Impedance of a material can be calculated from electromagnetic radiation measurements via permittivity and permeability.
See Eq.(3) from the attached paper about the calculation of impedance via permittivity and permeability based on the transmission line theory.
http://arxiv.org/ftp/arxiv/papers/1110/1110.3184.pdf
Thank you very much, Sergei Sergeenkov. From that equation, should I expect Z_in=Z_o when e_r = m_r?
No, it's a bit more complicated because Eq.(3) depends on the microwave frequency f and the thickness of the absorbers d. Case Z_in=Z_0 is given by Eq.(5) which should be resolved keeping in mind that both e_r and m_r are complex functions given by Eqs.(1) and (2). The relation between d and f is not arbitrary (see discussion on page 6 and also Fig.2).
Very interesting answer. Thanks so much.
Since Z must be Z_0 when e_r=m_r (as defined), do you think Eq.(3) is still valid and why?
Eq.(3) is the formula for impedance of absorbing material which should be made equal to that of the free space to achieve zero-reflection. The authors show that the condition Z=Z_0 when e_r=m_r is achieved for a particular choice of the absorbers thickness d and applied frequency f. Perhaps you need something simpler. Here is a paper on how to calculate impedance using just the reflection and transmission parameters. It has a clear-cut limit of Z=Z_0 when e_r=m_r.
http://cds.cern.ch/record/691907/files/project-note-203.pdf
Yes, I know. From eq. (2) of that paper, we expect Z=Z_o when epsilon=mu, whatever the sample is. That's why I was wondering. It has been very nice to talk to you, Sergei.
But you gotta pay attention for the real and imaginer value and sign, if not you end with a absurd physical interpretation. Specially when the permitivity and permeability comes from NRW alogarithm.
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