Two-step numerical procedure for complex permittivity retrieval of dielectric materials from reﬂection measurements Ugur Cem Hasar • Joaquim Jose ´ Barroso • Yunus Kaya • Mehmet Ertugrul • Musa Bute • Jose ´ M. Catala ´-Civera Received: 30 October 2013 / Accepted: 30 January 2014 / Published online: 20 February 2014 Ó Springer-Verlag Berlin Heidelberg 2014 Abstract A two-step measurement procedure has been proposed for measurement of complex permittivity of dielectric materials using one-port reﬂection measure- ments. In the procedure, as a ﬁrst step, a graphical method is applied to analyze on the complex reﬂection-coefﬁcient plane the general pattern of dielectric behavior of the sample. Then, as a second step, optimization algorithms are utilized for retrieving electrical properties of samples. The procedure requires measurement of complex reﬂection scattering parameters of at least two samples with different lengths. It has been validated by X-band measurements of three polyvinyl chloride samples with lengths 5, 10, and 20 mm. 1 Introduction The fast growth of the telecommunications, RF, and microwave industry and the rapid increase in the number of applications at ever higher operational frequencies have outlined the importance of precisely determining the dielectric properties of novel materials over a ﬁxed bandwidth [1, 2]. For example, for modeling or charac- terizing the systems such as printed circuit boards, trans- mission lines, and indoor wireless communications [3, 4, 5, 6] as well as metamaterials [7, 8, 9, 10, 11], precise knowledge of electrical properties of substrate materials is required. Many methods, each with its strengths and weaknesses, have been proposed for different purposes in the literature [1]. Among them, reﬂection-based methods have been used widely due to their proven effectiveness [2, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]. In particular, in some applications while the accuracy of transmission measurements is relatively low, that of reﬂection mea- surements is comparatively higher especially for low-loss or lossy materials or structures [22, 23, 24]. For instance, for highly absorbing materials, reﬂection measurements are preferred over transmission measurements due to their higher accuracy [23]. Besides, reﬂection scattering (S-) parameter measurements are needed when only the front side of the sample is accessible for inspection [17, 18, 19, 20, 21]. Additionally, so as to extract more information about the sample, reﬂection measurements of a sample can be combined with reﬂection measurements of the sample shorted with a short-circuit termination [1, 12, 13], or reﬂection measurements using shifted short-circuit termi- nations can be directly used [26]. Because of the presence of multi-valued complex exponential terms in the retrieval process, unique solution U. C. Hasar  M. Bute Department of Electrical and Electronics Engineering, University of Gaziantep, 27310 Gaziantep, Turkey U. C. Hasar (&)  M. Ertugrul Center for Research and Application of Nanoscience and Nanoengineering, Ataturk University, 25240 Erzurum, Turkey e-mail: uchasar@gantep.edu.tr J. J. Barroso Associated Plasma Laboratory, National Institute for Space Research, 12227-010 Sa ˜o Jose ´ dos Campos, SP, Brazil Y. Kaya Department of Electricity and Energy, Bayburt University, 69000 Bayburt, Turkey M. Ertugrul Department of Electrical and Electronics Engineering, Ataturk University, 25240 Erzurum, Turkey J. M. Catala ´-Civera Departamento de Communicaciones, Universitat Polite `cnica de Vale `ncia, 46022 Valencia, Spain 123 Appl. Phys. A (2014) 116:1701–1710 DOI 10.1007/s00339-014-8303-9