Estimation of Permitivitty and Loss Tangent of High Frequency Materials in the Millimeter Wave Band using a Hemispherical Open Resonator Robert Felbecker, Wilhelm Keusgen, Michael Peter Fraunhofer Heinrich Hertz Institute Einsteinufer 37, 10587 Berlin, Germany {robert.felbecker, wilhelm.keusgen, michael.peter}@hhi.fraunhofer.de Abstract—In this paper, a hemispherical open resonator is used to measure the quality factor and resonant frequency of various materials in the millimeter wave band. This measurement method allows us to determine the permittivity and the loss tangent of homogeneous materials. Materials like PTFE, PE and PS were used to validate the measurement system. Finally, we measured the resonant frequency and quality factor of samples of Rogers RO4003C and TMM10, which are up to now only characterized up to 10 GHz. I. I NTRODUCTION Today’s microwave designers have to deal with the demand for new wireless systems based on millimeter wave technol- ogy. Especially the 60 GHz band has attracted much attention over the past few years, as it may provide up to 9 GHz of unlicensed bandwidth. The designer of analog frontend and antenna systems for 60 GHz communication systems is now in need of the material parameters to simulate the frontends behavior in design tools for antennas and high frequency circuits. As most of the manufacturers of high frequency sub- strates specify the material parameters like relative permittivity and the loss tangent of their materials only for microwave frequencies, measurements have to be carried out allowing to determine the relative permittivity and the loss tangent for smaller wavelengths like for the millimeter wave band. In this paper, we use a hemispherical (plano-concave) open resonator combined with a vector network analyzer (VNA) to measure the quality factor and the resonant frequency of high frequency materials like Rogers RO4003C [1] and TMM10 [2] for frequencies from 50 to 72 GHz. So far, these materials are only characterized for frequencies up to 10 GHz. As this makes it difficult to validate our resonator with respect to accuracy, we measured the quality factor and resonant frequen- cies of various materials like polytetrafluoroethylene (PTFE), polystyrene (PS) and polyethylene (PE) which have frequently been analyzed before with an hemispherical open resonator at 9 GHz [3], 35 GHz [4], 50 GHz [5] and 100 GHz [6], whereas measurements in the 60 GHz range have been performed with open resonators using two spherical mirrors [7], [8]. We measured different test materials of different sample sizes and thicknesses to asses the accuracy of our resonator. Compared with the results achieved in the literature so far, this serves as a basis for the validation of our system. II. MEASUREMENT SETUP Traditionally, there are two efficient ways of using curved reflectors to bring TEM-modes into resonance in an open resonator. One is the use of two concave mirrors and the other uses only one concave and one plane mirror. In this work we are using a hemispherical (plano-concave) open resonator to excite several fundamental TEM-modes with a VNA. The principle of the measurement setup with a sketch and a picture of the open resonator setup can be seen in Fig. 1. The resonator consists of one concave mirror and Fig. 1. Sketch and picture of the hemispherical open resonator. a flat mirror machined out of brass. The concave mirror is 98 mm in diameter and has a radius of 80 mm in curvature. The flat mirror is a cylindrical block of brass with a radius of 15 mm. The distance between flat mirror and the center of the spherical mirror is 75 mm. Two WR15 waveguides are directly connected to the resonator coupling the power through two apertures into the resonator (see Fig. 1). They are connected to a Rohde & Schwarz ZVA24 via a frequency extension to measure the S 21 . The two coupling apertures are 1 mm in diameter with 4 mm spacing. The frequency extension