An accurate frequency measuring technique using paramagnetic resonance phenomena in the X-band region (2005)

This paper presents a method of measuring frequency in the microwave region by comparing it to a very stable low frequency standard. The technique described here was used to calibrate a cavity wavemeter for an experiment in microwave spectroscopy. The calibration procedure is based on the use of electron and nuclear resonances as they are observed in the presence of an applied r.f. field. A material containing spinning nuclei is inserted in an r.f. coil and the entire assembly is placed between the pole faces of an electromagnet which is capable of producing extremely homogeneous fields. The two resulting magnetic fields are then oriented at right angles to each other. By perturbing the magnetic field one can observe a resonance between the precessional frequencies of the nuclei and the applied r.f. field. The magnetic field is perturbed by means of a Helmholtz coil placed at right angles to the r.f. coil. Resonance takes place at about 14 mc in a 3300 gauss field when the sample consists of hydrogen nuclei or protons in water. By varying the magnetic field resonance will occur at a different frequency, and by varying it over a wide enough range a considerable spread of frequencies is obtained. These frequencies can be accurately measured by the use of an r.f. wavemeter or by an IF detection system. Once the frequency is known, the magnetic field strength may be calculated by using the following relationship: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{n} = \gamma_{n}H</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{n}</tex> = resonant frequency of nuclei in kc/sec, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\gamma_{n}</tex> = 4.25776 kc/gauss, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> = magnetic field strength in gauss. Commercial magnetometers are available to make these calibration curves and accuracies up to one part in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10^{7}</tex> are achievable. The electron sample is used in a similar manner and the same equation holds except that the value of the resonant frequency and the proportionality constant are different. A good paramagnetic material which has narrow lines in the X-Band region is diphenyl-picryl-hydrazyl. Its proportionality constant is equal to 2.7994 mc/gauss. A sample of this material placed in a microwave cavity at a point of maximum H field and at right angles to an applied magnetic field of 3300 gauss will give a resonance line at 9238 mc. If the field strength of the magnet is known from previous measurement with the nuclear sample the frequency of the electron resonance line may be calculated from the relationship: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{e} = \frac{2.7994 \times 10^{3}}{4.25776} \omega_{n}</tex> , or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_{e} \cong 655 \omega_{n}</tex> . In order to instrument this experiment a Numar M-2 Precision Gauss-meter was used to calibrate the magnet. The frequency was measured by using an IF measuring technique. The microwave frequency was observed by sweeping a klystron through the frequency range of the "low Q" cavity which held the paramagnetic sample. The resonance line was observed in the display of the detected output power from this cavity. The wavemeter pip was superimposed on the resonance line and the frequency calibration was thus established. One must use extreme care in the magnet design so that good homogeneity can be measured throughout the region in which the sample is placed. If this requirement is met and if a good r.f. frequency measuring scheme is used, accurate microwave frequency measurements of better than one part in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10^{7}</tex> may be obtained. The above method will appeal especially to the microwave spectroscopist because it makes use of the tools of his trade.