From: dhky@shaw.ca   
      
   On 23/09/2014 5:02 AM, tctomcosby@hotmail.com wrote:   
   ---------snip of past history----------------   
   >   
   > Tomtech, Thanks for the reply. I am not sure what you mean when you   
   > speak of H flux not existing or making a reference to it as one would   
   > call voltage a "current". Over the years electromagnetism has, I   
   > think, been confusing for many due to the many technical terms used,   
   > and most of them have been replaced by more modern terms. H flux is   
   > very "real" as real as the B flux density established in the iron   
   > core.   
      
   I agree that H is real but it isn't flux or flux density. I can use an   
   analogy for a magnetic circuit some length L and note that the MMF is   
   due to the sum of currents linking or surrounding this core. In that   
   case MMF=NIenclosed = integral around the closed path of H.dL where L is   
   the core length- analogous to saying that the voltage V applied to a   
   resistive closed circuit can be considered as being  V=integral of E.dl   
   L around the closed path.   
   Note that there is a direct analogy between this and the situation of a   
   voltage applied to a resistive loop. Hence the term reluctance. In the   
   magnetic case, it isn't as useful as in the electrical case because of   
   non-linearity- hence we need to use B-H curves for magnetic circuits.   
   but the MMF =NI enclosed is analogous to the applied voltage and the   
   flow or flux is B*area just as I or charge flow or flux is current   
   density * area.   
      
   > It is brought into existence by the MMF of current flowing in   
   > the (in this case) primary winding. under no load conditions the MMF   
   > produces, as we all know a flux to form in the iron core, know as B   
   > flux, or "working flux". The "EMF" I referenced is basic Maxwells,   
   > EMF around the time varying flux in the core.   
      
   You are correct, text   
   > books do no actually "ignore" the temporary drop in back EMF caused   
   > by the secondary current, but I think it is at time kinda glossed   
   > over. the Core flux MUST drop or the primary has no reason to change.   
   > It happens quickly, depending on circuit conditions of course.   
      
   Yes-most references deal with steady state operation -not the transient   
   situation when loads change. That transient situation exists and the   
   conventional circuit model of a transformer can be used to determine how   
   things vary in this transition from one steady state to another   
   (capacitances can be included).   
      
   >I agree some of the "leakage" flux is of no real value, and as the   
   > model shows acts exactly like a series choke. My reference to the   
   > solenoid being bent around to form a toroid is seen in many text book   
   > references in the field of electromagnetism. The only reason I   
   > mentioned it is the fact that when the core is closed no inducing EMF   
   > appears outside of the now "window" region.   
      
   Why? Since about 3/4 of the windings are outside the core window and   
   there is a voltage gradient along the winding- that implies that about   
   3/4 of the voltage across the primary (as also for the secondary) is   
   going to be external to the window. If you wind a 1 layer coil around a   
   solenoid then bend it into a circle and energize it -you will have an   
   emf between the adjacent terminals and the same emf distributed along   
   the coil- appearing as turn to turn voltages inside and outside.   
      
     This is somewhat off the   
   > subject of power transfer, but I mention it because many texts   
   > continue to state that the EMF is found ALL AROUND THE CORE, like it   
   > is in a straight solenoid.   
      
   So??   
      
   I FULLY AGREE with you regarding the use   
   > of the poynting Theorem for use in the case of the iron core   
   > transformer! It is surely a pain to work through it and, as you   
   > stated gives the same (correct) values that ordinary circuit theory   
   > would. Take for instance a secondary coil wound directly over a   
   > primary coil on  closed iron core. The MMF from the primary causes a   
   > flux to form in the iron core, which causes an EMF to be induced in   
   > the coils wound around the core (Maxwell . Under load the current   
   > flowing in the secondary also tries to "Buck" the flux already   
   > established in the core, du to the temporary drop in back EMF,   
   > NOW   
   > the secondary and primary MMF almost completely balance,(in the core)   
   > except for the magnetizing flux, and the "Leakage H flux field" is   
   > born, in the air and partially in a portion of the core, depending on   
   > geometry.   
   It would be there even if the core had infinite   
   > permeability. In this case, with the windings on top of each other,   
   > we find the "leakage H flux" normal to the induced EMF (from the   
   > changing core flux)at the location of the secondary, transporting   
   > power to the secondary, this "Leakage" flux did not have to penetrate   
   > the core proper first to end up as energy transferred to the   
   > secondary. As I understand it, this happens all the way around the   
   > winding, more concentrated inside the window region. It is the reason   
   > why some audio output transformer employ bi-filar windings, the   
   > primary and secondary are right next to each other, sometimes even as   
   > a twisted pair, for exceptional coupling coefficient.   
      
   Certainly this does improve coupling- and if such bi-filar windings were   
   perfectly coupled- then the core could be eliminated- as its' purpose is   
   only to ensure that there is good coupling.   
      
   If, on the   
   > other hand, the primary and secondary windings are quite a distance   
   > from each other, under load the primary and secondary "leakage"   
   > fluxes do not intermingle and do indeed act as chokes.  Some of the   
   > primary "leakage" H flux does find its way to the secondary, but not   
   > nearly as much as if the tow were wound close to each other.Remember,   
   > under loaded conditions there is more energy in the "leakage flux"   
   > (field intensity), than there is in the core flux.   
   >Of course the core   
   > flux density is always greater, but that is not the same as stored   
   > energy.   
      
   This is nonsense.   
      
   1)Let's get it straight. ALL primary leakage flux does not couple the   
   secondary and ALL secondary leakage flux doesn't couple the primary.   
   That is why it is called leakage rather than mutual flux.   
   2) Also as said before H is not flux.   
      
   3)Note that in an inductance (i.e in  this case leakage flux per ampere)   
   under steady state AC conditions has energy stored in part of the cycle   
   and energy returned to the supply in the other part of the cycle-   
   average =0 .  Further note that the (I^2)X (where X is leakage   
   reactance) is a measure of what is shuffled back and forth. Since the   
   total X of a transformer under normal operation is about 5% of the   
   rating of the transformer -this shuffled energy is about 5% of the   
   energy transferred through the mutual flux. It is not lost energy. The   
   main effect of this reactive volt-amps is that there is an associated   
      
   [continued in next message]   
      
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