Talk:Skin effect

Lower bound for skin depth in silicon

There is a statement about the skin depth in silicon not being less than about 11m. This statement does not have a reliable source and I believe that it is incorrect, so I will remove it. There does not need to be any justification other than there is no reliable source cited, but I will give a more elaborate justification. The formula, as given, is correct if you can neglect dielectric loss. Any type of loss will decrease skin depth. Using these equations from wavenumber:

$\delta ={\frac {1}{k''}}$

$k=k'-jk''={\sqrt {-j\omega \mu (\sigma +j\omega \epsilon )}}={\sqrt {-(\omega \mu ''+j\omega \mu ')(\sigma +\omega \epsilon ''+j\omega \epsilon ')}}\;$ ,

In the equation for wavenumber, you see $\sigma +\omega \epsilon ''$. The dielectric loss term ands to the conductivity term. This effectively reduces resistivity as frequency increases. It is straight forward, but tedious, to carry out all the multiplications, gather terms, and apply the formula for the square root of a complex numbers. The result shows that if there is any dielectric (or magnetic) loss, then there is no non-zero lower bound. If someone would like to check the math, I would be grateful.

I plugged numbers in, assuming a dielectric loss tangent of 0.3% at 10GHz I got 0.9m at 10GHz. The conclusion that skin depth in silicon is deep enough to ignore is still correct. Of course, I could have made a mistake. If anyone would like to run the numbers, I used ${\epsilon ''}/{\epsilon '}=0.003,\epsilon _{r}=12,\sigma =435\mu \;\mathrm {S/m}$ Constant314 (talk) 23:52, 21 February 2021 (UTC)

I assume that is $\epsilon _{r}'=12$. I got $k''\approx 175$ nepers/meter, i.e. a skin depth of around 6mm. I agree that with dielectric loss, $k''$ increases to infinity. Without it, I got ${\frac {\sigma {\sqrt {\epsilon }}}{2\epsilon }}$ as the asymptotic value of $k''$ (in this case, around 21 nepers/meter, or a skin depth of around 5cm). Unsure why our answers differ. XabqEfdg (talk) 06:16, 9 June 2024 (UTC)

Rather than clutter up other people's watch list, lets continue the discussion at User:Constant314/Derivation of skin depth. Constant314 (talk) 17:56, 9 June 2024 (UTC)

Current density graph

Hi, first contribution here I think the graph labeled as "Current_Density_in_Round_Wire_for_Variuos_Skin_Depths" is wrong, or maybe I don't understand the scale. If the number labeled on each curve is skin_depth/wire_radius, let's consider a 1.0 ratio (which is not showed here), then, at the center of the wire, current density shhould be 1/e (~0.37) of Js (current density at surface). And so, at <1 ratio, value at should then be <1/e. However, curves seem to show a value way higher (~0.95 just for 0.9 ratio curve), considering a linear Y scale. WaldenoffFR (talk) 21:14, 11 March 2023 (UTC)

I drew the graph. It is correct; it is simply the evaluation of the equation given in that section. The relation that you are thinking about only holds when skin depth is small with respect to the radius of the wire. Constant314 (talk) 22:34, 11 March 2023 (UTC)

Derivation of skin depth

The new material seems to be only a derivation of the wave equation. You need several more steps to derive skin depth. But it is not necessary, since the equation δ = 1/k" appears in many reliable sources. The derivation should probably be removed under WP:NOTTEXTBOOK. Constant314 (talk) 17:51, 9 June 2024 (UTC)

Agreed, the detail is not necessary. I think there should be a section on electromagnetic waves though, or the mention in the lead should be removed. XabqEfdg (talk) 20:34, 9 June 2024 (UTC)

Effect on single round wire self-inductance

In the Article there is no global Formula concerning the influence of the skin effect on a single round wire self-inductance...

The basic formula I use is : L = Lo x square root of ( 1 + square root of (delta / wire diameter) )...with (delta/diameter) inferior or equal to 1/e ...

Lo is the wire self-inductance when delta = 0 , and delta is the skin depth penetration ... Leveugel (talk) 11:24, 16 June 2026 (UTC)

$\delta ={\sqrt {\frac {2\rho }{\omega \mu }}}$

That would be the skin depth of a flat slab. It is a convenient quantity that depends only on the material properties and not on the radius of the wire. Constant314 (talk) 12:30, 16 June 2026 (UTC)

The formula is $L_{int}={\frac {{Im}(Z_{int})}{\omega }}$

L = Lo x square root of ( 1 + square root of (delta / wire diameter) ) is an empirical formula. Constant314 (talk) 18:22, 16 June 2026 (UTC)

The paragraph about the round wire inductance have to be revisited, I think...

When the frequency increase, the inductance L reduction is the result of the capacitance C raise caused by the electric charges migration to

the wire surface...

As L and C are linked by the velocity factor, equal to 1 for a straight wire , if C increase, L decrease and vice-versa... Leveugel (talk) 13:53, 25 June 2026 (UTC)

The ratio between Lmax and Lo seems to be 4/pi... 4/pi is the ratio cylinder/cone self capacitance...Leveugel (talk) 09:31, 20 July 2026 (UTC)

Skin effect cause

The picture in the Article do not fit with the text...

The skin effect is not due to the eddy currents..

It is due to the back EMF in the conductor center like specified in the Article...

Eddy currents like skin effect are both consequences of the back EMF...Leveugel (talk) 09:03, 6 July 2026 (UTC)