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Probe Qs

One parameter affecting sensitivity is the probe Q. Q is defined as the frequency of the resonant circuit divided by the half power bandwidth. Many of today’s probes have unloaded Qs greater than 300. If all other parameters are the same, the higher the probe Q the greater the sensitivity.
What determines the probe Q? The AC resistance of the resonant circuit. The lower the AC resistance, the higher the probe Q. A very simple answer to a very complex question. The probe has two components which can limit the AC resistance: the coil and the capacitor of the resonant circuit.

The Coil
The resistance of the coil (wire) goes up as the frequency goes up by a phenomenon called “Skin Effect”. The “Skin Effect” is caused by the magnetic field created by the current in the wire. The magnetic field forces the electrons to move in a curved path until they hit the surface of the wire. Therefore the current is forced to flow in a smaller part of the wire. Said in another way the, wire appears smaller to a high frequency current than a low frequency current. The smaller area for current flow raises the AC resistance to current flow and thereby lowers the Q of the resonant circuit. Some probe designers combat this by using foil, as opposed to wire, to increase the surface area. Other probe designs use separate coils in parallel. Since resistances in parallel are less than either individual resistance, the AC resistance of parallel coils is less than in either individual coil. Another advantage of parallel coils is that the total inductance of parallel coils is less than in either individual coil. Since the higher frequency probes tend to have very small capacitance values for resonance, the lower inductance makes it easier to reach higher frequencies with a given capacitance. Often the minimum value of this capacitance is limited by the stray capacitance. The parallel inductors lower the total inductance and therefore higher capacitor values can be used.

The AC resistance of the coil is also determined by its geometry. This can be a very complex issue, but some of its basic characteristics can be simplified. If the coil has any sharp turns, the electrons from the probe’s current generate a magnetic field causing them to crowd to the inside edge. This crowding reduces the effective amount of conductor available to the current, thereby raising its resistance and lowering Q. This effect is very similar to the “Skin Depth” effect discussed before. The electron crowding in the corners also raises the inductance per unit distance of electron flow. Therefore, to get the lowest resistance and inductance per unit of length, the degree of sharpness at all corners of the probe coil should be limited as much as possible.

The Capacitor
The AC resistance of the capacitors is usually related to the materials from which they are constructed. Air capacitors formed by two pieces of conductor in parallel have a very low resistance and therefore can have a very high Q. To obtain a given capacitance value, this type of capacitor needs to be very big or have its parallel surfaces very close. Mechanical tolerances and electrical arcing under the high voltages of an RF pulse limit the use of this type of capacitor. To get the surfaces closer together and increase the capacitance of a given surface area, capacitors have a dielectric between the conductive surfaces. This dielectric introduces higher resistance in the capacitor, which lowers the Q of the resonant circuit. The material from which the tunable capacitors are constructed is usually the most lossy and therefore lowers the Q the most. For this reason, a compromise between the desired tuning range and the probe Q is a problem many probe designers face.

The Sample
One component which limits probe Q is the sample. The sample increases losses in the resonant circuit by inducing eddy currents in the solvent. The more conductive the sample the more the losses and the lower the probe Q. This is often seen by the longer 90o pulses with water samples than with organic solvent samples.
The losses in the sample are induced by the electric field values inside the probe. The more distributed capacitance a probe has in its resonant circuit, the lower the electric field values. Therefore, a probe with distributed capacitance is less affected by the sample. Unfortunately, the capacitor usually has a higher resistance than the coil. Therefore, the use of distributed capacitance lowers the probe’s unloaded Q, but can raise the loaded Q. This statement reduces to the probe designer’s need to compromise probe design between organic and water samples.
As was indicated before, probe design entails many details and compromises. These can often be between mutually exclusive requirements.

Last updated: 01/22/03