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$ \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) ||		 || Material || Absolute<<BR>>Temperature || relative<<BR>>permeability || resistivity ||<-7> skin depth (mm) at frequency (Hz) ||
Line 14: Line 11:

Resistivity - for copper see Matula 1979 page 1161, for aluminum see Simmons 1960

[[ attachment:skindepth.ods | LibreOffice Spreadsheet]] 		|| [[https://www.libreoffice.org | LibreOffice ]]<<BR>>[[ attachment:skindepth.ods | Spreadsheet]] ||<-10|10> {{ https://upload.wikimedia.org/wikipedia/commons/f/f3/Skin_depth_by_Zureks.png }} ||
||$ { \Large { \delta = \sqrt{ 2 \rho \over { \omega ~ \mu_r ~ \mu_0 } } } } $<<BR>> in meters <<BR>><<BR>>$ { \Large { \delta = \sqrt{ 2.533e11 \rho \over { f ~\mu_r } } } } $<<BR>> in mm<<BR>><<BR>><<BR>>$ { \LARGE { { 2 \over { 2 \pi \mu_0 } } } } $ = 253303 m/H ||
|| ~+'''Permeability'''+~<<BR>><<BR>>WAG, need citation<<BR>><<BR>> ||
|| ~+'''Resistivity'''+~ <<BR>><<BR>> for copper see <<BR>>[[https://aip.scitation.org/doi/abs/10.1063/1.555614 | Matula 1979 ]]<<BR>>page 1161<<BR>><<BR>><<BR>>for aluminum see<<BR>> [[ https://journals.aps.org/pr/abstract/10.1103/PhysRev.117.62 | Simmons 1960 ]] ||
||<)>Graph by [[https://commons.wikimedia.org/wiki/User:Zureks | Zureks]]<<BR>>from Wikipedia<<BR>>article [[ https://en.wikipedia.org/wiki/Skin_effect | skin effect ]] ||

Skin Depth

Material

Absolute
Temperature

relative
permeability

resistivity

skin 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

LibreOffice
Spreadsheet

https://upload.wikimedia.org/wikipedia/commons/f/f3/Skin_depth_by_Zureks.png

{ \Large { \delta = \sqrt{ 2 \rho \over { \omega ~ \mu_r ~ \mu_0 } } } }
in meters

{ \Large { \delta = \sqrt{ 2.533e11 \rho \over { f ~\mu_r } } } }
in mm


{ \LARGE { { 2 \over { 2 \pi \mu_0 } } } } = 253303 m/H

Permeability

WAG, need citation

Resistivity

for copper see
Matula 1979
page 1161


for aluminum see
Simmons 1960

Graph by Zureks
from Wikipedia
article skin effect

SkinDepth (last edited 2018-07-18 17:58:39 by KeithLofstrom)