From: dhky@shaw.ca   
      
   On 19/09/2014 12:33 PM, tctomcosby@hotmail.com wrote:   
      
   >> 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.   
      
   Oh it has some effect as part of the leakage flux path is within the   
   core. Admittedly most of the related H.dl in the leakage path is   
   external to the core. For an open secondary the total NI of the primary   
   produces the sum of H.dl in the core equal to that sum in the eakage   
   path s(any path enclosing the primary winding only)   
      
   >>   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.   
      
   I disagree- suppose you have a primary and secondary separated by a   
   large distance so that the mutual flux is negligable (coupling   
   approaching 0). Then there will be leakage but negligable transfer   
   between the windings. Yes, one could use Poynting's theorem but in   
   trying to apply it to an iron core transformer is a messy and   
   complicated way to tackle a simple problem.   
   The problem is that Poyntings theorem is simply a way to express   
   conservation of energy which can be expressed equally well, for a   
   transformer by simply considering power in to the primary= losses and   
   power out from the secondary. and this can be handled adequately by the   
   conventional circuit approach.   
   >>   
   >> 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 is unclear. we have a core with two windings  and we can look at   
   the core as a loop for which we find that we have then total ampere   
   turns causing the total H.dl around the core loop is due to the sum of   
   the NI in the two windings. This sum is the magnetizing current.   
      
   >>   This H cannot be reduced by using a high permeability core material.   
      
   However, since there is a direct relationship between the voltage and   
   the peak flux (following from Faraday, it follows that for voltage, core   
   cross section, turns   and frequency fixed, the Bmax is fixed and if B   
   is fixed, H is fixed -so higher permeability does mean a lower H =B/mu   
   Otherwise there would be no reason to use a high permeability core as   
   the purpose is to provide a good magnetic path with low leakage and low   
   magnetizing current.   
      
      
   >> 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.   
      
   Leakage is always local to the windings. The important part of the flux   
   is that common to both windings---The MUTUAL flux.   
      
   >>   
   >> 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.   
      
   There may be an E field in the core hole but I think that you would find   
   that the E field of concern is distributed along the turns of the   
   windings- and yes, there will be an E field between windings of   
   different voltages- that is why insulation is needed.   
      
      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.   
      
   I doubt it but the modelling of the E fields is messier than that for   
   the B fields (in that the major part of these are in the core- not in   
   the leakage.) However the integral of E cross H will reduce to VI   
   >>   
   >> 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.   
   >...... 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.   
      
      
      
   By definition the "stray flux" that you mention IS the leakage flux. You   
   have been using the term "leakage flux" rather than "mutual flux"   
   Your reference to the old MIT text makes this clear in Chapter XII ,   
   equations 21 on where it clearly agrees with modern texts as to leakage   
   flux being that flux not linking both windings (and not taking part in   
   energy transfer. It is also a B*area term, not H per se (B is   
   fundamental (unit is the Tesla)  and H=B/mu (amp turns/m) is convenient.   
      
     The Wiki article on  transformers is not bad. and with fewer words and   
   details, agrees with your reference.   
      
   --   
   Don Kelly   
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