- #1
paul_harris77
- 52
- 0
Dear all
I am slightly confused over the equations for skin depth. My university notes give me the equations:
[tex]\delta = [/tex] tan-1 (tan[tex]\delta[/tex]) = [tex]\frac{\sigma}{\omega \epsilon}[/tex] (loss tangent)
where [tex]\delta[/tex] is skin depth and [tex]\sigma[/tex] is conductivity.
I am also given the equation:
[tex]\delta = [/tex] [tex]\frac{1}{\sqrt{\pi f \mu \sigma}}[/tex]
However, for the situation below, they both yield different skin depths.
f = 1MHz
w = [tex]2\pi f[/tex]
[tex]\sigma = 5.8 \times 10^{7}[/tex] Sm-1
Using the first equation:
[tex]\delta = [/tex] tan-1( [tex]\frac{5.8\times 10^{7}}{2\pi \times 1 \times 10^{6} \times 8.85 \times 10^{-12}} = 1.57m[/tex])
Using the second equation:
[tex]\delta = [/tex] [tex]\frac{1}{\sqrt{\pi \times 1 \times 10^{6} \times 4\pi \times 10^{-7} \times 5.8 \times 10^{7}}} = 66.09\mu m[/tex]
It seems like the first equation gives 1.57 for all large values of the loss tangent, whereas the second equation gives the correct result.
Is the first equation valid for a certain range of loss tangents only?
Any help would be greatly appreciated.
Many thanks
Regards
Paul
I am slightly confused over the equations for skin depth. My university notes give me the equations:
[tex]\delta = [/tex] tan-1 (tan[tex]\delta[/tex]) = [tex]\frac{\sigma}{\omega \epsilon}[/tex] (loss tangent)
where [tex]\delta[/tex] is skin depth and [tex]\sigma[/tex] is conductivity.
I am also given the equation:
[tex]\delta = [/tex] [tex]\frac{1}{\sqrt{\pi f \mu \sigma}}[/tex]
However, for the situation below, they both yield different skin depths.
f = 1MHz
w = [tex]2\pi f[/tex]
[tex]\sigma = 5.8 \times 10^{7}[/tex] Sm-1
Using the first equation:
[tex]\delta = [/tex] tan-1( [tex]\frac{5.8\times 10^{7}}{2\pi \times 1 \times 10^{6} \times 8.85 \times 10^{-12}} = 1.57m[/tex])
Using the second equation:
[tex]\delta = [/tex] [tex]\frac{1}{\sqrt{\pi \times 1 \times 10^{6} \times 4\pi \times 10^{-7} \times 5.8 \times 10^{7}}} = 66.09\mu m[/tex]
It seems like the first equation gives 1.57 for all large values of the loss tangent, whereas the second equation gives the correct result.
Is the first equation valid for a certain range of loss tangents only?
Any help would be greatly appreciated.
Many thanks
Regards
Paul