How does back EMF contribute to the operation of an autotransformer?

[kiki_danc]

I read the following fantastic explanation of the isolation transformer operation where the current appears in another windings without direct wire connection but via back emf feedback and magnetic flux dynamics.

https://www.physicsforums.com/threads/simple-transformer-power-draw-explanation-please.203093/

The physical mechanism for this "feedback" of loading from the secondary to the primary is via the "back EMF" that is generated by the secondary current flowing in the secondary coil. Transformer action is basically like this (although it occurs more simulatneously than the following words will make it seem like)...

The primary voltage source (the AC Mains in your example) impresses an AC voltage across the primary coil. If the secondary coil is not connected to any load, then the AC current flowing in the primary is the result of the AC voltage across the inductance (and parasitic resistance) of the primary coil alone. The AC voltage is generating an AC primary current, which generates an AC magnetic field in the magnetic material that the primary coil is wrapped around (the core). The higher the inductance of the primary, the lower the primary current, given a constant AC source voltage.

But when a load is connected to the secondary coil, things change. The AC magnetic flux in the core induces an AC voltage in the secondary coil, which causes a secondary AC current to flow through the secondary load. But that secondary current flowing in the secondary coil generates a magnetic back-flux that opposes the forward flux coming from the primary coil. This generates a "back EMF" or reverse voltage at the primary coil, which is what causes a larger current to flow from the AC source to still support the full AC source voltage. It is this reverse magnetic flux from the secondary to the primary coil that provides the "feedback" mechanism that varies with how heavy the load is. The heavier the load, the more secondary current, so the more back magnetic flux in the core cancelling the forward flux from the primary coil, so the more current required to flow in the primary coil in order to stabilize everything with the primary and secondary voltages and currents obeying the simple transformer equations.

Hope that helps. Things get more complicated when you include real parasitics of transformers (losses, leakage inductance, series resistance, etc.), but the above is the basics of transformer action. Check out this wikipedia.org page for more details and some drawings:

This is also more or less the explanation by others too when they described the isolation transformer where the primary and secondary windings are not connected.

However, when describing the Autotransformer where there is just one winding as follows:

Most references (I googled these for hours) no longer described it in terms of back EMF and magnetic flux but analogy of direct current flow like in DC. I know though that https://en.wikipedia.org/wiki/Autotransformer: "Since the volts-per-turn is the same in both windings, each develops a voltage in proportion to its number of turns. In an autotransformer part of the current flows directly from the input to the output, and only part is transferred inductively, allowing a smaller, lighter, cheaper core to be used as well as requiring only a single winding"

I'd like to understand how big is the contribution by direct current flow from input to output and how much is the contribution by back EMF in an autotransformer. Here does this description by Berkeman also applies? where (I change some words) "... but when a load is connected to the autotransformer output, things change. The AC magnetic flux in the core induces an AC voltage in the autotransformer output taps, which causes an AC current to flow through the output load. But that output current flowing in the tapped output coil generates a magnetic back-flux that opposes the forward flux coming from the main coil. This generates a "back EMF" or reverse voltage at the primary coil.. (see full description above).

Is this also how autotransformer work? But then there is the direct current flow since it has only one winding? So what is the contribution in percentage of direct current flow and back EMF principle?

And if there is no back-emf in the output, could it also produce a current in the primary to the load? Is the back-emf just parallel or dual to it, meaning current can be produced even without it?

 

[Svein]

If the "secondary" winding had been a real secondary winding and the primary and secondary had been connected at the bottom end, would that have been easier to understand?

 

[kiki_danc]

If the "secondary" winding had been a real secondary winding and the primary and secondary had been connected at the bottom end, would that have been easier to understand?

You mean a primary and secondary winding that is not directly connected but put at the top and bottom of the iron core?

But in an autotransformer, it's connected, so there is the analogy to DC circuit where the current takes direct path without any back EMF involved.. and inductance can be considered like resistance in ac circuit. So I want to know the contribution of each mechanism..

Or maybe you are saying that in an autotransformer, it's all about back EMF and no direct current flow similar to the isolation transformer?

 

[essenmein]

At the end of the day auto transformer or a real isolation transformer works on the same principle, each turn of the coil is tightly magnetically coupled to all the other turns, that is, the change in flux in the core affects all turns more or less the same. This effect is called mutual inductance, ie, the change in flux from one coil affects the other coil(s), the better the coupling the more the ratio of mutual to self inductance tends to 1.

For all cored transformers, which only work due to a changing flux (ie AC), if any DC is allowed to flow it quickly saturates the core and magnetically you end up with some wire in air and it ceases to be an effective transformer. An example of this is in switchmode power supplies you often see a DC blocking capacitor in series with the driven winding to ensure any PWM imbalance due to tolerances does not walk the core into saturation.

 

[kiki_danc]

At the end of the day auto transformer or a real isolation transformer works on the same principle, each turn of the coil is tightly magnetically coupled to all the other turns, that is, the change in flux in the core affects all turns more or less the same. This effect is called mutual inductance, ie, the change in flux from one coil affects the other coil(s), the better the coupling the more the ratio of mutual to self inductance tends to 1.

For all cored transformers, which only work due to a changing flux (ie AC), if any DC is allowed to flow it quickly saturates the core and magnetically you end up with some wire in air and it ceases to be an effective transformer. An example of this is in switchmode power supplies you often see a DC blocking capacitor in series with the driven winding to ensure any PWM imbalance due to tolerances does not walk the core into saturation.

In an autotransformer, what is the contribution of the direct current flow... remember it was stated :"In an autotransformer part of the current flows directly from the input to the output, and only part is transferred inductively".. how big is the percentage of each contribution?

 

[essenmein]

In an autotransformer, what is the contribution of the direct current flow... remember it was stated :"In an autotransformer part of the current flows directly from the input to the output, and only part is transferred inductively".. how big is the percentage of each contribution?

An auto transformer will conduct DC, the wires are all physically connected. However any real DC current will saturate the core (the exact amount needed will depend on a few things) and bad things happen if you have this DC flowing while your line is connected.

 

[kiki_danc]

An auto transformer will conduct DC, the wires are all physically connected. However any real DC current will saturate the core (the exact amount needed will depend on a few things) and bad things happen if you have this DC flowing while your line is connected.

I was talking about AC current being conducted via the direct wire conduction path. Most internet references described that autotransformers are not just magnetically connected.. but electrically connected. They always described how the current and voltage are divided in the taps. They no longer described it in terms of back-emf and stuff.

 

[essenmein]

I was talking about AC current being conducted via the direct wire conduction path. Most internet references described that autotransformers are not just magnetically connected.. but electrically connected. They always described how the current and voltage are divided in the taps. They no longer described it in terms of back-emf and stuff.

Well they are electrically connected, but the magnetic coupling is what makes those coils regulate (maintain) the voltage over load. The problem with ignoring the magnetic coupling, is that adding load on a simple tapped non coupled inductor would change the output voltage significantly.

 

[kiki_danc]

Well they are electrically connected, but the magnetic coupling is what makes those coils regulate (maintain) the voltage over load. The problem with ignoring the magnetic coupling, is that adding load on a simple tapped non coupled inductor would change the output voltage significantly.

Can you confirm that in autotransformer, the ac current doesn't really flow from input to output but the current in the output and input are separate just like in isolation transformer?

 

[gneill]

I was talking about AC current being conducted via the direct wire conduction path. Most internet references described that autotransformers are not just magnetically connected.. but electrically connected. They always described how the current and voltage are divided in the taps. They no longer described it in terms of back-emf and stuff.

Have you studied AC circuit analysis? If so you could write the equations and solve the mystery yourself

 

[essenmein]

Can you confirm that in autotransformer, the ac current doesn't really flow from input to output but the current in the output and input are separate just like in isolation transformer?

You can have an isolating transfromer and auto transformer have the same voltage/load characteristics, but they are not the same, one is referenced to the supply, the other allows you to reference to another ground.

 

[kiki_danc]

You can have an isolating transfromer and auto transformer have the same voltage/load characteristics, but they are not the same, one is referenced to the supply, the other allows you to reference to another ground.

Quoting from this site for example https://hubpages.com/technology/Auto-transformer
"In an auto -transformer energy transfer is mainly through conduction process and only a small part is transferred inductively."

Are you saying they are wrong in that all is still transferred inductively? If they are right. I'm asking the part where the current is transferred through conduction process. Please address this directly. Thanks.

 

[DaveE]

Can you confirm that in autotransformer, the ac current doesn't really flow from input to output but the current in the output and input are separate just like in isolation transformer?

Yes, you can model them as separate. It is the same analysis as a conventional transformer, except that the secondary current shares the same conductor as part of the primary. Because of the sharing of the secondary winding with the primary, some of those currents cancel. This can affect the detailed design of those windings vis-a-vis wire size. It can be confusing because people may talk about a direct path for power flow; that can be a simplifying assumption, but the physics is just a transformer.

 

[essenmein]

Quoting from this site for example https://hubpages.com/technology/Auto-transformer
"In an auto -transformer energy transfer is mainly through conduction process and only a small part is transferred inductively."

Are you saying they are wrong in that all is still transferred inductively? If they are right. I'm asking the part where the current is transferred through conduction process. Please address this directly. Thanks.

How does 5A become 10A in the 2:1 example above through just series conduction if the process does not involve inductive energy transfer?

In short the author is plain wrong.

 

[kiki_danc]

How does 5A become 10A in the 2:1 example above through just series conduction if the process does not involve inductive energy transfer?

In short the author is plain wrong.

Most references explain it that way.. that you analyze autotransformer similar to DC circuit in series... in the sense the current and voltage came about because they are in series treating the inductance as like resistance. They no longer described it in terms of back-EMF and feedback. This is why I'm asking this here to verify what is really the case. Even Electrical Engineering Stack Exchange doesn't help much. Berkeman explanation is the clearest. Hope he can comment on autotransformers too.

 

[kiki_danc]

How does 5A become 10A in the 2:1 example above through just series conduction if the process does not involve inductive energy transfer?

In short the author is plain wrong.

You mean in DC circuit.. if you tap it elsewhere (say between two resistors) and get one half the voltage, the current is still the same, whereas in autotransformers, the current becomes twice and can't be explained if they were treated just like in DC series analysis? You have a great point! Is my comment correct?

 

[essenmein]

You mean in DC circuit.. if you tap it elsewhere (say between two resistors) and get one half the voltage, the current is still the same, whereas in autotransformers, the current becomes twice and can't be explained if they were treated just like in DC series analysis? You have a great point! Is my comment correct?

Exactly, the magnetic action is doing the work of keeping the volts turns the same, then when you apply current laws 5A is coming from the supply, 5A is coming up from the lower tapped part of the coil making 10A going to the load. I can see why they explain it like that (part of the current is coming from the supply) it makes it simple, but if you ignore the magnetic part of the equation the "volts per turn is always the same" and the current direction in the lower part of the coil is not explained.

 

[kiki_danc]

Exactly, the magnetic action is doing the work of keeping the volts turns the same, then when you apply current laws 5A is coming from the supply, 5A is coming up from the lower tapped part of the coil making 10A going to the load. I can see why they explain it like that (part of the current is coming from the supply) it makes it simple, but if you ignore the magnetic part of the equation the "volts per turn is always the same" and the current direction in the lower part of the coil is not explained.

So in autotransformer. The current in load is reversed due to Lenz Law. But toward the end of your sentence. Why didnt you state the current doubling was not explained too? Is there circuit scenerio in DC or series where you can make current double at middle? How?

 

[kiki_danc]

If the "secondary" winding had been a real secondary winding and the primary and secondary had been connected at the bottom end, would that have been easier to understand?

It would become like the following. Please tell me why it would make it easier to understand.

 

[kiki_danc]

Exactly, the magnetic action is doing the work of keeping the volts turns the same, then when you apply current laws 5A is coming from the supply, 5A is coming up from the lower tapped part of the coil making 10A going to the load. I can see why they explain it like that (part of the current is coming from the supply) it makes it simple, but if you ignore the magnetic part of the equation the "volts per turn is always the same" and the current direction in the lower part of the coil is not explained.

If you don't agree that it is technically accurate to say that in autotransformer, part of the current really flows directly from the input to the output. Then perhaps you or others can edit the following entry in wiki?

https://en.wikipedia.org/wiki/Autotransformer
"In an autotransformer part of the current flows directly from the input to the output, and only part is transferred inductively, allowing a smaller, lighter, cheaper core to be used as well as requiring only a single winding."

If it is still correct. In what sense it is correct since you guys don't agree there is really direct current flows from input to output in an autotransformer?

 

[Svein]

"In an autotransformer part of the current flows directly from the input to the output, and only part is transferred inductively, allowing a smaller, lighter, cheaper core to be used as well as requiring only a single winding."

Yes. It has to. The current in the secondary winding also flows in the primary winding (after all, they share conductors).

If it is still correct. In what sense it is correct since you guys don't agree there is really direct current flows from input to output in an autotransformer?

Since the inductance is irrelevant for DC, the current through the transformer will be limited only by the resistance in the wires. And for a good transformer, the resistance is low (you do know that power dissipation in any part of the transformer is R⋅I²?) and thus the direct current through the primary will be U/R - which for a power transformer means it will blow the fuse or set fire to the transformer.

 

[kiki_danc]

Yes. It has to. The current in the secondary winding also flows in the primary winding (after all, they share conductors).

Are you describing AC or DC?

Since the inductance is irrelevant for DC, the current through the transformer will be limited only by the resistance in the wires. And for a good transformer, the resistance is low (you do know that power dissipation in any part of the transformer is R⋅I²?) and thus the direct current through the primary will be U/R - which for a power transformer means it will blow the fuse or set fire to the transformer.

When I mentioned "direct current through the primary". I was not referring to DC but just describing continuous AC current flow. Wrong choice of words.
Let's only talk about AC. I know DC can do all those.. but I just want clarification whether in AC, the AC current in the secondary winding also flows in the primary winding?

 

[kiki_danc]

Exactly, the magnetic action is doing the work of keeping the volts turns the same, then when you apply current laws 5A is coming from the supply, 5A is coming up from the lower tapped part of the coil making 10A going to the load. I can see why they explain it like that (part of the current is coming from the supply) it makes it simple, but if you ignore the magnetic part of the equation the "volts per turn is always the same" and the current direction in the lower part of the coil is not explained.

Analyzing in more details. I think the 10A going to the load from the addition of the two from supply and lower tapped part of the coil can be considered as "In an auto -transformer energy transfer is mainly through conduction process and only a small part is transferred inductively".

However the argument now is whether only a small part is transferred inductively. For the lower tapped part, can the ampere be larger than that coming from supply? If yes, then perhaps the statement is wrong that "only a small part is transferred inductively". For without induction, the lower tapped part can't form an opposite current. But if the lower tapped part can't produce current more than the suppy, then perhaps it is accurate that "only a smart part is transferred inductively." What do you think?

 

[kiki_danc]

Analyzing in more details. I think the 10A going to the load from the addition of the two from supply and lower tapped part of the coil can be considered as "In an auto -transformer energy transfer is mainly through conduction process and only a small part is transferred inductively".

However the argument now is whether only a small part is transferred inductively. For the lower tapped part, can the ampere be larger than that coming from supply? If yes, then perhaps the statement is wrong that "only a small part is transferred inductively". For without induction, the lower tapped part can't form an opposite current. But if the lower tapped part can't produce current more than the suppy, then perhaps it is accurate that "only a smart part is transferred inductively." What do you think?

I've been doing a lot of reading about it. I know the more turns, the higher is the voltage and the less is the current.
That is why there are such things as single turn secondary output transformer to produce very high current. https://www.lcmagnetics.com/transformers/single-turn-high-current-transformer/

Can this also occur in an autotransformer? That is, supposed the input is 1000VA at 120v. Can you just tap one turn of the secondary of the autotransformer? And can the current at let's say 1 volt output become 1000A? . If this can occur. Then it refutes the statement that "only a small part is transferred inductively".

 

[essenmein]

I've been doing a lot of reading about it. I know the more turns, the higher is the voltage and the less is the current.
That is why there are such things as single turn secondary output transformer to produce very high current. https://www.lcmagnetics.com/transformers/single-turn-high-current-transformer/

Can this also occur in an autotransformer? That is, supposed the input is 1000VA at 120v. Can you just tap one turn of the secondary of the autotransformer? And can the current at let's say 1 volt output become 1000A? . If this can occur. Then it refutes the statement that "only a small part is transferred inductively".

Yes it can, but you would need to make that singular turn sufficiently sized to carry the 1kA.

 

[Merlin3189]

I don't know whether it helps at all, but I like to think of the primary and secondary currents both flowing through the common winding.

So in the step up version, the full primary current flows through the common winding and the full secondary current flows through both the common and series windings. Similarly in the step down, Ip flows through both and Is only through common.

In both cases, in the common winding they are in the opposite sense, so the net current is lowered.there.

For the series winding there is one current flowing, either the full secondary current in the step up case or the full primary current in the step down case. It is meaningless to ask whether that current comes from the supply or the other winding - it comes from the node between the the two windings.

You can see easily that the efficiency is greatest when the two currents are closest, since then they nearly cancel. So for small step up or down, the voltage ratio is near to 1 and the current ratio will also be near to 1. Then the common winding is much larger than the series winding and the common winding carries very little net current.

For your high current step down transformer, the one turn common winding needs to be thick to carry 992 A, but the primary series winding carries only a bit over 8 A and can be much thinner wire. There is not much advantage here over a double wound transformer with 120 turn primary carrying 8 A and 1 turn secondary carrying 1000 A. I understand that thinking of the primary current splitting (in the step up case) is another valid viewpoint, but I don't see how it is helpful in either understanding or analysing the autotransformer.

I also don't like the idea that current is transferred inductively. In my view it is energy that is being transferred - which is why the current ratio is the inverse of the voltage ratio. Again, I see no benefit of talking about current transfer: it's just another way of obscuring the simple relations that do exist.

 

[kiki_danc]

I don't know whether it helps at all, but I like to think of the primary and secondary currents both flowing through the common winding.
View attachment 234024
So in the step up version, the full primary current flows through the common winding and the full secondary current flows through both the common and series windings. Similarly in the step down, Ip flows through both and Is only through common.

In both cases, in the common winding they are in the opposite sense, so the net current is lowered.there.

For the series winding there is one current flowing, either the full secondary current in the step up case or the full primary current in the step down case. It is meaningless to ask whether that current comes from the supply or the other winding - it comes from the node between the the two windings.

You can see easily that the efficiency is greatest when the two currents are closest, since then they nearly cancel. So for small step up or down, the voltage ratio is near to 1 and the current ratio will also be near to 1. Then the common winding is much larger than the series winding and the common winding carries very little net current.

When the two currents are closest and they nearly cancel then the load would have minimal current (Is=Ip+ I' below).. why do you say it's more efficient?

Unless you mean the primary current will cancel while the secondary current add up?
What if the primary current doesn't cancel or large?

For your high current step down transformer, the one turn common winding needs to be thick to carry 992 A, but the primary series winding carries only a bit over 8 A and can be much thinner wire. There is not much advantage here over a double wound transformer with 120 turn primary carrying 8 A and 1 turn secondary carrying 1000 A.I understand that thinking of the primary current splitting (in the step up case) is another valid viewpoint, but I don't see how it is helpful in either understanding or analysing the autotransformer.

I also don't like the idea that current is transferred inductively. In my view it is energy that is being transferred - which is why the current ratio is the inverse of the voltage ratio. Again, I see no benefit of talking about current transfer: it's just another way of obscuring the simple relations that do exist.

 

[DaveE]

the load would have minimal current

No. It IS the load that determines the current. The load voltage will be equal to the fraction of the primary voltage determined by where the load is connected to the winding. If the secondary tap is at 30% of the winding you will get 30% of the primary voltage across the load, then the load impedance will determine the amount of secondary current. Then the primary current will be determined from the secondary current and the transformer ratio.
Think of the voltage being determined from the primary side and, as the consequence, the current being determined from the secondary side.

 

[kiki_danc]

I'd like to understand a bit about the physics of the formula. The volt per turn is determined from the iron core magnetic flux. So the more turn, the bigger is the voltage because you are adding each turn voltage.. this is why voltage is proportional to turn and flux. But why is current smaller for more turns? What is the physics of it.

Also for the singular turn in the secondary that can give very high current. Should it only work if that material wound around the secondary is a conductor?

What would happen if you wound your fingers around the bald secondary core (of an isolation transformer.. I'm aware the concept doesn't apply in autotransformer since existing turns are being tapped and no bald core). I know the fingers won't form back-EMF. So there is no current demand. But would you get a shock or electrocuted? Of course I won't try it.

(imagine the blue secondary wiring doesn't exist and instead a person wound his finger around the right side)

Can someone give an example of what it would be like to be surrounded by huge magnetic flux like in the core of transformers? What current could be induced in the body? What weapons use this concept?

 

[Merlin3189]

... The volt per turn is determined from the iron core magnetic flux. So the more turn, the bigger is the voltage because you are adding each turn voltage.. this is why voltage is proportional to turn and flux. But why is current smaller for more turns?

I think you may be getting it back to front.
The turns ratio determines the output voltage; say, 10:1 turns ratio, then 120 V applied to primary gives 12 V emf at secondary. The current is then determined by the load, as Dave said, and that determines the output power, V x A. The power input must match that, but since the input voltage is 10x bigger, the input current can be 10x smaller to give the same power. That is why the current is lower in the primary - which has more turns because it operates at a higher voltage.

Conservation of energy (ignoring any losses !) requires V I to be the same. V is proportional to turns, so I is inversely proportional to turns. If no load is connected, the V is still there, but I isn't. The load determines the output current and the primary current has to follow.

Also for the singular turn in the secondary that can give very high current. Should it only work if that material wound around the secondary is a conductor?

As above, the secondary turns determines the emf. Your finger is one turn and will get a single turn's worth of emf. That is quite small usually. Your finger has a high resistance, which means a very small secondary current flows through your finger.

... I know the fingers won't form back-EMF. So there is no current demand. But would you get a shock or electrocuted? Of course I won't try it.

I don't know why they won't ? If a current, albeit small, flows, then it causes a small emf. You won't get a shock because the voltage and current are so small.

... what it would be like to be surrounded by huge magnetic flux like in the core of transformers? What current could be induced in the body? What weapons use this concept?

It would have to be a changing flux, so not a big permanent magnet. Though I suppose if you were moving trough a static field, that would work.
But the general point is that you only get significant currents in good conductors.
Transformers don't generally have single turn windings, because you'd need a very large flux to cause a significant emf in one turn. A 120 V to 12 V transformer wouldn't have 10 t primary and 1 t secondary, nor even 120 t to 12 t. More likely 1200 t to 120 t or higher. Then the volts per turn is 0.1 V/t. So if you want to draw say 4 A, the resistance per turn has to be very much less (maybe 100x less) than 0.25 Ω, which is 0.0025 Ω/t. That means a very good conductor,. If the secondary IS the load, then you still need 0.25 Ω per turn to get 4 A, still a better conductor than you.

 

[Merlin3189]

When the two currents are closest and they nearly cancel then the load would have minimal current (Is=Ip+ I' below).. why do you say it's more efficient?

Is= Ip + I' , so when Is nearly equals Ip, then I' is small. That's what makes it so efficient.
The large common winding carries little current I', so the I²R loss is small in this large winding.

But don't think this is something that can be arranged for any transformer ratio. It's just that autotransformers are very efficient when making small changes in voltage, because then the current in the bulk of the winding is small. As the step up/down ratio increases, the autotransformer advantage decreases.

 

[kiki_danc]

Is= Ip + I' , so when Is nearly equals Ip, then I' is small. That's what makes it so efficient.
The large common winding carries little current I', so the I²R loss is small in this large winding.

But don't think this is something that can be arranged for any transformer ratio. It's just that autotransformers are very efficient when making small changes in voltage, because then the current in the bulk of the winding is small. As the step up/down ratio increases, the autotransformer advantage decreases.

How about for typical 240v to 120v step down transformers? How efficient is it? When you mentioned efficient.. you were just referring to the winding being bigger or smaller to support bigger or smaller current demands (smaller wire for smaller current demand).. isn't it? You were not describing the operating losses? I know Isolation Transformer has more core loss (in terms of hysteresis and eddy current losses), so were you describing resistance loses in the efficiency of the winding or just the material during construction or both?

Why is current and magnetic field connected? What higher laws of physics require them to be binded? It seems strange that it is only an accident of nature. Sometimes I wonder if they are made that way so transformers and ac power is possible so humans can use them.

 

[Merlin3189]

Yes, I was using efficiency in a rather vague way, thinking of I²R losses in the windings. As you say, real losses include eddy and hysteresis. And autotransformer design may well say, use thinner wire and have similar I²R losses with a smaller, cheaper transformer.

For your example, both the series and common windings carry the same current as the primary of a similar dual wound transformer, but then you have no secondary winding at all. In the DWT the secondary would be half the turns of the primary, carrying double the current. So the AT saves that amount of copper and all the secondary I²R loss.
In a DWT if primary and secondary were the same size wire (usually the secondary would be thicker) the AT would have 1/3 the total I²R losses of the DWT. If the secondary used wire with double the area and half the resistance per unit length, the AT still has 1/2 the I²R losses and only uses half the copper of the DWT.

I know Isolation Transformer has more core loss (in terms of hysteresis and eddy current losses),

Than what? Core losses depend on core properties and winding losses on winding properties. Winding losses can be reduced by using more copper to have thicker wires. The AT always scores some reduction in winding losses against a DWT for a given amount of copper.

Why current and magnetic field are connected, is a bit beyond me. I only got as far as, they are connected and some of the rules for that.

 

[kiki_danc]

Yes, I was using efficiency in a rather vague way, thinking of I²R losses in the windings. As you say, real losses include eddy and hysteresis. And autotransformer design may well say, use thinner wire and have similar I²R losses with a smaller, cheaper transformer.

For your example, both the series and common windings carry the same current as the primary of a similar dual wound transformer, but then you have no secondary winding at all. In the DWT the secondary would be half the turns of the primary, carrying double the current. So the AT saves that amount of copper and all the secondary I²R loss.
In a DWT if primary and secondary were the same size wire (usually the secondary would be thicker) the AT would have 1/3 the total I²R losses of the DWT. If the secondary used wire with double the area and half the resistance per unit length, the AT still has 1/2 the I²R losses and only uses half the copper of the DWT.

For a similar rated 500VA 240v-120v step down isolation transformer vs 500VA 240v-120v step down autotransformer. Are their primary windings same sizes? Or could either one be larger and why?

Than what? Core losses depend on core properties and winding losses on winding properties. Winding losses can be reduced by using more copper to have thicker wires. The AT always scores some reduction in winding losses against a DWT for a given amount of copper.

Why current and magnetic field are connected, is a bit beyond me. I only got as far as, they are connected and some of the rules for that.

 

[kiki_danc]

Yes, I was using efficiency in a rather vague way, thinking of I²R losses in the windings. As you say, real losses include eddy and hysteresis. And autotransformer design may well say, use thinner wire and have similar I²R losses with a smaller, cheaper transformer.

For your example, both the series and common windings carry the same current as the primary of a similar dual wound transformer, but then you have no secondary winding at all. In the DWT the secondary would be half the turns of the primary, carrying double the current. So the AT saves that amount of copper and all the secondary I²R loss.
In a DWT if primary and secondary were the same size wire (usually the secondary would be thicker) the AT would have 1/3 the total I²R losses of the DWT. If the secondary used wire with double the area and half the resistance per unit length, the AT still has 1/2 the I²R losses and only uses half the copper of the DWT.

Than what? Core losses depend on core properties and winding losses on winding properties. Winding losses can be reduced by using more copper to have thicker wires. The AT always scores some reduction in winding losses against a DWT for a given amount of copper.

Why current and magnetic field are connected, is a bit beyond me. I only got as far as, they are connected and some of the rules for that.

Oh before it forgot. I want to understand more this phenomenon of floating secondary output of isolated transformer. Say a 240v-120v step down isolation transformer produced 120v output. And one of its leads is not connected to ground. What are the situations when the voltage can rise above 120v? Like 1000V. Is it not the output will always be 120v? But if you let the neutral or one of the leads touch say 1000v.. the output can become 1120v? how? by series? How does this work when output is supposed to be 120v but the actual is 1120v? how is the 1120v measured? between the load (but it should be 120v).. hence the confusion.