`
Measurement
error correction of `*S*-parameters in determining the complex permittivity
and permeability of magneto-dielectric composites in free space using the
diaphragm

**K. M.
Baskov, A. A. Politiko, V. N. Semenenko, V. A. Chistyaev**

**Institute
for Theoretical and Applied Electromagnetics of the Russian Academy of Sciences
(ITAE RAS), Moscow**

The paper is received on
March 15, 2017

**Abstract. **The method is developed for error correction of measurement results of *
S*-parameters. This correction is conducted during determining complex
permittivity and permeability of material samples in the centimeter wavelength
range. The measurements of properties of materials are carried out in free space
using the specific diaphragm of certain diameter by means of specialized
measurement bench developed by ITAE RAS. The correction procedure is necessary
when the size of test sample is less than two wavelengths of electromagnetic
radiation in free space. The correction algorithm of reflection coefficient
(parameter ) and transmission
coefficient (parameter ) based on the representation of measuring bench in the
terms of equivalent long-distance line is shown. The mathematical justification
of correction algorithm in non-strict statement is described. The submission is
suggested that a space of measurement bench has a wave impedance that differed
in *a *times from the wave impedance of free space. A sample under the test
is a quadripole with transmission matrix
for measurement bench (*d* –
sample’s thickness, *e* and *m *– effective complex permittivity and permeability of test
sample accordingly). Iterative procedure with fast convergence is proposed for
determining effective permittivity and permeability obtained from measurement
results of S-parameters. Error correction was done for measurement of material
properties using small-sized diaphragm 80 mm in diameter which dimension is less
than falling wavelength of electromagnetic radiation in the long-wave region
of spectrum. As results the comparative dependences of complex permittivity and
permeability of material properties of test samples in the low-frequency range
in initial state and after correction procedure are submitted. Test samples are
presented as thin films of sheet materials based on organosilicone or
fluororganosilicone binder filled with modified iron with both different
concentration and various degree of treatment. The obtained results allow us to
minimize measurement errors of material properties in a frequency vicinity from
3 to 6 GHz. Due to this reason the accuracy of analytical estimates in designing
of radio absorbing materials is essentially increased.

**Key words:** *S*-parameters, reflection
coefficient, transmission coefficient, complex permittivity and permeability,
measurement error correction.

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**

**
For citation:**

K. M.
Baskov, A. A. Politiko, V. N. Semenenko, V. A. Chistyaev.
`
Measurement
error correction of `*S*-parameters in determining the complex permittivity
and permeability of magneto-dielectric composites in free space using the
diaphragm.
*Zhurnal Radioelektroniki - Journal of Radio Electronics*,
2017, No. 5. Available at http://jre.cplire.ru/jre/may17/7/text.pdf.
(In Russian)