Attenuation constant (low-loss dielectrics)

So if it's wrong then we're both wrong.In summary, the \epsilon \prime \prime term signifies the real and imaginary parts of the actual permittivity in the equation for the absorption \alpha. It is often used in approximations and can be reexpressed as \frac{\sigma}{\omega} for a low-loss dielectric.
  • #1
big man
254
1
[tex]\alpha =\frac {\omega \epsilon \prime \prime} {2} \sqrt {\mu \epsilon \prime} [/tex]

My question is what exactly does the [tex]\epsilon \prime \prime[/tex] term signify??

I see sections of my notes that say [tex]\epsilon \prime \prime << \epsilon [/tex], but what is it?

I mean when I am trying to find the attenuation constant and the material happens to be a low-loss dielectric and you are given the actual permittivity [tex]( \epsilon )[/tex] I don't know what to do with the [tex] \epsilon \prime \prime[/tex] term. It's the only value I don't know in the problem?

I would REALLY appreciate any help on this because I really need to understand this before my exam on Monday.
 
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  • #2
Sorry I was looking up how to correctly write up the primes using Latex. It's fixed now.
 
  • #4
Dan is probably right.

The basic equation for the absorption [itex]\alpha[/itex] is

[tex]\alpha = 2\Im(k) = 2\omega \frac{\mu}{2}\sqrt{\sqrt{\Re(\epsilon)^2+\Im(\epsilon)^2}-\Re(\epsilon)}[/tex]

And my guess is that your expression is some approximation of that.

But are there really 3 epsilons?! a non prime, a primed and a double primed?!?
 
  • #5
quasar987 said:
Dan is probably right.

The basic equation for the absorption [itex]\alpha[/itex] is

[tex]\alpha = 2\Im(k) = 2\omega \frac{\mu}{2}\sqrt{\sqrt{\Re(\epsilon)^2+\Im(\epsilon)^2}-\Re(\epsilon)}[/tex]

And my guess is that your expression is some approximation of that.

But are there really 3 epsilons?! a non prime, a primed and a double primed?!?

[tex] \epsilon = \epsilon \prime + i \epsilon \prime \prime[/tex]
 
  • #6
That is the most sensible guess, but then the expression e''<<e doesn't make sense since e is not real.
 
  • #7
The [tex]\epsilon[/tex] in my notes is the permittivity given by this expression:

[tex]\epsilon = \epsilon_r \epsilon_0 [/tex]

Thanks for the quick replies guys and I understand this a little better, but could you just tell me if I have this right.

OK let's say that you are wanting to find the attenuation constant for a low-loss dielectric with the following properties:

[tex]\sigma=5.80*10^-^2 (S/m)[/tex]
[tex]\omega = 100 GHz[/tex]
[tex]\epsilon_r = 1[/tex]
[tex]\mu = \mu_0[/tex]

You first test to see if it is a low-loss dielectric or a good conductor.
Then finding that at that the material is a low-loss dielectric you can proceed to use the previsously stated equation for the attenuation constant (in first post). Do you say that it doesn't behave like a perfect dielectric, which means that the conduction current is not negligible and this means that you can reexpress the magnitude of the complex part as follows:

[tex]\epsilon \prime \prime = \frac {\sigma} {\omega}[/tex]

Am I right in doing this??
,
 
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  • #8
big man said:
[tex]\epsilon \prime \prime = \frac {\sigma} {\omega}[/tex]

Am I right in doing this??
That apperas to be consitent with the approach taken in that link I posted earlier
 

Related to Attenuation constant (low-loss dielectrics)

1. What is the attenuation constant in low-loss dielectrics?

The attenuation constant, also known as the absorption coefficient, is a measure of how much energy is lost as an electromagnetic wave travels through a material. In low-loss dielectrics, the attenuation constant is relatively small, indicating that there is minimal energy loss.

2. How is the attenuation constant related to the dielectric constant?

The attenuation constant is directly related to the dielectric constant, also known as the relative permittivity. The dielectric constant is a measure of how much a material can store electrical energy, and a higher dielectric constant typically results in a higher attenuation constant.

3. What factors affect the attenuation constant in low-loss dielectrics?

The attenuation constant in low-loss dielectrics is affected by several factors, including the frequency of the electromagnetic wave, the temperature of the material, and the composition of the material. Generally, higher frequencies and temperatures lead to higher attenuation constants, while materials with a low concentration of impurities have lower attenuation constants.

4. Can the attenuation constant be modified in low-loss dielectrics?

Yes, the attenuation constant in low-loss dielectrics can be modified by adjusting the composition of the material or by using special techniques such as doping or annealing. These modifications can alter the material's dielectric properties and therefore affect the attenuation constant.

5. What are the applications of low-loss dielectrics with a low attenuation constant?

Low-loss dielectrics with a low attenuation constant are commonly used in high-frequency electronic devices, such as antennas, satellite communications, and radar systems. They are also used in optical fibers for telecommunications and in medical imaging equipment.

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