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| || Material || Temp || perm. || res. ||<-6> depth (m) at frequency || || || K || μ,,r,, || Ω-m || 60 Hz || 400 Hz || 1 KHz || 5 KHz || 20 KHz || 200 KHz || || 3% Si Transformer Steel || 300 || 700 || || || || || || || || || 3% Si Transformer Steel || 700 || 700? || || || || || || || || || Aluminum || 300 || 1 || || || || || || || || || Aluminum || 700 || 1 || || || || || || || || || Copper || 300 || 1 || || || || || || || || || Copper || 700 || 1 || || || || || || || || |
$ \delta = \sqrt{ 2 \rho / \omega \mu_r \mu_0 } $ in m $ ~=~ \sqrt{ 2.533e11 \rho / f \mu_r } ~~$ in mm $ ~~~~~~ 2 / 2 \pi \mu_0 $ = 253303 m/H || Material || Temp || perm. || resis. ||<-7> depth (mm) at frequency (Hz) || || || K || $\mu_r$||$\rho~~\Omega$-m || 1 Hz || 60 Hz || 400 Hz || 1 KHz || 5 KHz || 20 KHz || 200 KHz || || 3% Si Transformer Steel || 300 || 700 || 5e-7 || 13 || 1.7 || 0.67 || 0.43 || 0.19 || 0.95 || 0.030 || || 3% Si Transformer Steel || 600 || 300? || 7e-7? || 24 || 3.1 || 1.2 || 0.77 || 0.34 || 0.17 || 0.054 || || Copper || 300 || 1 || 1.7e-8 || 66 || 8.5 || 3.3 || 2.1 || 0.93 || 0.46 || 0.15 || || Copper || 600 || 1 || 3.8e-8 || 98 || 13 || 4.9 || 3.1 || 1.4 || 0.69 || 0.22 || || Aluminum || 300 || 1 || 2.8e-8 || 84 || 11 || 4.2 || 2.7 || 1.2 || 0.60 || 0.19 || || Aluminum || 600 || 1 || 5.9e-8 || 122 || 16 || 6.1 || 3.9 || 1.7 || 0.86 || 0.27 || || '''Resistivity'''<<BR>><<BR>> for copper see <<BR>> Matula 1979 page 1161<<BR>>for aluminum see Simmons 1960 ||<-10> {{ https://upload.wikimedia.org/wikipedia/commons/f/f3/Skin_depth_by_Zureks.png }} || || Graph by [[https://commons.wikimedia.org/wiki/User:Zureks | Zureks]]<<BR>>from Wikipedia<<BR>>article [[ https://en.wikipedia.org/wiki/Skin_effect | skin effect ]] || || [[ attachment:skindepth.ods | LibreOffice Spreadsheet]] || |
Skin Depth
\delta = \sqrt{ 2 \rho / \omega \mu_r \mu_0 } in m ~=~ \sqrt{ 2.533e11 \rho / f \mu_r } ~~ in mm ~~~~~~ 2 / 2 \pi \mu_0 = 253303 m/H
Material |
Temp |
perm. |
resis. |
depth (mm) at frequency (Hz) |
||||||
|
K |
\mu_r |
\rho~~\Omega-m |
1 Hz |
60 Hz |
400 Hz |
1 KHz |
5 KHz |
20 KHz |
200 KHz |
3% Si Transformer Steel |
300 |
700 |
5e-7 |
13 |
1.7 |
0.67 |
0.43 |
0.19 |
0.95 |
0.030 |
3% Si Transformer Steel |
600 |
300? |
7e-7? |
24 |
3.1 |
1.2 |
0.77 |
0.34 |
0.17 |
0.054 |
Copper |
300 |
1 |
1.7e-8 |
66 |
8.5 |
3.3 |
2.1 |
0.93 |
0.46 |
0.15 |
Copper |
600 |
1 |
3.8e-8 |
98 |
13 |
4.9 |
3.1 |
1.4 |
0.69 |
0.22 |
Aluminum |
300 |
1 |
2.8e-8 |
84 |
11 |
4.2 |
2.7 |
1.2 |
0.60 |
0.19 |
Aluminum |
600 |
1 |
5.9e-8 |
122 |
16 |
6.1 |
3.9 |
1.7 |
0.86 |
0.27 |
Resistivity |
|
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Graph by Zureks |
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