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# Help me calculate the increase in resistance of a conductor caused by the skin effect

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#### anisnn

##### Newbie level 6
Hi all,

Can someone help me calculate the increase in resistance of a conductor due to the skin effect?

The skin depth of a conductor is given as d=sqrt(1/pi*f*u*sigma)
where sigma=conductivity, u=permeability, f = frequency

Once we have obtained the skin depth, how can we calculate the resistivity of the conductor at a particular frequency if the conductor radius < skin depth?

Thanks,
Anis

Re: Skin Effect

Resistivity of a metal is a constant. so you can calculate Resistance offered by the metal conductor as P*l/A where P = resistivity, l=length of the line and A = Area of cross section of the transmission line.The cross sectional dimensions have to have atleast 3 skin depths, o'wise the resistance of the line will become significant.

Skin Effect

How we calculate the resistance of the line if the cross-section dimensions are less than 3 skin depths?

Re: Skin Effect

For surface impedance of a line of thickness t, see eq. 5 in my paper:

J. C. Rautio and V. Demir, "Microstrip Conductor Loss Models for Electromagnetic Analysis," IEEE Tran. Microwave Theory Tech., Vol. 51, No. 3, pp. 915–921, Mar. 2003.

This equation is for current flowing on only one side of the conductor. This is pretty close for microstrip because current typically flows mostly on the bottom side. If you have stripline, where current flows equally on both sides, you have to cut Rrf in half.

If you do not have access to IEEE Xplore, email me at rautio((at))sonnetsoftware.com and I will email you a copy. I am not posting the paper here because it is copyrighted. The IEEE copyright agreement, however, does allow me to personally send copies of the paper to anyone I like.

### anisnn

Points: 2
Skin Effect

Re: Skin Effect

I can not upload the paper because it is copyrighted. There are some people who ignore copyright. I obey copyright. I can email the paper to you if you want. Send me an email at rautio((at))sonnetsoftware.com and I will email a copy to you by reply email. This is permitted by the IEEE copyright.

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