Pulse Power Expressed in Hz

On several occasions I have been asked what it means when a power level for a pulse is expressed in frequency units (e.g. "The proton decoupling power was 75 kHz"). The frequency here is the precession frequency about the magnetic field due to the pulse in the rotating frame of reference and NOT the frequency within the pulse itself. The power level expressed in Hz is simply the reciprocal of the time required for a magnetization vector to travel 360° (one cycle) under the influence of the pulse (i.e. the reciprocal of the 360° pulse duration). The algebra is as follows where the power level in Hz is expressed with respect to the 90° pulse rather than the 360° pulse.

Field Homogeneity and VT Gas

In order to obtain optimum resolution, NMR spectroscopists always correct the inhomogeneity of the magnetic field around the sample by adjusting the current in the the room temperature shim coils. The magnetic field homogeneity around the sample depends not only on the quality of the superconducting magnet but also on the magnetic susceptibility of the materials in the vicinity of the coil and the sample. The careful selection of materials in probe manufacturing and their use around the coil are essential for being able to produce a homogeneous field in the vicinity of the sample using the shim coils. This is one of the reasons why high resolution NMR probes are very expensive. One "material" near the coil which is often overlooked by the NMR user is the VT (variable temperature) gas being passed over the sample. The two most common VT gasses are air and nitrogen. One might think that these are very similar to one another as dry air is approximately 80% nitrogen. The magnetic susceptibility between the two however, is quite large and they will distort the magnetic field around the sample to differing extents. This is demonstrated in the figure below. A sample of CHCl₃ in acetone-d₆ was placed in a 500 MHz magnet equipped with a probe using air as the VT gas. The magnet was shimmed and the spectrum acquired is shown in the top trace. The air source was then replaced by a source of nitrogen gas at the same flow rate. The spectrum was measured again without re-shimming the magnet and is displayed in the lower trace. The difference in line shape and width is due to the difference in magnetic susceptibilities between the two gases. It should be noted that a spectrum of similar quality to the one obtained using air can be obtained after re-shimming the magnet to correct for the susceptibility difference.

Measuring Power

Anyone who takes care of NMR equipment knows that visits from service engineers are very expensive. These visits can often be avoided by becoming familiar with the components of the NMR spectrometer and learning how to make simple diagnostic measurements. These measurements can be sent to service engineers who can provide advice on replacement parts. One such measurement is the determination of the output power from the amplifiers of the spectrometer. This measurement requires an oscilloscope with a band width greater than the output frequency from the amplifier. Since properly functioning amplifiers put out tens to hundreds of watts, the output must be attenuated in order to prevent damage to the oscilloscope. An attenuator of 30 or 40 dB (rated for at least 10 watts of CW power) is suitable. Also, the measurement must be made at 50 Ω impedance. The spectrometer must be set up to take pulses at regular intervals (e.g. 10 µsec pulses every second). For oscilloscopes with only a 1 MΩ input impedance setting, the measurement can be made according to the following figure using a "T" connector and a low power 50 Ω terminator to match the impedance. The "T" connector and 50 Ω terminator are not required if the oscilloscope has in input impedance setting of 50 Ω. In this case, the connections can be made according to the following figure. The output power (in Watts) is determined by the peak to peak voltage, V_pp , of the pulse as follows.

NMR Facility now on Twitter

The University of Ottawa NMR Facility is now on Twitter ( http://twitter.com/Uottawanmr ). NMR users at the University of Ottawa can check here for timely news specifiic to the NMR Facility (for example if an instrument is out of service for repair).

Gradient Recovery Times

Many pulse sequences employ pulsed field gradients for coherence selection thereby minimizing or eliminating the need for phase cycling. The routine use of pulsed field gradients has dramatically reduced the data collection times needed for many 2D experiments and therefore increased the throughput and productivity of NMR spectrometers. The field gradient coils in modern high resolution NMR probes surround the rf coils and are powered by an amplifier in the NMR spectrometer console. When a pulsed field gradient (typically 1 -2 msec in duration) is applied, the sample is no longer in a homogeneous magnetic field. When the gradient is turned off, the system must recover from the disturbance. This recovery is not instantaneous. Pulse sequences typically have delays of 50 - 200 μsec following a gradient pulse to allow for recovery of field homogeneity. The time for recovery after a gradient pulse depends on the design of the NMR probe, the strength and shape of the gradient pulse as well as the shielding between the gradient coils and the shim coils. One can measure the time required for recovery by applying a gradient pulse, and then collecting an NMR spectrum after a variable delay. In the figures below, the gradient recovery time was measured using a console equipped with gradients of maximum strength 50 G/cm, and a narrow bore 500 MHz broadband probe adapted to fit in a wide bore magnet. The duration of the gradient pulses was set to 1 msec. The first figure below shows the proton NMR data for a sample of doped 1% H₂O in D₂O with a line width of approximately 4 Hz with short term recovery times from 1 to 20 µsec.The top trace shows the data for a rectangular gradient at 100 % strength. The middle trace shows the results for a rectangular gradient of 50% of full strength and the bottom trace shows the data using a sine bell shaped gradient pulse of 100 % strength. One can see that for the rectangular gradients the full intensity of the line is recovered in as little as 10 µsec. When the sine bell shaped gradient pulse is used, the full intensity of the line is recovered in less than 1 microsecond. This faster recovery is the result of the gradual rise and fall of the gradient strength in the sine bell shaped pulse.

A 4 Hz line is not a very sensitive gauge for the measurement of recovery times, so the experiments were repeated for a sample with a line of ~0.3 Hz in width where the line shape could be examined in detail at longer recovery times. The second figure shows the proton NMR data for a sample of 1% CHCl₃ in acetone-d₆ with a line width of approximately 0.3 Hz with long term recovery times from 50 to 800 msec.The top trace shows the data for a rectangular gradient at 100 % strength. The middle trace shows the results for a rectangular gradient of 50% of full strength and the bottom trace shows the data using a sine shaped gradient pulse of 100 % strength. One can see that in all cases a reasonable line shape is recovered in ~ 400 msec. The shape of the gradient pulse does not seem to influence the time required to recover a good line shape.