On Saturday, December 11, 1999 3:00:00 AM UTC-5, BillyFish wrote:   
   > Essentially, the following problem was posed on this newsgroup:   
   > ***************   
   > Consider a transformer wound on a large toroidal core using a high    
   > permeability material so that very little magnetic field is outside the   
   core.    
   > That is, there is little leakage reactance.  Put a primary winding along a    
   > small length around the circumference of the core.  Put a similar secondary    
   > winding on the diametrically opposite of the primary.  Connect the primary   
   to    
   > a low impedance ac power source and the secondary to a variable resistance    
   > load.  As the load resistance changes, current in the primary and secondary    
   > changes in such a way as to keep the flux in the core relatively constant.   
   >    
   > Using the Poynting theorem, for example, how does power get transferred from    
   > the primary to the secondary?  The flux in the core is not greatly affected    
   > by the power.  That flux is also longitudinal.  There is no change in the E    
   > field.  The same voltage is across each winding at low and high loads.   
   >    
   > Suppose you set up a plane symmetrically between the two winding cutting the    
   > core into two halves.  If you integrate the Poynting vector over this plane,    
   > I do not see that the E x H to be very different for high and low resistive    
   > loads.  There is no physical current flow across the plane other than    
   > displacement current.   
   > **********   
   > This problem vexed me.  After I got up to go to the bathroom last night, I   
   > could not go back to sleep.  I pondered the problem, and I believe I have the   
   > answer.  It was partially formed in a conversation with someone who had some   
   > glimmerings but not the full insight.  The description above is, not   
   > surprisingly, a *red herring*.   
   >    
   > One key to the problem is to realize that the leakage reactance of a   
   > transformer is *independent *of the core!  The core increases the magnetizing   
   > inductance and coupling coefficient but has NO effect on the leakage   
   reactance.   
   >  This is well known to designers of pulse transformers, for example.  In   
   > equivalent circuit diagrams, current from the primary to the secondary   
   > transfers *through* the leakage reactance.  Most transformer engineers do not   
   > think in terms of Poynting's theorem.   
   >    
   > In a transformer as described above, the main portions of the core, that are   
   > not covered by windings, act as two pole pieces.  A magnetic field component   
   > fringes between them.  It is driven by the bucking currents flowing in the   
   two   
   > windings producing an H field proportional to the ampere turns in each   
   winding.   
   >  This H cannot be reduced by using a high permeability core material.  The   
   core   
   > enables this leakage field to be distributed over a larger volume.  Without   
   > this core, the leakage would be local to the individual windings.  This H   
   field   
   > produced by opposing currents in the primary and secondary  windings.  It   
   > provides an H that can be crossed with an E field to give a power transfer   
   from   
   > primary to secondary.   
   >    
   > Where does the E field to do this come from?  The magnetic field B through   
   the   
   > core is proportional to the voltage across the primary and secondary and 90   
   > degrees out of phase with this voltage.  According to Faraday's law, this   
   flux   
   > produces an E field through the core hole proportional to the rate of change   
   of   
   > flux inside the core.  Thus, this E field is proportional to the voltage in   
   > each winding and 90 degrees out of phase with the flux.  The result is that   
   the   
   > transverse components of the E and H fields, for resistive loads, are in   
   phase   
   > and contribute to a real transfer of power from primary to secondary.   
   >    
   > I do not know if this description for energy transfer has ever been presented   
   > before.   
   >    
   > William Buchman   
      
   Tomtech,   
    Thanks for the reply, I know bantering back and forth can get taxing, and if   
   there is no knowledge or understanding gained, by anyone involved, it just   
   becomes a labor. Even though we cant seem to agree on leakage flux, I feel,   
   from reading just a few    
   posts of yours, that you have a good understanding adn working knowledge of   
   transformers. I was going thru some of the old posts last night, some go back   
   to as far as 1999 I believe. I an not quoting you, but I think it was one of   
   your postings that    
   stated that the Poynting vector and "standard model" of the transformer are in   
   agreement. I apologize if I am misquoting. I do agree with that, it also   
   states that the power (energy) is transferred thru the "series' elements or   
   paths. This is the "   
   leakage" flux. Not to be confused with stray flux. To save time and space and   
   give someone else a chance to chime in, I will go back and hit the books to   
   increase my understanding more. I do not just read, I perform experiments with   
   lab grade gear to    
   verify the math and to get my head fully wrapped around the principles   
   involved. I think the greatest problem in these discussions is the lack of   
   hard definitions. The term "leakage" flux is a misnomer. Nothing leaks from   
   the core, under loaded    
   conditions. If you  think using an iron core with infinite permeability would   
   reduce the "leakage" flux, then we are at an impass, until it is cleared up. I   
   appreciate your time and thank you for the many postings you have made. I may   
   have some terms    
   confused in my mind, and it is preventing me from reaching the conclusions you   
   have. I will be back soon. Thank You   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)