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# Physics/The Skin Effect

Question
QUESTION: Hello Steve. I work in the train control industry where 8 different frequencies ( frequency range is from 1700 to 4049HZ) are modulated at different modulation rates down train tracks to a receiver for the purpose of train detection. My question is two fold. First of all, intuitively, how much does the skin effect  affect the modulated signals as they modulate down the train tracks to the receiver? Secondly, diameter of a conductor( in this case the cross sectional area of the rail) is used to compute skin depth but train rail shape is irregular ( fatter at the top. Skinny in the middle and less fat at the bottom).  How then is the diameter measurement made to compute skin depth?

I appreciate that you asked for my intuitive thoughts. I have not studied the skin effect since college. As I understand it, you do not send the frequencies down the rail as a means of sending energy but for signal detection. Therefore I expect the current would be quite low. Since the current is low, the increase in resistance due to the current being limited to the skin should not cause a significant loss. Perhaps the distances involved are such that the skin effect causes losses that add up to a problem over the length involved. In that case, you might benefit from modification of the receiver such that its input resistance is higher, therefore drawing less current from your broadcast frequency.

You ask about an effective diameter. The only formula I found that needs a figure for diameter is to compute not skin depth, but effective resistance. See the site
http://en.wikipedia.org/wiki/Skin_effect_(electricity)#Formula
Scroll down to the heading "Resistance".

The rail's shape yields a conductor with more surface area than if the rail were a cylinder. Therefore the rail has proportionally more skin to carry your frequency. The resistance would therefore not increase as much as for a conductor with circular cross-section.

I hope this helps,
Steve

---------- FOLLOW-UP ----------

QUESTION: Thank you for your prompt reply. You were correct about the current being low ( 180 - 200ma plus or minus 40ma ). The need for increased resistance on the receive end is minimized because there are impedance matching transformers to match circuit impedance on the transmit side to the rail and the signal from the rail to the receiver on the receive end. So, am i correct to say that the skin effect would come into play at low audio frequencies limiting the signal to the surface.

Hello Ric,

Yes, the skin effect would come into play. The current would concentrate near the surface. I've found that the material affects the depth. If the material is iron, the current concentrates significantly closer to the surface than if the material is copper.

After further thought, I see that I should retract what I said in my previous reply about low current decreasing the affect. 63% of the current will be within the skin depth of the surface regardless of the value of the total current.

I used the skin depth calculator at the site
http://www.rfcafe.com/references/calculators/skin-depth-calculator.htm
I input a frequency of 1.7 kHz and data for iron and found that the skin depth was 0.0173 cm.

I hope this helps,
Steve

Physics

Volunteer

#### Steve Johnson

##### Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

##### Experience

I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

Education/Credentials
BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University