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,   
    Again I am moved to post hopefully helpful thoughts regarding this whole mess   
   of power transfer in the iron core transformer. Most of the older textbooks   
   that I and others have referred to do not emphatically state that power is   
   transferred via the iron    
   core from primary to secondary winding. It is inferred that the core   
   "conducts" energy to the secondary by using terms like "working flux" or "Main   
   flux". I think one thing that would put us all on the same page is having a   
   hard fast definition of the    
   various fluxes involved. The term "Leakage flux" is a misnomer from days when   
   it was thought that the flux actually "Leaked" from the iron core. I think it   
   should be known that leakage flux and stray flux are not necessarily the same.   
   I think it can be    
   said that all stray flux is leakage flux, but not all leakage flux is stray   
   flux. I think many find leakage flux to mean some aspect negative aspect of   
   transformer design. If indeed, the core conducts all energy to the secondary   
   winding, would it not    
   change amplitude when on load? Not a good argument, I realize a section of   
   wire can conduct many values of electric power at the same current value,if   
   the load impedance and sending voltage changes properly. Anyway, just thought   
   I would chime in, I will    
   try to keep my future postings to the point with text references, not just an   
   opinion................   
      
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