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In Reply to: Re: Hi JC posted by john curl on May 06, 2004 at 15:32:26:
JC: ""Yes the skin effect, itself, would only change by 4 or so.""ok...so far we agree..
JC: ""But that does not imply that a further multiplier could not be made by the steel due to its 'u of 100' by what else is happening internally in the wire.""
The skin effect enhancement within the wire, the factor of 4 we are accepting, already includes that factor of 100 change in mu.
By your statement, you are implying that when skinning occurs, the mu somehow changes, and causes some nefarious, unknown, subtle thing.
The mu used within the skin equation is the initial permeability of the steel. It will change only when the flux density is high enough to begin the saturation process. Internal to the wire, when skinning occurs, the flux density is going down, so it is opposite to what it is you are implying.
And, if it occurs on the surface, then we'd have to be able to measure the inductance and hf, which is a problem in it'self.
However, the point is moot, as I don't think anyone other than cutting edge scientists are interested in that. We are discussing copper, and your hypothetical thinking does not apply to copper..If you wish to further discuss the non linearity possibilities of steel, that'd be cool..But you are attempting to discuss possible errors in Hawksford's test setup as a result of him switching to steel.
JC: "" At this time I don't have any direct reference giving the multiplier for u for the change in internal inductance. Is it direct or square root? ""
I also have no direct reference..and the equations I have seen are shall we say, uncut? As in, pages and pages of integrals.
The closest to useable I've seen is the Terman nomograph, which you have, for copper.
But as skinning occurs, mu will not change internal to the conductor, as the skin equation uses the zero flux permeability.
I'd stick with the skin equation I posted before, and using the skin depth number (inaccurate as the exponential equation is), consider all the inductance below that radius to be simply gone. Yes, it is an approximation, but integrating the bessels here would be murder. That assumes that no current exists below the "shell" radius, but at least that approximation can be solved in our lifetime..
So internal inductance would be proportional to the integral of the full current, from the radius of skin depth, to the surface..And, I'd also recommend treating the current as uniform in that region, to further simplify the math..
Follow Ups:
For those that follow this stuff: When iron wire is used, instead of copper, there appear to be several significant changes.
One, the skin effect becomes significant at a lower frequency.
Two, the internal inductance is increased by some amount by the mu of the material (mu = 100 for iron, mu =1 for copper)
I am looking for an exact equation for 'Two' at the moment.
I am NOT talking about a change in mu with frequency. I am referring to a REDUCTION in internal inductace as the frequency approaches a region with considerable skin effect. This makes for a varying inductance with the square root of frequency. This could explain what Dr. Hawksford measured. I need the EXACT equation for internal inductance with both mu and skin effect included to go further. Mu, itself, can stay essentially the same.
JC: ""I am NOT talking about a change in mu with frequency. I am referring to a REDUCTION in internal inductace as the frequency approaches a region with considerable skin effect.""I know..that is what I have been saying all along..
If you look at the Terman equation, the last component is the mu times delta. That is the internal inductance of the wire. From the simple copper wire example, he has delta as .25, and as the frequency increases, delta drops to zero, essentially zeroing out the internal inductance.
I make the assumption that delta is simply a skin depth derived entity, and that it can be scaled in frequency by that factor of 4, meaning that the frequency in the delta vs frequency nomograph can simply be scaled. Mu, of course, is left alone..so the internal inductance is still mu times delta, but that delta starts at .25, goes to zero at 1/4 the frequency as copper.
JC: "" This makes for a varying inductance with the square root of frequency. This could explain what Dr. Hawksford measured.""
That is what I have been saying all along..
JC: ""I need the EXACT equation for internal inductance with both mu and skin effect included to go further. Mu, itself, can stay essentially the same. ""
I think I explained it well enough..if you find any source that differs from my explanation, I'd love to hear it..
I now have the exact equation for internal inductance. It is in 'Engineering Electromagnetics' William Hayt, eq (20-21). pp 436-437 I will have to analyze it further to predict exactly what it implies.
My 'Terman' doesn't say too much, I have a different edition than yours, but what page or chapter are you finding your results?
I do not have the book.I do have the equation, and the text describing what it is. It is from the '47 handbook. I thought that is the one you picked up?
I' re-aquire it from the research library, if you have more questions, though..(I can't buy all the books I want, unfortunately).
It fits accurately all inductance equation derivations, but he is sadly lacking in the "delta" component of the equation, which is of course, the part we are talking about.
For end of range effects, DC, low frequencies where skinning does not occur, and for very high frequencies, where depth is essentially zero, the equation is just fine, and boils down to 15 nanohenries per inch times mu..at dc, that is the number, and at hf, it is zero. You have to integrate using skin current densities to get the inductance at any one frequency.
But for the internal inductance component that Hawksford saw, it was simply about mu times 15 nH per inch..
Cheers, have a nice weekend.
Sure, you can by all the books you want, (at least most of them) my copy of 'Engineering Electromagnetics' cost less than $10+postage. It came in 2 days. It is in perfect condition. However, I could have bought a $2 copy from the same source: Amazon.com, used books section
Thanks for the tip, John..I'll be sure to try that.The biggest problem I have, though..is space. I'm afraid I don't have enough yet.
Right now, I'm scanning all my old magazines into my computer. Just the articles I wanted to keep, but it allows me to toss the paper, burn a cd to archive.
So far, I've cleared about 4 feet of shelving.
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