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,   
    I will try to contact you if time permits. You cannot on one hand state that   
   "leakage Flux" whatever you think it means has no role in the power transfer   
   process, and on the other hand state the poynting vector is correct view. I do   
   not know the problem    
   you are having with H flux? IT IS FLUX, formed in the air spaces, due to the   
   MMF from winding current, either primary or secondary. Perhaps what we have is   
   a semantics problem. IF you do not think H flux is real, remove the core from   
   an energized    
   transformer, A SMALL ONE, LIKE A DOOR BELL TRANSFORMER. Yeah the exciting   
   current will go thru the roof, BUT a back EMF will still be produced and the   
   same "FLUX" will form, but NO CORE to form in, only the air. I am not trying   
   to say the core flux is    
   not important, only that the ENERGY does not travel thru the iron core from   
   one winding to another via the B flux in the core. If core flux did transfer   
   the energy it would, by one working definition of REAL power, have to be in   
   phase with the primary    
   voltage, it is lagging 90 degrees... No nonsense at all, the other item   
   probably hard to see is that the Leakage flux DOES NOT have to LINK with the   
   secondary to transfer power. I agree, some of the leakage flux does not   
   participate in power transfer,    
   only to act as a choke. Standard practice for transformer builders used to be   
   to short the secondary and gradually apply voltage to the primary until the   
   rated secondary current is reached. Percent impedance used to be stamped on   
   power and distribution    
   transformers. At you request, because our discussion has run on, and I would   
   like to hear and learn more from you, I will try to e-mail or at least clean   
   up my posts as to make them readable....Thanks...   
      
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