A square cavity resonator would have to be constructed on the dielectric that you are interested in characterizing. This resonator must resonate at the frequency you are interested in extracting the permittivity at. This cavity can be constructed on a board with a via fence or the cavity can have solid walls. As shown in the diagram below, the port pins should be inserted one-quarter the distance inwards from the corners. This is a shorted cavity resonator, where the pins are shorted at the base of the cavity.
The cavity resonator needs to be measured on a VNA. Enough points must be used in order to attain smooth peaks at the resonance frequencies.
The width and height of the cavity along with the port locations should be verified by measurement.
The two-port Touchstone measurement file can be imported into Kappa Extractor and all the parameters of the particular resonator can be entered into the fields.
Finally, you can choose whether to optimize or keep fixed the dielectric constant, loss tangent, cavity height, and/or surface roughness.
Engin, Arif Ege, et al. “Nonoverlapping Power/Ground Planes for Suppression of Power Plane Noise.” IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 8, no. 1, 2018, pp. 50–56.
Associated cavity parameter file for import [.xlsx] is pa.xlsx.
Example with HTCC
A. Ege Engin and Pavithra Pasunoori (2012) Automated Complex Permittivity Characterization of Ceramic Substrates Considering Surface-Roughness Loss. Additional Conferences (Device Packaging, HiTEC, HiTEN, & CICMT): September 2012, Vol. 2012, No. CICMT, pp. 000613-000620.
Engin, A.E. “Extraction of Dielectric Constant and Loss Tangent Using New Rapid Plane Solver and Analytical Debye Modeling for Printed Circuit Boards.” IEEE Transactions on Microwave Theory and Techniques, vol. 58, no. 1, 2010, pp. 211–219.