From: Paul
Date: Wed, 20 Dec 2000 19:46:02 +0000
Subject: Re: [TSSP] Proximity effect and Terman
Bert, Thanks very much for enlightening us on the proximity effect - you were burning the midnight oil there! I'll order the Dowell and Carsten papers, but as usual with the British Library I'll not hold my breath! The 'proxy' article http://kosys.home.mindspring.com/articleproxy/articleproxy.html is very good and I'll return to that shortly. First a question on Terman's analysis. Medhurst in 1947 reported empirical results on loss resistance which differed from the predictions made by Butterworth, finding that at high spacing ratios the loss did not rise quite so dramatically as Butterworth predicted. You mention that Terman's analysis is based on the work of Butterworth, so I wonder whether Terman also over-estimates the loss at high spacing ratios, since Terman predates Medhurst? The proxy article shows a nice simple formula for the loss in a single layer of uniform current, apparently derived from the work in J. P. Vandelac, "A Novel Approach for Minimizing High Frequency Transformer Copper Loss," 0275-9306/87/0000 1987 IEEE Can we take it that this formulation does not suffer the problem mentioned above at high spacing ratio I wonder? The equation given in proxy is remarkably simple and it prompts me to put forward a tentative suggestion as to how we might use it for the non-uniform case, given that we have some additional information available to us about the current distribution and thus also the magnetic field distribution along our single layer. Let me elaborate. For use in the simulator we would like to know the effective AC resistance on a turn by turn basis, since the 'turn' is the basic element size of the finite element LCR network of our model. Lets say that we have already worked out the current profile (by running the simulator using some uniform nominal value of AC resistance). Then, if we focus on an arbitrary turn within the solenoid, we know the current that it will be carrying. We can also calculate the magnetic field strength H in the vicinity of that turn. Now for the crucial bit - suppose we then calculate what *uniform* current the solenoid would need to carry in order to generate the same H at our turn. We could then use the proxy formula to obtain the loss and from our artificial uniform current we obtain an effective Rac for the turn. My reasoning goes: since the loss in the turn appears to depend only on the H in its locality, then if we pretend to generate that H from a uniform current the loss should still be valid and be calculable from the proxy formula. That gives Rac for that turn - repeat for all the other turns. OK, I can see a couple of problems. The proxy formula gives us the total loss for the layer, and we would have to assume that the loss was representable by a uniform resistance per turn all along the winding, which is probably not the case, even when the current is uniform. Also, it could be quite a big job to calculate the off-axis H field of the solenoid, and we'd need to do it twice - once for the actual current, and again for a uniform current. Finally, the whole process might just turn out to be equivalent to calculating the total loss for an arbitrary uniform current, derive a total Rac, and then distribute it weighted according to I(x)^2. I suppose the answer would be to try it and see if it performs better than a Medhurst table lookup. Meanwhile I hope the group will forgive me for dumping a half formed idea onto the list, but these are desperate measures! PS, the proxy formula contains no omega - is the frequency dependence entirely contained in the skin depth terms? Remarkable if so. Cheers, -- Paul Nicholson, Manchester, UK. --
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.