A Method to Measure Complex Dielectric Permittivity with Open-Ended Coaxial Probes

Ismail Dilman, Mehmet Nuri Akinci, Tuba Yilmaz, Mehmet Cayoren*, Ibrahim Akduman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


This work presents a new method to measure the complex dielectric permittivity (CDP) variation of materials under test (MUTs) with open-ended coaxial probes. The CDP variation of an MUT is a continuous function of frequency as modeled with various dielectric relaxation models. Hence, the accuracy and the repeatability of CDP measurements can be improved by enforcing such spectral continuity. Here, we derive a new formulation that explicitly enforces the spectral continuity via the Debye relaxation model. In particular, we construct a cost functional based on an admittance integral at the tip of an open-ended coaxial probe. The Debye model parameters are substituted into the admittance integral to form a set of nonlinear equations. Later, these equations are iteratively minimized by a Gauss-Newton-based minimization scheme, for measured reflection coefficients when the tip of the probe is in contact with the MUT. The presented method differs from the conventional CDP measurement techniques in two aspects. First, the method looks for a global solution across the investigated frequency spectrum instead of solving CDP values individually at each frequency step. Second, the Debye parameters are directly retrieved without any data-fitting. The presented method is experimentally verified with various liquid samples, and the accuracy of obtained results is compared against the literature.

Original languageEnglish
JournalIEEE Transactions on Instrumentation and Measurement
Publication statusPublished - 2022

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.


This work was supported in part by The Scientific and Technological Research Council of Turkey (TUBITAK) under Project 216S415 and in part by the European Union s Horizon 2020 Research and Innovation Programme through the Marie Sklodowska-Curie Grant under Agreement 750346.

FundersFunder number
European Union s Horizon 2020 Research and Innovation Programme750346
Türkiye Bilimsel ve Teknolojik Araştirma Kurumu


    • Complex dielectric permittivity (CDP)
    • microwave dielectric spectroscopy
    • microwave material characterization
    • open-ended coaxial probes


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