Reflection and Loss Tangents

In summary, the question is about the effect of a lossy dielectric or medium on the reflection coefficient. While the reflection coefficient for a lossless medium is easy to determine, it is more complicated for a lossy medium. The absorption in a dielectric is closely tied to its dispersion, which can be described using the Kramers-Kronig relations. These relations also apply to lossy microwave dielectrics and complex impedances in passive electric circuits. A helpful resource for finding the solution is the book "Ruck" by Ruck, which covers this topic in detail.
  • #1
jmckennon
42
0
I've been reading over Balanis' Advanced Engineering Electromagnetics in an effort to teach myself a bit about Electromagnetism.

I've stumbled across a question (not one in the book) that I can't seem to wrap my head around.

If there's a lossy dielectric or medium, how does the reflection coefficient change/get effected as opposed to a lossless medium or dielectric?

It's easy to determine the reflection coefficient for a lossless medium, I'm fine with that portion, but I'm having trouble understanding how to do it for a lossy medium.

I've googled around, but can't seem to find an answer. As a side, but possibly unrelated note, is reflection coefficient the same as the complex propagation constant for the case of a lossy dielectric/medium? That's about all I was able to find on the topic. Hope someone can clear this up!
 
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  • #2
If a dielectric is lossy, the refraction coefficient must be dispersive.

At a single frequency, the index of refraction (and reflection coefficient) and the absorption are independent. So I don't believe at a single frequency, a change in the absorption (attenuation) will affect the reflection coefficient.

However, the absorption (loss tangent) in a dielectric is very closely tied to the dispersion (frequency dependence of index of refraction). The refractive index is complex when absorption is present, and the absorption is determined by the dispersion in the refractive index. Mathematically, this relation is shown in the Kramers-Kronig relations. See http://www.scholarpedia.org/article/Kramers-Kronig_relations [Broken]

These relations apply to lossy microwave dielectrics, and even to comples impedances in passive electric circuits. See book by Bode Network Analysis and Feedback Amplifier Design, and Morse and Feshbach Methods of Theoretical Physics Vol 2.
 
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  • #3
Get a copy of Ruck volumes one and two. It's very hard to find but itself presents the solution you seek in its most general and perfect form. Sorry I no longer have access to it so I can't give you the correct formula.
 

What is reflection loss?

Reflection loss, also known as return loss, is a measure of the amount of signal that is reflected back from a material or surface. It is typically expressed in decibels (dB) and is caused by impedance mismatches between two materials or surfaces.

What is a loss tangent?

A loss tangent is a measure of the dissipation of energy in a material due to losses such as resistance or dielectric losses. It is a ratio of the imaginary part of the complex dielectric constant to the real part and is used to characterize the dielectric properties of materials.

How are reflection and loss tangents related?

Reflection and loss tangents are related because they both measure the loss of energy in a material. In fact, the reflection loss can be calculated from the loss tangent and the material's impedance. Both values are important for understanding the performance of materials in high-frequency applications.

Why are reflection and loss tangents important in materials science?

Reflection and loss tangents are important in materials science because they provide valuable information about the electrical properties of materials. These values can help engineers and scientists design and optimize materials for specific applications, such as in electronic devices or in microwave technology.

How are reflection and loss tangents measured?

Reflection and loss tangents are typically measured using a technique called vector network analysis. This involves sending a signal through a material and measuring the reflected signal to determine the amount of energy lost. Other methods, such as time-domain reflectometry, can also be used to measure these values in certain materials.

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