The broadband dielectric spectroscopy is widely used for charackterization of electromagnetic charackteristics of materials in microwave range. For experimental measurements, a large number of different methods have been developed, which are described in detail in Ref. [1].  The EM-calculator project is focussed on practical problems which may arising during chrackterization of materials in microwave frequency range using coaxial or waveguide-based measurments.  

In order to obtain a spectrum of complex dielectric permittivity and magnetic permeability (Eps-Mu), the S-parameters for a given sample must be used. They can be obtained, for example, using a vector network analyzer. See Tutorial for more information on experimental measurements of S-parameters.

After you have performed measurements, you must save the data in .s2p format. This is the standardized format for storing S-parameters. A typical .s2p file looks like this:

Typical structure of .s2p file

This spectrum was obtained on a vector circuit analyzer and contains information about the manufacturer, the date of measurement, and the S-parameters themselves. For example, the typical S-parameters spectra  of PTFE (Ls=4 mm) inside coaxial cell (Lc=34 mm) loacated at Lpos=20 mm is  here.

In total there are 9 data columns: the first column contains the spectrum of frequencies at which measurements were made, and the other columns contain the S-parameters in the order Abs(S11) (in decibels), Arg(S11) (in degrees), Abs(S21), Arg(S21), ..., Arg(S22). The number of lines is equal to the number of points into which the frequency range is divided. In addition to the .s2p format, which has 2^2 = 4 S-parameters, there are also formats of a more general .sNp form, which contain N^2 S-parameters. However, at our website the calculations are performed only with .s2p files.

The available S-parameter spectrum can be converted to Eps-Mu spectrum using special algorithms, which is performed in the "Epsilon-Mu Calculator" section. There are two algorithms to choose from: NRW (Nicholson-Ross-Weir) and iterative. The first one is faster, but in order to use it you have to know the position of the sample inside the cell. In the iterative method, however, you do not need to know the sample position, but you do need to set the initial approximation for Eps and Mu. These algorithms are described in detail in [2], [3], [4]. If the corresponding measurements were made using a waveguide, we recommend referring to the standard [5]. If the sample is non-magnetic, this should be specified, and then Mu = 1 will be assumed during the calculation.


[1] Basics of Measuring the Dielectric Properties of Materials, Keysight Application note, Literature number 5989-2589EN
[2] A. M. Nicholson; G. F. Ross, Measurement of the intrinsic properties of materials by time domain techniques. IEEE Transaction on Instrumentation and Measurement, vol. IM-19: 377-382, 1970 November
[3] W. B. Weir, Automatic measurement of complex dielectric constant and permeability at microwave frequencies. Proceedings of the IEEE, vol. 62: 33-36; 1974 January
[4] Baker-Jarvis, J. R., Janezic, M. D., Grosvenor, J. H., and Geyer, R. G., “Transmission/Reflection and Short-Circuit Line Methods for Measuring Permittivity and Permeability,” NIST Technical Note 1355, May 1992 
[5] Standard Test Method for Measuring Relative Complex Permittivity and Relative Magnetic Permeability of Solid Materials at Microwave Frequencies Using Waveguide, An American National Standard ASTM D556808 (2009).