Description
The cavity used has been worked out in our laboratory and enables ones to measure the complex permittivity, e'-je", and thus the associated losses (tan d). It, therefore, consists in a single-frequency measurement. The materials characterized with this method are isotropic and can be solid, liquid or in powder.

Principle
The resonator cavity has a cylindrical shape and a circular section. The resonant modes used are the transverse magnetic ones, TM₀₁₀ et TM₀₂₀. As shown in the Top Figure (or right-side figure) the cylinder-shaped (bar-like) sample is placed at the center of the cavity where the electrical field is maximum and quasi-constant over a radius of a few millimeters. The dielectric constant and the loss tangent are calculated from the variation of resonant frequency, Df, and from the change in the cavity quality factor, DQ, which both result from the presence of the sample inside the cavity.

Analysis of measured data
The program used to analyze the measured data is based on low perturbation theory. This approach consists in using simplifying hypotheses to analytically express e'-je", versus Df and DQ, i.e. the two parameters measured. To comply with the starting hypotheses, the relative variation in resonant frequency must not exceed 10%. The main parameters are the respective volumes of the cavity and sample, the resonant frequencies as well as the quality factors of the cavity unloaded and loaded with  the sample. To measure the parameters of powders and liquids, the electromagnetic study takes into account the sample holder.

Results

• Frequencies used : close to 5 and 12 GHz (network analyzer HP8720A).
• Type of material tested: dielectric with low losses, i.e. tan d < 10^-3
• Accuracy: relative errors < 2% for ; absolute error = 5.10-4 for tane' d.
• Dimensions of the tested samples:
  • 2 mm < height < 24 mm
  • 4 mm < diameter < 6 mm
  • volume of liquid or powder: about 0.3 cl.

Comments
In order to improve reproducibility, and then accuracy in the measurements the measuring cell is being modified. These changes deal, in particular, with the metal used to make the cell walls and the automation of measurement procedure. This characterization method has been developed within the framework of a contract with Thomson Multimedia at Rennes.

1. R.A. Waldron ,"Perturbation theory of resonant cavities", Proc .Inst. Elec. Eng., April 1960, vol. 107C, pp. 272-274.

2. B. Meng, J. Booske and R. Cooper, "Extended cavity perturbation technique to determine the complex permittivity of dielectric materials", IEEE Transactions on Microwave Theory and Techniques, Vol. 43, No. 11, pp. 2633-2636, November 1995.

3. S. Li, C. Akyel, R. G. Bosisio, "Precise calculation and measurements on the complex dielectric constant of lossy materials using TM₀₁₀ cavity perturbations techniques", IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-29, No. 10, pp. 1041-1047, October 1981.