From: dhky@shaw.ca   
      
   On 19/09/2014 4:29 AM, tctomcosby@hotmail.com wrote:   
      
      
      
   >   
   > Tomtech,   
   >   Thanks for all that replied with additional info.There is still confusion   
   when speaking of "flux Density" and "Field Intensity" when referring to   
   transformer fluxes. Yes, when not on load, there is some slight leakage flux,   
   for example in spaces    
   between the winding and the core. The H MMF still produces some, small amount   
   of flux in that space, even thought the core flux (flux density, not flux   
   intensity) is MUCH larger. When the secondary is under load,(resistive), the   
   MMF produced by the    
   secondary is almost exactly balanced by the additionl (load component) of MMF   
   from the primary. These two fluxes produce NO additional flux in the iron core   
   as they balance each other. The tow are not EXACTLY in phase with each other,   
   and that is the key    
   to understanding some of the aspects of power transfer in the Transformer.   
   Under load conditions, the Leakage flux is conducted in the iron up to the   
   secondary winding, depending on winding geometry, so is not all in the air,   
   but the air path   
   does contribute to the lions share of the reluctance. Remember, on load the   
   "Leakage" flux does not have the same "Flux Density" as the core, but many   
   times the "Flux Intensity" and MUCH more energy than the B flux in the core.   
   Take a look at textbook "   
   Magnetic Circuits and Transformers, A first course for Communications   
   Engineers, still in print from staff at MIT. It is well worth the effort to   
   digest it. Yeah, on my reference to signal transit times thru audio inter   
   stage transformer, I neglected    
   some other but important transfer mechanisms, namely capacitive coupling as   
   well as the bothersome inter winding resonances, etc. It is a rater involved   
   subject, that appears simple at first blush. For sure the alternating core   
   flux does indeed created    
   the induced EMF in the secondary, you can have a air core too, at 60 HZb but   
   the large magnetizing current would render the transformer so inefficient as   
   to be useless, as the low permeability of air would require many, many primary   
   turns...   
   ...   
   >   
      
   I read what you wrote and I am sorry that, for some reason when I try to   
   reply, your message is quoted as a single long line. I don't know why.   
   Hence, I won't quote it.   
      
   However, there is much that you say that is correct and there is much   
   that I question. Your apparent need for a phase shift for power transfer   
   is not true. In an ideal transformer , where leakage reactance and   
   winding resistance as well as having an ideal core- the conditions for   
   power transfer exist. Now bringing in the non-ideal factors we find that   
   I1 =(N2/N1)*I2  +Imag,  where the reactive component of Imag is simply   
   providing the necessary H.dl around the core.  The leakage and   
   resistance as well as core loss result in a T model with all values   
   referred to the primary (or secondary). This is simply using circuit   
   models bases on operation where linearity can be assumed. This model,   
   for higher frequencies, where needed, can be  adapted to deal with   
   interwinding capacitances.   
   I have looked at your 1943 (MIT)reference and have no problem with it   
   -but it is pretty general in that it covers a lot of things and in doing   
   so does obscure some key factors. Admittedly some of the approach and   
   units used were still around 10 years later- Ten years later, much of   
   what this MIT text was still quite dominant in approach, including the   
   oddball variety of units that were used. In the 60's 70's and beyond you   
   will find a different approach. I have 4 Electromagnetic Engineering   
   Conversion texts (one from MIT-White and Woodson)) and 3 of them don't   
   even bother with the transformer per se (it is essentially a coupled   
   winding circuit device in nearly all applications where non-linearity of   
   the B-H curve is accounted for where needed). No big deal-just some   
   added mess in the model.   
   The 4th presents introductory chapters involving fields, then   
   ferromagnetic "circuits" and then transformers- using these as a basis   
   for further concepts. (this is V Gourishankar & D.H. Kelly   
   "Electromagnetic Energy Conversion" (1973 -royalties didn't amount to   
   what a good(sic) porn novel would have produced) -so I have both a bias   
   and a knowledge of its many limitations  (among which is that much has   
   developed in practice since then, and much that I have learned since then).   
      
   Don Kelly   
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