle may be necessary to ensure complete relaxation between scans. As with many aspects of NMR, the choice is a tradeoff and requires consideration of which factors are most important for the case at hand.

The easiest way to determine the 90 degree pulse length is to determine a 180 degree pulse length and divide by 2. A 180 pulse will give zero signal, and is very sensitive to small offsets from the exact value. It is much easier to determine zero signal than to determine the maximum, as it is a fairly broad maximum, making it difficult to distinguish among values that are close to the maximum. So, start with a small pulse length and increase it, viewing the signal. The signal amplitude will go through a maximum and back to zero as the pulse length is increased from 0 degrees to 180 degrees.

The center of the spectrum is determined by the carrier frequency, which is the sum of the Spectrometer Frequency (in MHz) and the Spectrum Offset (in Hz). On many spectrometers, the Spectrum Offset varies depending on the deuterated solvent being used for the Field-Frequency lock, and therefore changes from sample to sample. If the Spectrum Offset is set incorrectly, some peaks of interest may fall outside the the Spectral Window, which then appear "folded".

As the Offset value is increased, the spectral window is moved to lower field, which is to the left as the spectrum is normally viewed. Therefore, peaks will appear to move to the right.

The number of data points which will be acquired. The algorithm used to perform a Fourier transform requires the number of data points in the time domain function (FID) to be a power of 2. For this reason, most spectrometers, including the Virtual Spectrometer, limit the choices for data size to be a power of 2. If a value is entered which is not a power of two, the value will be changed to the next higher power of 2.

To accomplish quadrature detection (which provides the ability to distinguish positive and negative frequencies), data are acquired in 2 channels, related by a 90 degree phase shift. Therefore, the data exist as 2 halves, usually referred to as real (in-phase) and imaginary (90 degree phase shifted) parts. Because these 2 halves are really complex pairs of data points, the NUTS program expresses the number of data points as the number of complex pairs, but that is not true of all spectrometers. Some spectrometers give the data size as the total number of points (the sum of the number of points in the 2 channels). In that case, the number of points which will define the final spectrum will be half of the total data size. For example, starting with 4K (4096) total points (2K real and 2K imaginary) yields 2K points in the final spectrum. By contrast, NUTS considers this size of data to be 2K complex. This is of concern when calculating the data size required to yield the desired digital resolution.

The digitizer, or Analog-to-Digital Converter (ADC), digitizes the signal coming from the NMR probe at a rate determined by the user’s chosen value of Spectral Width. The time between data points is called the Dwell Time, equal to the reciprocal of the spectral width. However, signal acquisition is not started immediately after the excitation pulse, but after a small delay, necessary to allow the circuitry to recover from the effects of the intense excitation pulse. By default, most spectrometers (including the Virtual Spectrometer) set the DE value equal to the dwell time, meaning that a delay of 1 data point is used.

However, this is not usually the optimum DE setting. This is because the filters used to eliminate frequencies outside the chosen range cause a finite delay in the signal reaching the ADC. DE must be empirically chosen to match the delay introduced by the filters. When the DE value does not match the filter delay, baseline distortions (baseline "roll") are seen in the spectrum which make phasing and integration more difficult. If the DE value is too low, the baseline will have a hump ("frown") and the first-order phase value required to phase the spectrum will be negative. If the DE value is too high, the opposite is true: the baseline will have a dip ("smile") and the first-order phase value required to phase the spectrum will be positive. At the optimum DE value, the baseline will be flat and the first-order phase value required to phase the spectrum will be zero.

The signal to noise ratio of a spectrum can be increased by repeating scans and adding the data. Signal from the sample will add with each repeat scan. Noise, which is random in phase, will add at a slower rate. Therefore the signal to noise ratio increases as the square root of the number of scans; eg, four times the number of scans is required to double the signal to noise ratio.

This controls an amplifier through which the signal passes just before it reaches the receiver (analog-to-digital converter, or ADC). This should be adjusted to the maximum amplitude that the ADC can handle without overloading it. If the signal amplitude is too low, small signals will not be discernible. If the ADC is overloaded, the signal will be truncated, or "clipped", resulting in distortion of the resulting spectrum. This can have the appearance of an undulating baseline, in the case of a small degree of clipping, or spurious signals in the case of more severe clipping. The optimum setting can be determined by increasing the gain until clipping is observed and then re

ducing it from that value. In the case of NUTS, the cutoff occurs at about +/- half of full screen.

Note that receiver gain affects signal and noise equivalently, so will not affect the signal/noise ratio.

This is the delay between the end of acquisition of each scan and the next excitation pulse. For nuclei with long relaxation times, more time must be allowed between successive excitations to permit the magnetization to return to equilibrium. Distortions of the spectrum, including distorted integration, results from too short a relaxation delay. On the other hand, one does not want to waste time in acquiring data. Another trade-off.

This sets the range of frequencies which will be observed. In the case of NUTS, this is the size of the entire range, from one end to the other. (Note that some instruments set this parameter to be +/- on either side of center.) It must be set large enough to include all peaks of interest, but too large a setting reduces digital resolution and results in "wasting" data by acquiring regions which include only noise. Peaks which fall outside the spectral width, or "window", will be partially filtered out by the spectrometers filters, but not totally. They will appear "folded" or "aliased" into the spectrum, meaning that they appear at a frequency which is not their correct value. This can be detected by the appearance of peaks at anomalous frequencies and by the fact that folded peaks are often out of phase when all other peaks are phased correctly. The most foolproof way to determine the correct spectral width is to start with a value that is much larger than estimated, to determine where the peaks are, then reduce the value to encompass all peaks.

The spectral window is centered at the frequency of the NMR transmitter, commonly referred to as the "carrier" frequency.

This is the quotient: Spectral width / number of data points, expressed as Hz/pt. The digital resolution must be great enough (Hz/pt value small enough) compared to the width of the lines being observed, to define and resolve narrow peaks. Usually, the spectral width is fixed by the range of frequencies being observed. Therefore, the only parameter which can be varied is the number of data points. Acquiring more data points requires more time. We again have a trade-off between enough points to adequately digitize the NMR signal, but not so many points that time and disk space are wasted.

FT-NMR data is collected as a function of time following an excitation pulse. This time-domain data is referred to as a Free Induction Decay, or FID. It consists of a sum of sinusoids oscillating at different frequencies, one for each peak in the spectrum. The signal decays to zero as a function of time, as the excited spins relax back to equilibrium.

The time required to collect data points for each FID. Acquisition time = (number of data pts) / spectral width.

Last updated 2/14/99.