I keep struggling with the same question. Why do smaller transformers put out less power.
The only factor that makes sense is that they have a higher impedance which limits output.
If the load starts to approach the transformer's own impedance, my understanding is that a higher relative amount of voltage drop will occur across that transformer than the load on the transformer.
Does that sound right?
And if it is, what is the main factor behind smaller transformers having a higher impedance?
Higher copper resistance? Some factor having to do with the core size and maximum flux density? Some factor having to do with the impedance through the windings as the load on the transformer increases?
The only factor that makes sense is that they have a higher impedance which limits output.
If the load starts to approach the transformer's own impedance, my understanding is that a higher relative amount of voltage drop will occur across that transformer than the load on the transformer.
Does that sound right?
And if it is, what is the main factor behind smaller transformers having a higher impedance?
Higher copper resistance? Some factor having to do with the core size and maximum flux density? Some factor having to do with the impedance through the windings as the load on the transformer increases?
A transformer is limited primarily by its core size. The core's magnetic flux is the mechanism by which power (or better termed, VA) is transferred from one winding to another. For a given core size (cross section) you can only transform by magnetic flux a limited amount of VA. Attempt to transform much more than that, and the core saturates, which prevents further mutual linkage. That hopefully answers your first question about why a smaller transformer outputs less power. In some respects, it's like asking "why is a larger motor able to produce more hp"
Gauge of the windings, in smaller transformers, is the significant impedance factor. That is, for a given transformer core size, voltage rating, and the targeted V/turn design criteria, you will end up with a range of practical wire gauges. Bean counters rule, so the smallest possible gauge wire is typically used, as long as it fits the current requirements. This resistance is the dominant impedance. The size of the winding also affects to a certain extent the core shape, as too much copper ends up with a big winding, and you need a core that can fit (or vise versa, you need to be able to squeeze that winding into the core window).
In larger transformers (tens of kVA through hundreds of MVA), leakage flux is the dominant impedance, which equates to a reactive inductance XL impedance. It essentially is a more significant term than the winding resistance at those larger sizes.
The impedance of a transformer is measured by the following (simplified) procedure:
1. Short secondary winding.
2. Apply enough primary voltage such that you draw rated secondary current.
3. Measure this primary voltage, now called the 'impedance voltage'.
4. Transformer impedance based on the VA size conditions (rated secondary voltage, rated secondary current) is defined as Z = impedance voltage / rated primary voltage. Usually specified in percent, as it is a ratio.
5. X/R ratio can be either assumed from charts or actually measured by watts loss tests. This measurement is really only practical in large transformers. For audio use, assume X/R is anything from 0.1 to 0.001. I suppose you could also measure DCR in each winding and reflect the values, since the ratio is knowingly low, but that is not the 'official' test.
This Z with X/R ratio can then be used to calculate voltage drops in the per unit system. Per unit allows you to compare the impedance differences between 'small' and 'large' transformers. This is a little beyond the scope of your question.
Clear as mud?
Gauge of the windings, in smaller transformers, is the significant impedance factor. That is, for a given transformer core size, voltage rating, and the targeted V/turn design criteria, you will end up with a range of practical wire gauges. Bean counters rule, so the smallest possible gauge wire is typically used, as long as it fits the current requirements. This resistance is the dominant impedance. The size of the winding also affects to a certain extent the core shape, as too much copper ends up with a big winding, and you need a core that can fit (or vise versa, you need to be able to squeeze that winding into the core window).
In larger transformers (tens of kVA through hundreds of MVA), leakage flux is the dominant impedance, which equates to a reactive inductance XL impedance. It essentially is a more significant term than the winding resistance at those larger sizes.
The impedance of a transformer is measured by the following (simplified) procedure:
1. Short secondary winding.
2. Apply enough primary voltage such that you draw rated secondary current.
3. Measure this primary voltage, now called the 'impedance voltage'.
4. Transformer impedance based on the VA size conditions (rated secondary voltage, rated secondary current) is defined as Z = impedance voltage / rated primary voltage. Usually specified in percent, as it is a ratio.
5. X/R ratio can be either assumed from charts or actually measured by watts loss tests. This measurement is really only practical in large transformers. For audio use, assume X/R is anything from 0.1 to 0.001. I suppose you could also measure DCR in each winding and reflect the values, since the ratio is knowingly low, but that is not the 'official' test.
This Z with X/R ratio can then be used to calculate voltage drops in the per unit system. Per unit allows you to compare the impedance differences between 'small' and 'large' transformers. This is a little beyond the scope of your question.
Clear as mud?
Most of that makes perfect sense.
So the predominate limiter in output power is the core size because it limits flux?
I read that the maximum flux density was at no load. I think that confused me, because under load I assumed the core would not saturate.
But it still limits power transfer, I guess. That would explain things well even though I don't fully understand it. I appreciate your help and understanding of my ignorance.
So the predominate limiter in output power is the core size because it limits flux?
I read that the maximum flux density was at no load. I think that confused me, because under load I assumed the core would not saturate.
But it still limits power transfer, I guess. That would explain things well even though I don't fully understand it. I appreciate your help and understanding of my ignorance.
You might want to consider temperature in all of these discussions. It is after all, the thing that finally destroys the transformer, when the losses from the watts being pulled through, are more than the total surface area can emit into the surrounding environment. This relates amps of current, to circular mils of wire surface, to watts lost to heat. All due to impedance created by all of the loss mechanisms zigzagflux provided.
It is very easy to design a small transformer, provide the coil with 220C insulation and get amazing amounts of power from the device. Increasing the operating frequency and limiting the duty cycle to less than 50% is another way to drop the size to power ratio. Eventually, you will use up the thermal lifetime of even these tough materials and bare wires will touch, many amps of short circuit current will be drawn and the transformer will catch fire.
So, your real size limit is how hot you can stand to run the transformer. Commercial materials will allow operating temperatures of 220 degrees C, sustained, for 300,000 hours mtbf. Please note, that is degrees Celsius, more than twice the temperature of boiling water.
Be happy to provide you with a power transformer, for your next amplifier, that will run at that temperature, with perfect safety.
Bud
It is very easy to design a small transformer, provide the coil with 220C insulation and get amazing amounts of power from the device. Increasing the operating frequency and limiting the duty cycle to less than 50% is another way to drop the size to power ratio. Eventually, you will use up the thermal lifetime of even these tough materials and bare wires will touch, many amps of short circuit current will be drawn and the transformer will catch fire.
So, your real size limit is how hot you can stand to run the transformer. Commercial materials will allow operating temperatures of 220 degrees C, sustained, for 300,000 hours mtbf. Please note, that is degrees Celsius, more than twice the temperature of boiling water.
Be happy to provide you with a power transformer, for your next amplifier, that will run at that temperature, with perfect safety.
Bud
That transformers saturate at high load is a common misconception and it is not correct. Actually, the flux even decreases somewhat with increased load in most of the commonly used winding configurations. The reason why bigger transformers can transfer more power is purely because of heat dissipation and efficency concerns. Overloading a transformer makes it overheat eventually.
Larger transformers have:
Greater surface area - more heat can be dissipated
Greater core cross section - less turns per volt needed which lowers resistance
Greater winding window area - thicker wire fits which lowers resistance even more
These are the reasons why large transformers can transfer more power than small ones when the same frequency, cooling method, temperature rise and core material is used.
May I alter the original question a bit into "what makes a good transformer" - say for ss power amp?
I'm always struggling between low resistance I love to have - which leads directly to the torroides - and the mechanic hum they show.
This is especially true (and becomes really anyoing) when driven with slight DC in the AC mains, as it happens when you have strong device nearby that pull current only at one half of the mains sine - cheap hair dryer this is, operating at half power (a simple diode to supress the second half sine at mid power setting).
Michael
I'm always struggling between low resistance I love to have - which leads directly to the torroides - and the mechanic hum they show.
This is especially true (and becomes really anyoing) when driven with slight DC in the AC mains, as it happens when you have strong device nearby that pull current only at one half of the mains sine - cheap hair dryer this is, operating at half power (a simple diode to supress the second half sine at mid power setting).
Michael
I also read that flux is at maximum density when there is NO load. Rodd Elliott reiterates this a number of times in his article on transformers.
Let me ask this. I put a wall wart into a 4 ohm load. Voltage dropped a LOT. A high impedance from the transformer could explain a high voltage drop according to my calculations - if the load impedance gets close to the impedance at the secondary, a higher percentage of voltage drop will happen in the transformer, and not the load. So that makes sense to my limited knowledge of electronics.
Ignoring the possibility of burning up your transformer, it would seem like transformer impedance would explain the power output difference between a wall wart, and 600 VA amp. And according to the above explanation, copper is the main factor here.
Unfortunately, I can't seem to either get a concensus answer, or an answer I understand to this question.
What is the main factor which makes a wall wart put out so little power compared to a high power transformer? Copper related resistance? I would think that as temp goes up, it would only get worse with impedance increasing. I can see voltage decreasing when I measure the voltage across a 4 ohm load connected to a wall wart.
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Yes, short-term, power is limited by the output impedance of the transformer. You get most power through it when the load impedance is matched to this. Often it's wire resistance that dominates but inductance can also be a limiting factor. Sometimes transformers are made with high series inductance by purpose to limit current. For example, neon sign transformers and some kinds of welders are made this way. Zigzagflux wrote that inductance is the dominating impedance in very large transformers and this makes sense as you really need to keep those resistive losses down. Just 1% of resistive voltage drop in a 100MVA transformer means that the cooling system needs to get rid of 1 million watts of losses!
Through big transformers you can get a huge amount of power compared to their rating for a short while. A 1kVA unit may have 4% regulation which means you can theoretically get 13kW from it for a short while. 13kW will cause the output voltage to halve, from 104% of its nominal value to 52%. This won't work for very long though, as there will be the same amount of loss in the transformer as in the load. 13kW of copper loss instead of the rated 40W isn't going to work for very long...
There are also repulsion forces between primary and secondary windings which try to tear the transformer apart. I heard it's something that is most important to consider for distribution transformers where very large short circuit energies are involved. It's no good if the transformer suffers mechanical damage if (when) a short circuit occurs.
However, very small transformers, like in your wall-wart, have much looser regulation than larger types and this means less power can be coaxed out of them short-term. A 20% regulation transformer is only going to be able to provide three times it rated power for instance. Really small transformers are often made with impedance high enough that transformer heating isn't excessive even with shorted load. These aren't going to be able to supply much overload power at all.
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All cool stuff, so to speak.
I had read about leakage inductance before. I appreciate you explaining it again though.
I do have another question. What does flux density limit?
What if you build an air core transformer which does not allow for a very high flux density if I understand correctly? What's the drawback? Efficiency?
I had read about leakage inductance before. I appreciate you explaining it again though.
I do have another question. What does flux density limit?
What if you build an air core transformer which does not allow for a very high flux density if I understand correctly? What's the drawback? Efficiency?
Air core devices suffer primarily from not having a ferrous bounding box for at least a portion of their activity. The ferrous bounding box (core of any type) provides at least a 1000 times multiplication factor in power transformation over air cores. Again this is watts that are useful as opposed to watts that just create heat.
A cautionary note about big transformers vs small transformers. As size increases the volume to surface area ratio declines. This means you can run the copper wires much harder in a small transformer, to get the same overall temperature rise you would get from a larger transformer. This is not intuitive so do think about it. It is simply the ability of a surface area to dump heat and the bigger the ration of heater to surface area the higher the temperature rise is.
Bud
A cautionary note about big transformers vs small transformers. As size increases the volume to surface area ratio declines. This means you can run the copper wires much harder in a small transformer, to get the same overall temperature rise you would get from a larger transformer. This is not intuitive so do think about it. It is simply the ability of a surface area to dump heat and the bigger the ration of heater to surface area the higher the temperature rise is.
Bud
I made a little mistake, saturation does in fact limit the amount of power that can be transferred, but not if the primary voltage is at its rated value. I didn't think of this because most of the time transformers are connected to a voltage source, at least in typical power supplies.
You can increase powertransfer two ways of course - increase current or increase voltage. If you increase voltage without increasing the frequency, the transformer will saturate. You get the most power transfer when the voltage is increased to just below where the transformer saturates and the load is matched to the transformer output impedance.
The 25% voltage drop in the primary if the load is matched means you could increase primary voltage by 18% (1/.75 - 1) and get about 40% more power than I said earlier through. These numbers are quite meaningless for things like power amplifiers however.
Here are some I can think of:
Very low magnetizing inductance -> Very high magnetizing current -> High power loss
Bad coupling -> High leakage inductance -> Bad regulation
High stray fields.
Induction heaters sometimes need to be air core, and then capacitors are used to provide the reactive power needed by the coil. The amount of reactive power circulating in this resonant circuit can be orders of magnitude larger than the real power transferred to the load! The windings need often be water cooled because of the large losses. Air core is kind of useless if you need efficency due to the large reactive power needed. Induction heating is done at pretty high frequency too. It will be even worse at 50Hz/60Hz.
You can increase powertransfer two ways of course - increase current or increase voltage. If you increase voltage without increasing the frequency, the transformer will saturate. You get the most power transfer when the voltage is increased to just below where the transformer saturates and the load is matched to the transformer output impedance.
The 25% voltage drop in the primary if the load is matched means you could increase primary voltage by 18% (1/.75 - 1) and get about 40% more power than I said earlier through. These numbers are quite meaningless for things like power amplifiers however.
Here are some I can think of:
Very low magnetizing inductance -> Very high magnetizing current -> High power loss
Bad coupling -> High leakage inductance -> Bad regulation
High stray fields.
Induction heaters sometimes need to be air core, and then capacitors are used to provide the reactive power needed by the coil. The amount of reactive power circulating in this resonant circuit can be orders of magnitude larger than the real power transferred to the load! The windings need often be water cooled because of the large losses. Air core is kind of useless if you need efficency due to the large reactive power needed. Induction heating is done at pretty high frequency too. It will be even worse at 50Hz/60Hz.
Hello All,
Just reading and stumbled upon some transformer info that may need a correction. It comes as great surprise to many that energy is NOT transferred thru
the iron core of the transformer. The magnetizing flux only induces an electric
field around the core. When on load, the primary current has the "magnetizing" component of current lagging the applied EMF by almost 90 degrees, and the
"load" component that is in phase with the primary EMF, (assuming a resistive load). The core flux remains the same, almost save for resistive drops and the
Load component of flux IN PHASE with the voltage is found as leakage flux outside of the core. If you look at the Poynting Theorem, it is pretty well illustrated. For many years it has been almost completely ignored, even in college level texts, as circuit theory has almost completely replaced the use of "field theory" as far as day to day engineering is concerned. Some of this "leakage" flux does indeed leak away as stray flux and is a loss. Energy is flowing in the dielectric medium between windings as the "electric" field induced by changing core flux and the "leakage" H filed outside the core. It the windings are close to each other, or wound on top of each other this "H" filed is almost impossible to access and measure. Many find this hard to believe, because we are all led to think power naturally flows thru the core. Poynting theorem is generally saved for higher frequency uses, like RF transmission lines and antennas, but it is still valid for transformers and DC circuits as well. The windings themselves limit volt-amps more than the core. If you need more power, and use larger gauge wire to limit IR losses, yo need a larger window for it to fit in, then the core must get larger to accommodate the wire, but you must make the core thicker as well because the reluctance of a given core will get larger as the core gets "lomger" in diameter. Look at high frequency transformers, like that used in aviation at 400 hz. A one kilowatt transformer si MUCH smaller than its 60 hz counterpart. Audio transformers, well, same theory, BUT a whole 'nother bag of worms..........
Tomtech
Just reading and stumbled upon some transformer info that may need a correction. It comes as great surprise to many that energy is NOT transferred thru
the iron core of the transformer. The magnetizing flux only induces an electric
field around the core. When on load, the primary current has the "magnetizing" component of current lagging the applied EMF by almost 90 degrees, and the
"load" component that is in phase with the primary EMF, (assuming a resistive load). The core flux remains the same, almost save for resistive drops and the
Load component of flux IN PHASE with the voltage is found as leakage flux outside of the core. If you look at the Poynting Theorem, it is pretty well illustrated. For many years it has been almost completely ignored, even in college level texts, as circuit theory has almost completely replaced the use of "field theory" as far as day to day engineering is concerned. Some of this "leakage" flux does indeed leak away as stray flux and is a loss. Energy is flowing in the dielectric medium between windings as the "electric" field induced by changing core flux and the "leakage" H filed outside the core. It the windings are close to each other, or wound on top of each other this "H" filed is almost impossible to access and measure. Many find this hard to believe, because we are all led to think power naturally flows thru the core. Poynting theorem is generally saved for higher frequency uses, like RF transmission lines and antennas, but it is still valid for transformers and DC circuits as well. The windings themselves limit volt-amps more than the core. If you need more power, and use larger gauge wire to limit IR losses, yo need a larger window for it to fit in, then the core must get larger to accommodate the wire, but you must make the core thicker as well because the reluctance of a given core will get larger as the core gets "lomger" in diameter. Look at high frequency transformers, like that used in aviation at 400 hz. A one kilowatt transformer si MUCH smaller than its 60 hz counterpart. Audio transformers, well, same theory, BUT a whole 'nother bag of worms..........
Tomtech
The Poynting Theorem doesn't say what many people think it says: 'the Poynting vector shows you where the power flows'. What it actually says is 'the surface integral of the Poynting vector around a closed surface shows you the net power flow through that entire surface' - that is all, and these two statements are not equivalent.
Having said that, yes transformers don't work in the way we might expect. I seem to recall reading somewhere that a full explanation of transformers involves use of the vector potential - which most people regard as simply a calculation tool, yet may in fact be part of the real EM field (with electric and magnetic fields being merely tools for calculating forces on test charges).
Having said that, yes transformers don't work in the way we might expect. I seem to recall reading somewhere that a full explanation of transformers involves use of the vector potential - which most people regard as simply a calculation tool, yet may in fact be part of the real EM field (with electric and magnetic fields being merely tools for calculating forces on test charges).
Thanks for the reply. The Poynting theorem does state that, but remember there is NO load component of flux to be found in the iron core, a magnetizing flux lagging the primary EMF. Secondary load current is countered with MMF from the primary coil IN PHASE with the EMF, that represents real power. The theorem also requires the electric field, from the the changing core flux to be crossed with a magnetic flux for real power, the B core flux, almost all contained in the core cannot do this. IF you measure, ON LOAD the energy found in the "leakage" flux is FAR greater than that in the core. not FLUX DENSITY, but
FIELD INTENSITY. Some of this "leakage flux" does thread part of its path in the iron, but the lions share is in air and in the copper of the windings. The term leakage flux is a misnomer from the days when it was thought that flux leaked from the core. Core permeability has no effect on this, even with an infinite core permeability, leakage flux will still develop. I think a lot of the confusion results from the fact that, on no load, the leakage flux is nil, and for all intents can be ignored. I can reference several excellent papers that show all of this in great detail, and I had to prove it to myself with lab grade equipment before I believed it. Circuit theory is much simpler to use and gives us hands on day to day parameters to deal with, voltage, current, watts, etc. There is no need to use gear to evaluate, design or build transformers, all needed values can be determined without the poynting theorem. It is taken form granted, from using terms like "working flux" that energy flows thru the core. It can be shown that it does not. It is guided by the core, much like a copper wire guides energy just outside its walls, in the dielectric space. S= V x H is valid for transformers too. I never found much used for the vector potential, but many find it useful and I am sure it is valid, I was only speaking of the path the energy takes from primary to secondary......
FIELD INTENSITY. Some of this "leakage flux" does thread part of its path in the iron, but the lions share is in air and in the copper of the windings. The term leakage flux is a misnomer from the days when it was thought that flux leaked from the core. Core permeability has no effect on this, even with an infinite core permeability, leakage flux will still develop. I think a lot of the confusion results from the fact that, on no load, the leakage flux is nil, and for all intents can be ignored. I can reference several excellent papers that show all of this in great detail, and I had to prove it to myself with lab grade equipment before I believed it. Circuit theory is much simpler to use and gives us hands on day to day parameters to deal with, voltage, current, watts, etc. There is no need to use gear to evaluate, design or build transformers, all needed values can be determined without the poynting theorem. It is taken form granted, from using terms like "working flux" that energy flows thru the core. It can be shown that it does not. It is guided by the core, much like a copper wire guides energy just outside its walls, in the dielectric space. S= V x H is valid for transformers too. I never found much used for the vector potential, but many find it useful and I am sure it is valid, I was only speaking of the path the energy takes from primary to secondary......
well to answer OP's question from 5 years ago
a transformer's power density follows core area, and window area.
if i double the dimentions of a transformer, core area is squared.
so is window area.
this means i can get 16 times as much power through the transformer.
volume only increased 8 fold.
keeping the same flux density, iron loss is 8 fold, and keeping the same current density, copper losses are 8 fold.
but power through put is 16 fold.
leakage inductance also scales by the 4th power, but i don't understand why yet.
in real life power draw must be reduced because surface area decreases.
also in real life, a 50 megawatt transformer might weigh 50 tons and operate at 99% efficiency.
try getting 1 kilowatt per kilogram out of a 2 kilogram transformer at line frequency. let me know how that goes.
a transformer's power density follows core area, and window area.
if i double the dimentions of a transformer, core area is squared.
so is window area.
this means i can get 16 times as much power through the transformer.
volume only increased 8 fold.
keeping the same flux density, iron loss is 8 fold, and keeping the same current density, copper losses are 8 fold.
but power through put is 16 fold.
leakage inductance also scales by the 4th power, but i don't understand why yet.
in real life power draw must be reduced because surface area decreases.
also in real life, a 50 megawatt transformer might weigh 50 tons and operate at 99% efficiency.
try getting 1 kilowatt per kilogram out of a 2 kilogram transformer at line frequency. let me know how that goes.
The answer is in the last line of your statement, "At line frequency". Of course the higher the frequency the less core mass is needed, I was wrong to make the comparison of 60 hz and 400 hz transformers. The wire is a far greater limiting factor than is the core, depending on what core steel is used. I am not saying that the core is not important, it is VERY important. Core flux remains the same regardless of the power level, with a given transformer, and not driving the core into saturation. IF larger wire is needed, one must increase the size of the core. Ever consider experimental transformers with superconducting coils? The are not for every day use, but with essentially no resistance in the windings, very large power can be handled with a small core..
well no crap.
i should also mention that most all 1MW and larger transformers are built up core stacks which are grain aligned and fitted precisely and they run at 1.9T.
many toroidal cores from reputable manufacturers used by many on this forum run at 1.9T.. at 1 watt per kilogram at 60Hz core loss, but that's only possible for a toroid.
I have a few 400hz cores that run at 1.5T at 400hz and they don't get warm.. they are also .003" thick steel.
a transformer's power density follows flux squared -- this is why it makes absolutely no sense to run the core at anything less than just below the "knee" in the flux curve/
i should also mention that most all 1MW and larger transformers are built up core stacks which are grain aligned and fitted precisely and they run at 1.9T.
many toroidal cores from reputable manufacturers used by many on this forum run at 1.9T.. at 1 watt per kilogram at 60Hz core loss, but that's only possible for a toroid.
I have a few 400hz cores that run at 1.5T at 400hz and they don't get warm.. they are also .003" thick steel.
a transformer's power density follows flux squared -- this is why it makes absolutely no sense to run the core at anything less than just below the "knee" in the flux curve/
Yes, I agree on the flux level, no sense in paying for a good, high quality steel,
and work it at a level some cheaper steel would be happy with. I need to go and re-examine the scaling factors for 60 hz power transformers, you provided some thought provoking info regarding that. I think much confusion exists around the topic of "leakage" flux as it applies to transformers. It sounds like, by its very name, an unwanted, aspect of transformer construction, that is a flaw in design. When on load (resistive) the MMF from the secondary is matched by an equal and ALMOST in phase MMF from the primary winding. When the primary and secondary are would real close together, (Like Frank Mcintosh did with his famous Unity Coupled transformers, the "Load component" flows between these two wires. Of course, the two wires cannot occupy an identical space at ones, so some, A very small amount, of this H component of Load flux, does "leak" away. Even if you could wind the primary inside the secondary, like in a coaxial cable, this load component of H flux would still exist, but between the wire surfaces. This is done frequently with balun type transformers, albeit at much higher frequencies. So, yes it is probably impossible to build a working transformer without some leakage flux. There is no need to use the poynting theorem to design and build good transformers, as if good, well known engineering techniques are followed,a good, efficient device will result. Now, for audio output transformers,well, I am interested in them as well, but they open up new vistas as they cover so much ground. I may have some questions for you regarding them.....
and work it at a level some cheaper steel would be happy with. I need to go and re-examine the scaling factors for 60 hz power transformers, you provided some thought provoking info regarding that. I think much confusion exists around the topic of "leakage" flux as it applies to transformers. It sounds like, by its very name, an unwanted, aspect of transformer construction, that is a flaw in design. When on load (resistive) the MMF from the secondary is matched by an equal and ALMOST in phase MMF from the primary winding. When the primary and secondary are would real close together, (Like Frank Mcintosh did with his famous Unity Coupled transformers, the "Load component" flows between these two wires. Of course, the two wires cannot occupy an identical space at ones, so some, A very small amount, of this H component of Load flux, does "leak" away. Even if you could wind the primary inside the secondary, like in a coaxial cable, this load component of H flux would still exist, but between the wire surfaces. This is done frequently with balun type transformers, albeit at much higher frequencies. So, yes it is probably impossible to build a working transformer without some leakage flux. There is no need to use the poynting theorem to design and build good transformers, as if good, well known engineering techniques are followed,a good, efficient device will result. Now, for audio output transformers,well, I am interested in them as well, but they open up new vistas as they cover so much ground. I may have some questions for you regarding them.....
Yes, I was surprised at the post I saw in another Thread that transformer regulation gets worse as core flux is reduced.
I test many of my transfoermers for no load primary current off the Variac.
The Curve does not have a pronounced knee. It just curves over nearly becoming horizontal @ 260Vac.
The increase in primary current from 244Vac to 254Vac can approach 2times.
that makes a transformer run very hot.
How do we determine from the transformer PriI vs PriV curve, what optimum voltage we should run at?
Or rephrased, how many extra Primary Turns should we add on to get onto the optimum part of the knee?
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