Use of multi-length TDR data aimed to infer the dispersion law of nonmagnetic materials
Authors: Farhat Iman , Persico Raffaele , Farrugia Lourdes , Sammut Charles 
Published: March 2020

&lt;p&gt;This contribution presents a method of multi-length transmission lines, filled with or embedded in the material under test (MUT), based on time domain reflectometry (TDR), to measure the dispersion law of a nonmagnetic material. This approach is essential and can be exploited in both radiofrequency and microwave applications. The proposed technique expands on studies presented in [1-2], where dielectric, magnetic and conductive losses are accounted for by the complex relative permittivity and permeability of the MUT.&lt;/p&gt;&lt;p&gt;Many materials of interest in geophysical [3-4] and biomedical [5-6] applications are non-magnetic but preliminary measurements with the proposed technique can help to determine if the MUT indeed has magnetic properties. Moreover, it is shown that establishing the non-magnetic nature of the MUT constitutes meaningful a-priori information that allows disambiguating experimental results, even with limited data in the frequency range of interest.&lt;/p&gt;&lt;p&gt;Results relative to two different types of multi-length measurement data, namely data acquired by considering different lengths of a TDR probe entirely embedded in (or embedding) the MUT and data achieved from a sequential progressive embedding of the probe in the MUT (or, vice-versa, of the MUT in the probe) are presented to illustrate the method. The pros and cons of presented cases are also discussed. &amp;#160;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Acknowledgements&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;This work is supported by the European Cost Action &amp;#8220;Mywave&amp;#8221; CA17115.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;&lt;p&gt;[1] R. Persico, M. Pieraccini, Measurement of dielectric and magnetic properties of Materials by means of a TDR probe, Near Surface Geophysics, vol. 16, n.2, pp.1-9, DOI:10.3997/1873-0604.2017046, 2018.&lt;/p&gt;&lt;p&gt;[2] R. Persico, I. Farhat, L. Farrugia, S. d&amp;#8217;Amico, C. Sammut, An innovative use of TDR probes: First numerical validations with a coaxial cable, Journal of Environmental &amp; Engineering Geophysics, doi.org/10.2113/JEEG23.4.437, 23 (4): 437-442, 2018.&lt;/p&gt;&lt;p&gt;[3] R. Pierri, G. Leone, F. Soldovieri, R. Persico, &quot;Electromagnetic inversion for subsurface applications under the distorted Born approximation&quot; Nuovo Cimento, vol. 24C, N. 2, pp 245-261, March-April 2001.&lt;/p&gt;&lt;p&gt;[4] R. Persico, M. Ciminale, L. Matera, A new reconfigurable stepped frequency GPR system, possibilities and issues; applications to two different Cultural Heritage Resources, Near Surface Geophysics, vol. 12, n. 6, pp. 793-801 (doi: 10.3997/1873-0604.2014035), December 2014.&lt;/p&gt;&lt;p&gt;[5] R. Pethig, &quot;Dielectric Properties of Biological Materials: Biophysical and Medical Applications,&quot; in&amp;#160;IEEE Transactions on Electrical Insulation, vol. EI-19, no. 5, pp. 453-474, Oct. 1984.&lt;br&gt;doi: 10.1109/TEI.1984.298769&lt;/p&gt;&lt;p&gt;&amp;#160;[6] C. Gabriel,&amp;#160;S. Gabriel&amp;#160;and&amp;#160;E Corthout, &amp;#8220;The dielectric properties of biological tissues: I. Literature survey,&amp;#8221; Physics in Medicine and Biology, vol. 41, no. 11, pp. 2231-2249, Nov. 1996.&lt;/p&gt;