From: Bert Hickman
Date: Sat, 23 Dec 2000 10:37:29 -0600
Subject: Re: [TSSP] Proximity effect and Terman
Paul, My responses are interspersed below... -- Bert -- Paul wrote: > > 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? Undoubtedly, since Terman published his Radio Engineers Handbook four years prior to Medhurst's report. Terman's tables appear to be a summary of Butterworth's work... > > 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? It's not clear without seeing a copy of the article. However, I would "guess" that only the closewound case was evaluated (at least for any given layer) since the application studied was HF power transformers for switching power supplies and inverters - these tend to be closewound applications to maximize winding density & efficiency. > > 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. Your assumptions certainly sound reasonable, at least for the bulk of internal turns where the fields are mostly tangential. Turns on the ends would see a different field pattern, but your proposed approach may be "close enough". > > 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. Agree, but it may still be close enough. I wonder if coil "end effects" were ignored by Vandelac since he was dealing with windings on high permeability cores(?). Hard to see how they could be ignored for outer layers though... > 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. Suspect this would indeed work if coil end effects were known to have a minimal impact on Rac versus inner turns... > > 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! > No problem! Interesting speculations! > 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. > -- Apparently, because they have the same root cause - internal shifts in preferred conduction regions induced by the total magnetic field environment around and inside the conductor, with skin effect stemming from self-produced fields, and proximity effect from the fields of neighboring conductors. And both effects should have similar frequency dependency - the author apparently chose to normalize the equations using skin depth. What I find fascinating is that setting wire diameter to the skin depth (for highest frequency component) eliminates frequency as a variable! I've seen this principle (along with inductance cancellation techniques) used to make very thin, tubular foil elements for precision current viewing resistors to insure similar impedance for DC and the HF components of fast transients. Interesting stuff! -- Bert Hickman Stoneridge Engineering Email: bert.hickman@aquila.net Web Site: http://www.teslamania.com
Maintainer Paul Nicholson, paul@abelian.demon.co.uk.