From: dhky@shaw.ca   
      
   On 22/09/2014 4:22 AM, tctomcosby@hotmail.com wrote:   
   > 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 all you responding and helping me to increase my   
   > incomplete understanding of electromagnetic energy transfer in the   
   > iron core transformer. I don't know why my text replies are not   
   > grouped properly.   
      
   I found the problem- I have set my response to re-wrap and this seems to   
   work. it certainly makes it easier for me   
      
     One topic that needs to be further defined and may   
   > cause all of us confusion is the somewhat "loose" descriptions of the   
   > fluxes involved. "Stray" flux, as I understand it is in NO way   
   > involved in the energy transfer process.   
      
   Right- but the term "stray flux" is not generally used- as the stray   
   flux is what is called "leakage flux. One can look at the flux linking   
   both windings - the mutual flux. The flux linking winding 1 is the sum   
   of the mutual and the leakage which doesn't link winding 2 For winding 2   
   the same sort of situation exists   
   In terms of inductances we have L11, L22, L12 and L21. The latter two   
   are generally the same and are often indicated as M for mutual.   
   L11=L1 +M and L22=L2 +M where L1 and L2 are the "leakage inductances for   
   primary and secondary. Your reference also expresses this in terms of   
   the greek phi to represent flux.   
   Some of the leakage flux does not enter the core-simply because no   
   winding is exactly centered on the core boundary and there is a gap   
   (sometimes large). However, the much leakage will be partly in the   
   core-simply because a flux path of length A in air presents nearly twice   
   the reluctance of a path of the same length but only half in the air.   
      
   >It is a component of the   
   > leakage flux that completely strays from the core and escapes the   
   > transformer. It is important in some situations, such as when pole   
   > distribution transformers are driven into core saturation, a large   
   > component of "stray" flux leaves the transformer core and ends up   
   > inducing and EMF and current flow in the metal tank enclosing the   
   > transformer. It can cause heating large enough to blister the paint   
   > off. Look up at distribution transformers sometime, and note how many   
   > have really rusted looking tanks.   
      
   True enough- However this may be due to the improper use of the   
   transformer- say by pushing a bit too much beyond rated voltage-   
   resulting in saturation and high exciting currents- It may , through the   
   leakage reactance changes cause higher voltage drops due to an increase   
   of the impedance of the transformer windings (after all it is  leakage   
   reactance that is the dominant part of the  impedance of the transformer.   
   Hwever, there are technical reasons for the design of a transformer but   
   there are also economic reasons in that the best technical result is   
   minimization of the average losses -and that involved the balance   
      
   [continued in next message]   
      
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