Russian Physics Journal, Vol. 61, No. 2, June, 2018 (Russian Original No. 2, February, 2018)
MEASUREMENT OF THE ELECTRIC PARAMETERS OF
MATERIALS USING THE RESONATOR BASED ON A BELOW-
CUTOFF WAVEGUIDE SECTION
A. S. Zav’yalov UDC 621.317.3
The feasibility of measuring the complex dielectric permittivity of sheet materials using the resonator based on
a below-cutoff waveguide section is considered. Measuring equations are derived with allowance for the edge
resonator capacitance and incomplete filling by the sample of the region of interaction with the electric field.
The electric parameters of some sheet materials have been measured in the decimeter wavelength range.
Keywords: dielectric permittivity, resonator, below-cutoff waveguide.
To measure the dielectric permittivity of materials in a wide range of frequencies, coaxial resonators with
a face end gap  are used. When the length of the coaxial section becomes commensurable with the size of its cross-
section, the resonator becomes toroidal. The main disadvantage of coaxial and toroidal resonators is that they must be
disassembled and assembled again after changing samples which leads to excessive time expenditures during
measurements. It is easy to get rid of this disadvantage proceeding from coaxial sections to rectangular waveguide
sections at below-cutoff frequencies.
The feasibility of application of resonators based on below-cutoff waveguides for measuring the parameters of
materials was first pointed out already in . However, more recent works devoted to measuring the parameters of
materials, including review , demonstrated that the work  was forgotten. The resonator used in  represented the
section of a rectangular waveguide with a transverse rod at the end of which a disk was arranged. During measurements
Teflon samples with thickness of 600 m, whose area exceeded the disk area, were used.
In the present work, the resonator of the same design, but with elements having different sizes was used for
measuring the electrical parameters of sheet materials (Fig. 1). In calculation of the resonant frequencies of toroidal
resonators, the assumption about independent localizations of electric and magnetic fields is conventionally used. Parts
of the resonator are thus described by equivalent capacities and inductances.
The capacitance between the disk and the wide waveguide wall can be calculated from the known formula for
the capacitance between two disks (for example, see ). In the employed designations, the capacitance between the
disk and the infinite plane is written as follows:
is the disk diameter,
is the distance between the disk and the plane, and
electric constant. The first component in the square brackets of Eq. (1) represents the face end wall capacitance divided
National Research Tomsk State University, Tomsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh
Zavedenii, Fizika, No. 2, pp. 26–29, February, 2018. Original article submitted December 14, 2016; revision submitted
April 11, 2017.
1064-8887/18/6102-0232 2018 Springer Science+Business Media, LLC