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,   
    Another thought occurred to me as I was pondering this interesting   
   subject,and it related to ones ability to "visualize" the power transfer. We   
   are used to seeing the transformer depicted in textbooks as a square core with   
   primary and secondary winding    
   wound on opposite sides for easy of illustration. No power transformer would   
   be built that way, ironically because the "leakage" flux, that is the H field   
   that is involved in power transfer would weaken or end up stray flux before it   
   ever reached the    
   secondary. Neon sign transformers are sometimes made this way on purpose to   
   have a "drooping voltage" characteristic. As a point of illustration, look at   
   the way old ""constant Current" street lightning transformer are constructed   
   with a "movable"   
   secondary coil. The core is made extra long and the secondary coil when on   
   load would thru "leakage flux" force its way up a distance away from the   
   primary. It had a counterweight and would be adjusted to match the   
   characteristics needed for a given type    
   of lamp. As lamps were added and the current would drop, less H flux would be   
   developed in the secondary and it would fall closer to the primary where it   
   would be closer to the"leakage flux" carrying energy to it. If all power was   
   indeed transferred thru    
   the core, then movement of the secondary away from the primary would have   
   little or no effect on the secondary voltage or current. Also , when the   
   secondary is wound directly over the primary as is usually done,(except for   
   high voltage types) the "   
   Leakage flux" passes between windings, never seeing the iron core. I must   
   admit applying the poynting theorem is messy in the case of the iron core   
   transformer, and using lumped circuit techniques is far less troublesome an   
   renders the correct values as    
   well.....   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)