## Matching and Tuning

Every electrical device that supplies power (such as a battery) has an internal resistance associated with it. For example, if you short out the two terminals of a battery, you will get a very large current but not the infinite current that would result from zero resistance (Ohm's law: current = voltage/resistance). This is because the battery's voltage is applied across the total resistance of the circuit: the sum of the external load (zero resistance) and the internal load (the internal resistance of the battery). In the case of the short circuit, all of the power (power = current2 x resistance) is delivered to the battery itself since there is no resistance in the "load," and the battery heats up. If, on the contrary, the resistance of the load is very high, there will be very little current flow and very little power will be transferred to the load. It turns out that the maximum transfer of power from the source (the battery) to the load (e.g., a light bulb) is obtained if the resistance of the load equals the internal resistance of the battery. In RF electronics we use the term impedance instead of resistance, but the principle is the same: Matching the impedance of the load to the impedance of the source will maximize the transfer of power to the load. The internal impedance of the RF amplifiers is 50 so we are always trying to match the probe coil to 50 The other factor to consider is the resonant frequency of the probe. The probe circuit may be very complex, but we can view it as an inductance (the coil) connected in parallel with a variable capacitor (the tuning capacitor). The resonant frequency of this tuned circuit is determined by the amount of inductance in the coil and the (variable) amount of capacitance in the capacitor. By rotating the tuning rod we change the capacitance and move the resonant frequency to higher or lower frequency.

If the probe is not properly tuned and matched, the pulse will "reflect" off of the probe and return to the amplifier rather than reaching the sample. The simplest way to tune a probe is to introduce a continuous RF source at very low power and measure the amount of reflected power using a bridge circuit that compares the probe to a 50 ^ resistor. The probe tuning and matching knobs are adjusted to minimize the reflected power reading on the bridge. This is a bit like shimming, except that we are trying for a minimum signal rather than a maximum signal. As with shimming, sometimes the tune and match interact, so it is necessary to "detune" one of the settings a bit and readjust the other to get a lower minimum. Varian still uses this method with a built-in tune display on the preamplifier. The cable from the probe has to be moved from the preamplifier connector to the "probe" connector of the tune interface. Bruker (AMX, DRX) uses a "wobble" tuning method that sweeps the tune frequency back and forth around the desired frequency and records the probe response as a graph on the computer screen. A "dip" in the curve occurs at the resonant frequency of the probe, and the tune knob can be adjusted to position the bottom of the dip (left and right) exactly at the desired frequency. The match knob makes the dip sharper and deeper, so this can be independently adjusted to bring the dip to its lowest value (best impedance match).

The probe tuning rods are long extensions of the variable capacitors located at the top of the probe, near the probe coil. The capacitors are delicate and there are two ends of the travel of the knob: If any force at all is applied at the end of the travel, the capacitor will break. This will usually require that the probe be sent back to the manufacturer for repair, a process requiring a week or two and costing many thousands of dollars. For this reason many NMR labs do not allow users to tune the probe!

### 3.5.2 Types of Probes

All multinuclear probes have more than one probe coil: one is dedicated to XH and the other is for one or more heteronuclei (e.g., 13C). They are positioned concentrically about the NMR tube, with a cylindrical glass insert separating the tube from the inner coil and another larger insert separating the inner coil from the outer coil. The inner coil is much more sensitive for detection of the FID, so usually we detect using this coil. RF pulses can be applied on either coil, but pulses applied on the inner coil will require less power to excite the nuclei. The inner coil is also more sensitive to the electronic disturbance of the sample, so it is much more important to tune the inner coil when a new sample is introduced. Probes with the heteronucleus (e.g., 13C) coil on the inside are called "direct" probes and those with the 1H coil on the inside are called "inverse" probes. In many probes the coils are "double tuned" so that more than one nucleus can be detected. For example, 19F and 1H, 13C and 31P, or 13C and 15N can be paired together. Some double-tuned probes can have as many as eight tuning knobs at the probe head, and getting a good compromise between the two nuclei can be very complicated. "Broadband" probes try to cover a very wide range of frequency, nearly all of the NMR-detectable nuclei in a single probe coil. This often involves "tuning rods": long rods with a fixed capacitor at the end. The rod is inserted into the probe head from the bottom, and the capacitor screws into the circuit near the probe coil. By using a set of rods with different capacitor values, the entire range of NMR frequencies can be tuned with the tuning knob of the heteronuclear coil. This kind of probe is essential for working with "exotic" nuclei such as 57Fe, 29 Si, and 77 Se. Usually a spectrometer will have a number of probes optimized for different purposes; for example, a direct 13C probe (13C inside, XH outside) for 13C spectra, a direct broadband probe for "exotic" nuclei, an inverse13 C probe (1H inside,13 C outside) for heteronuclear 2D experiments, and an "HCN" or "triple-resonance" probe (1H inside, double-tuned 13C/15N outside) for biological work. Changing probes takes about 15 min, but it should only be done by expert users. For biological samples (usually in 90% H20/10% D2O) you need a "water suppression probe" with shielded wires coming from the probe to avoid picking up the very strong H20 signal on these wires.

For a heteronuclear experiment, such as a 1D13C spectrum with 1H decoupling, you need to tune and match both the 1H and the 13C coil. First, set the spectrometer frequency to the 1H frequency and tune and match the 1H coil at the probe head. Then set the spectrometer frequency to the 13C frequency and tune and match the 13C coil. If you are using a direct probe (the most sensitive for 13C detection) the 1H tuning is less important because it varies only slightly from sample to sample (outer coil). If you try to get a 13C spectrum with an inverse probe you will get poor sensitivity, but if you have lots of sample you may be able to overcome this. The baseline may not be flat since you are observing on a coil not designed for observing the FID. If you do not tune and match the 1H coil, you may get no spectrum at all because 1H decoupling will not work if the probe is very badly tuned for 1 H, and as the inner coil, the 1H coil is most sensitive to sample differences.

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