If I Can Figure Out NMR Electronics So Can You

I've already given you an ultra-rough block diagram of an nmr spectrometer:

Of course there is much more to it than this but we will go at it slowly, piece by piece. First let's look at the transmitter. This electronic device must provide a pulse of sufficient power at the proper frequency to do something to the appropriate nucleii in the sample. Actually, the transmitter block in the above diagram would, on most spectrometers, consist of several discrete components. A programmable frequency generator, a phase shifter, a gate and a linear power amplifier would be the minimum needed:

The rf synthesizer is programmed to generate an rf frequency that is the nmr reference frequency. This signal is routed through the phase shifter which is controlled by the pulse programmer. The phase shift is to provide pulses along the different axes in the vector model. By convention, a phase shift of 0 is an x-phase pulse, a 90 degree phase shift corresponds to a y-phase pulse, 180 degree phase shift is a -x-phase pulse and a 270 degree phase shift is a -y-phase pulse. See the vector model area of these web pages for a pictorial explanation of this.

The pulse programmer is the ringmaster of the electronics. It's function is to set the timing of the pulses and delays and to program the phase shifter depending on the needs of the pulse program that the user has selected. A pulse is issued to the amplifier when the pulse programmer opens the gate (or closes the switch, whichever you like) and lets the low voltage rf signal proceed to the amplifier.

The amplifier then ... amplifies it. Usually, 1H amplifiers are capable of amplifying to between 50 and 100 watts maximum. X-nucleus (any nucleus not 1H) amplifiers are more powerful at about 300 watts while solid state amps range up to 1000 watts. Also, modern amplifiers are linear, which makes pulse width calculation at different power levels simple. Usually, the software can do this for you ... as long as you know the 90 degree pulse width at power level x then you can calculate pulse widths for other power levels. This is nice for things such as shaped pulses. Also, nowadays, rectangular pulses and shaped pulses go through the same amplifier and there are no phase issues ... in the stone age we had different amps for rectangular and shaped pulses with different cables leading out them that lead to phase differences that had to be measured and accounted for. You folks don't know how good you have it these days! Here are a pair of Bruker amplifiers:

Now what? After the signal is amplified it goes to the probe, right? Not quite. There is a very interesting piece of equipment between the probe and the power amplifier. This device is called a directional coupler and its function is to route the signal from the amplifier to the probe:

When a high power pulse from the amplifier comes into the directional coupler it is routed to the probe and the coil in order to irradiate the sample. After the pulse is issued the signal that comes back from the probe goes through the directional coupler but is now routed to the receiver. Actually, it first goes into a preamplifier, usually located as close as possible to the magnet:

This is to boost the weak nmr signal before it gets lost in the thermal noise of the cables. There's that sensitivity thing again! The latest sensitivity enhancement in nmr spectroscopy (as of 2006) is the cryoprobe. In this device the receiver coil is cooled to about 77K thus decreasing the thermal noise. With the thermal noise lower the signal-to-noise ratio is therefore higher. The improvement is startling. We have seen a S/N enhancement of approximately 10 times with these probes!

After the signal leaves the directional coupler and preamp, it moves on to the receiver, mounted in the main electronics console.

Via the reference signal and a 90 degree phase shifter in the receiver, two signals are produced, the real (R) and imaginary (I) signals. This is known as quadrature detection. The nmr reference signal is used to generate the pulses and in the receiver to mix the signal down to much lower frequencies. This is also the rotating frame frequency. This frequency is placed in the middle of the spectrum and signals fall on either side of it. In order to tell whether or not a signal has a positive or a negative frequency with respect to the reference frequency we receive two signals that are 90 degrees out of phase. This will allow us to tell what the sign of the frequency is. Only one signal would not be sufficient. The receiver, the pulse programmer and various other modules on a Bruker spectrometer look like this:

Let's do a simple kindergarten experiment to convince ourselves of this. Let's pretend the we are the digitizer. Our job is to open our eyes at regular intervals and note the position of vector. From our point of view we are looking at the vector from the side, just as the nmr spectrometer would be doing in the probe coil. We do not see the rotation of the vector but rather we see it moving back and forth.

Furthermore, let us say that a positive frequency corresponds to a counterclockwise rotation and a negative frequency to a clockwise rotation. Ok, here is a series of 'single channel' observations from our point of view:

Which direction is the vector rotating? Is it a positive frequency or a negative frequency? You cannot tell from the information given. We need another 'channel' of information ... in our kindergarten example, we need another eye. Furthermore we need to use our second eye at 90 degrees away from our first eye:

Here is what we might see with our 'two-eye' receiver:

where represents the vector pointed towards or away from the viewer. In this diagram you can see that the vector is rotating counterclockwise or in a positive sense as per our definition.

The digitizer takes the two analog signals and changes them to digital data by sampling the analog signal at regular intervals, usually called the dwell time, and converting the signal from an analog voltage to a digital number which represents the magnitude of the voltage. Analog-to-digital converters cannot acceptably digitize megahertz frequencies but do a rather good job of converting audio-range frequecies. Thus the use of 16-bit audio digitizers and mixdown from megahertz frequencies to audio frequencies in the receiver. We do have to be somewhat careful when doing this (although less so now than in the old days) ... the Nyquist theorem says that in order to adequately digitize a sinusoidally varying signal it must be sampled at least twice every cycle. Thus, if the signal frequency is, say, 100 Hz the digitizer would have to be sampling the signal at a rate of at least 200 Hz in order to properly represent the signal digitally.

What would happen if we ignored the Nyquist theorem and sampled at, say, 1 sample per cycle? Well, we would still have a set of sampled data from the digitizer but the frequencies would be scrambled or, aliased in digitzer parlance or 'folded' in nmr parlance. That is, they would show in the wrong place in the spectrum and probably be difficult or impossible to phase correct properly. On newer spectrometers there is a digital filter which eliminates this problem ... any peak (frequency) that lies outside of the spectral window is not shown. This is both good and bad. On the one hand it gets rid of the folding problem but on the other hand any peaks outside of the spectral window you would be unaware of. Also, the digial filter operates only in the acquisition channel which means that in a 2D spectrum there will be digital filtering in the f2 dimension but not in the f1 dimension. You still have to be aware of folding if you are doing a lot of 2D nmr spectroscopy.