Error Tolerant Method of Dielectric Permittivity Determination Using a TE₀₁ Mode in a Circular Waveguide at the W-Band

Abstract

We propose a new method for the precise measurement of dielectric permittivity of ceramics and polymers at millimeter-wave frequencies that employs the TE01 mode of a circular waveguide. At higher frequencies, accurately measuring the dielectric permittivity of materials becomes extremely challenging by using the fundamental TE10 mode of a rectangular waveguide. As the frequency increases, the dimensions of the dielectric sample that has to be fit into the waveguide become very small. Therefore, small fabrication imperfections that produce air gaps between the sample and the wall of the waveguide result in significant errors during measurements. In contrast, the TE01 mode of the circular waveguide that does not have an electric field at the surface of the waveguide is insensitive to small imperfections during fabrication. We measured the dielectric permittivity in small samples of alumina (Al2O3), magnesium calcium titanate (MCT) ceramics, and Teflon placed in a circular waveguide. The results showed that the method was very robust with respect to manufacturing imperfections: when dimensions of the alumina and Teflon samples varied by as much as 10% and 20%, the differences in the computed dielectric permittivity of the alumina were only 1.26% and 3.06%, respectively, and those of Teflon were 1.98% and 2.12%. In addition, when the high-dielectric permittivity material MCT samples were deformed by 5% and 10%, the differences were just 0.04% and 0.14% each, respectively. We believe that this new proposed method is also applicable to even higher frequencies in the THz regime and at a very high relative dielectric permittivity of larger than 10.