How to compute complex relative permittivity

In summary: It is important to note that different factors drive tau at different frequency ranges and it is best to refer to credible sources for more information on this topic. In summary, to use an equation with a complex frequency term, you must first determine the necessary values and then plug in a value for omega to calculate the permittivity at that frequency. It is also important to refer to reliable sources for more information on the factors that drive tau at different frequency ranges.
  • #1
kris287
1
0
Greetings. I don't know how to use an equation with a complex frequency term, specifically this one (aka Debye expression) for frequency-dependent permittivity:

epsilon(omega) = epsiloninfinity + delta-epsilon/(1 + j*omega*tau)

where epsilon(omega) is the permittivity at omega angular frequency, epsiloninfinity is the limit of permittivity at high frequency (omega*tau >>1), tau is the time it takes to polarize the dielectric, delta-epsilon = epsilons - epsiloninfinity (where epsilons is the permittivity at omega*tau<< 1), a measure of a permittivity dispersion region that is driven by tau (different factors drive tau at different frequency ranges, q.v., e.g., http://en.wikipedia.org/wiki/Complex_permittivity#Complex_permittivity), and j = -11/2.

How do I put frequency values in for omega, such as in what units, and crank it to get permittivity at a given frequency out? General comments on using complex frequency are welcome, too.

Thanks (and hopefully in my first post I described the problem so it's not gibberish :-).
 
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  • #2
In order to use the equation, you need to first determine the values of epsiloninfinity, delta-epsilon, and tau. Once you have these values, you can then enter a value for omega (in angular frequency units, usually in Hertz) into the equation to calculate the permittivity at that frequency. You can also use this equation to graph the relationship between frequency and permittivity.
 

1. What is complex relative permittivity?

Complex relative permittivity, also known as complex dielectric constant, is a measure of how much a material can store electrical energy when subjected to an electric field. It is a complex number that includes both a real and imaginary component.

2. How is complex relative permittivity calculated?

Complex relative permittivity is calculated by dividing the capacitance of a material by the capacitance of a vacuum. This ratio is then multiplied by the permittivity of a vacuum to account for any differences in the material's ability to store electrical energy compared to a vacuum.

3. What is the significance of the real and imaginary components in complex relative permittivity?

The real component of complex relative permittivity represents the material's ability to store electrical energy, while the imaginary component represents the material's ability to dissipate electrical energy. These components are important in understanding the behavior of materials in the presence of an electric field.

4. How does temperature affect complex relative permittivity?

Temperature can affect complex relative permittivity by changing the molecular structure of a material, which can alter its ability to store and dissipate electrical energy. As temperature increases, the real component of complex relative permittivity typically decreases while the imaginary component increases.

5. What factors can affect the accuracy of complex relative permittivity calculations?

The accuracy of complex relative permittivity calculations can be affected by various factors such as the frequency of the electric field, the physical properties of the material, and the measurement techniques used. It is important to carefully consider these factors when conducting experiments or simulations involving complex relative permittivity.

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