Can you flip a transformer around to step up a voltage? ??? I ask this because I can't find a transformer that'll increase voltage so I wanted to use a 120vac to 12vac and invert it so it takes 12vac and steps it up to 120vac. :icon_idea:
Sure, you can. That's exactly what EHX does with their tube pedals.
Yes, you can. BUT, if you exceed the power rating of the transformer, you will melt the insulation on the wiring inside, effectively destroying the transformer! You should see a schematic for the power supply for the "Real McTube" (Google it). This is exactly what he did...but he used a 2nd step down transformer to limit the current.
If you try this, be VERY, VERY cautious, use a fuse, well-insulated connections, and watch how much current you try to pull out of it! Possible FIRE HAZARD, ARCING, LETHAL VOLTAGES. Be ready to disconnect the transformer in a snap!
By posting how much current you need at 120V, the forum members would be able to advise you better. What are you planning on doing with the 120V?
Alright thanks guys. I'll be extra cautious on this one. ;D
I plan on powering a 12ax7 in a tube wah. The current I believe is fairly low; in the milliamps range.
There are two things you must be very careful not to exceed. One is the overall power rating as noted. The other is the rated voltage on any one winding.
You may not, for instance, drive a 60V secondary winding with 120 V to cause the intended primary to run at 240V. This will saturate the core and cause overheating and death. In fact, exceeding the rated voltage by more than about 10-20% will cause this.
The commonest way to power tubes in pedals is to run two 120:12Vac transformers back to back: that is, 120Vac on the input primary, then the 12V secondary driving the other 12V secondary and the tube filaments. The second "primary" can now be rectified to get 140Vdc or so.
Yeah I forgot to mention the first transformer 120 to 12 and then I have the 12 to 120. The second 120 will supply power to the tube and I'll have the 12 go to the pedal.
One more question: is it ok to supply 12vac to 12.6v transformer? ???
You'll be fine, the 12v isn't set in stone, it's just close. Honestly, I would just buy an iso transformer with a heater winding. You can find them for 25-35 bucks from tubesandmore.com Then you don't have to worry about any of the issues with using two transformers to rig a 12v tap and 120v HT.
Cool. Thanks alot.
> 12vac to 12.6v transformer?
Lower is OK. Gross under-volting, like 6V into a 12V winding, is "wasteful" of your iron-money, but in small iron it is often the sweetest way to find 60V AC in a tube amp.
Transformer and wall voltage is all +/-10% anyway.
As R.G. said: "exceeding the rated voltage by more than about 10-20% will cause ... overheating and death." That's maybe conservative: I have seen large good iron barely hot enough to fry an egg at 140% of rated voltage. And there is a widely-used set of parts that feeds 12.6V into a 10V winding without problem. OTOH I have seen too many reports of trouble at 20% over-voltage.
Quote from: PRR on June 11, 2010, 08:38:09 PM
As R.G. said: "exceeding the rated voltage by more than about 10-20% will cause ... overheating and death." That's maybe conservative: I have seen large good iron barely hot enough to fry an egg at 140% of rated voltage. And there is a widely-used set of parts that feeds 12.6V into a 10V winding without problem. OTOH I have seen too many reports of trouble at 20% over-voltage.
You're right - it is being very conservative. A lot of times it's possible to get away with higher than nominal voltages. The reason I go conservative on the advice in a public forum is that the actual reality is hidden inside the tranny's design, the head of its designer and the materials that were actually used.
I like transformers, designed them for a living for a while, and so I always tell people about them, whether they want to hear it or not. :icon_lol: You probably already know this stuff, Paul, but I figure some of the audience doesn't and may be interested.
Electrically the primary side of a transformer looks like a big inductor in parallel with the transformed secondary load, whatever that is. But the primary inductance is always with you no matter what the secondary load does. The primary inductance is what limits the incoming AC power line current to non-destructive levels and the current this lets flow is the second-law-of-thermo's price for charging the iron up magnetically so the transforming action can happen.
The primary inductance is nonlinear. It is both different values for different levels of drive and also hysteretical - it does not trace the same B-H curve going positive as going negative. Each AC power line cycle, the core magnetics trace out a magnetic field intensity/magneto-motive force (B/H) curve and the interior of that curve is a little bite of power the core gets heated by. Also, the inductance drops as you approach saturating the core with all the flux density it can contain. Drive it with too much volt-time integral (that is, too much voltage or too long a time/low a frequency) and the core gets saturated.
When you hit saturation the inductance starts not limiting the non-transformed primary current. In a well designed transformer, this magnetizing current is perhaps 1% to 5% of the full load current. But saturate the core and the magnetizing current shoots up to whatever the wire resistance limits it to. That can be massively bigger than the designed full load current. Or not. Depends on the details.
The details that matter are:
- how close to the edge of saturation the trannie was designed for in the first place
- how sharp the edge of saturation is in the iron alloy of the core
- the mechanical history of the iron's rolling direction, annealing, etc.
- the stacking method and how carefully the core stack was joggled to minimize air gap; air gap does not saturate, and if the tranny was otherwise designed to cope with a sloppy air gap, it will not fail as suddenly when overvolted.
- the resistance of the primary wire; in this case, really small transformers are better because they are handicapped by a large primary resistance to start with
Small EI transformers may be almost immune to overvoltages up to 150% on the primary because of the primary resistance being so large. Small trannies also have secondaries designed for too-high secondary voltages because of the big resistive losses in the primary, so a "12V" secondary in a 3VA transformer may be designed for 15V open circuit so it can sag back down to 12V under full load. So a small transformer used backwards gets an extra boost from the designed-in too-high secondary voltage used as a primary.
Bigger transformers, especially toroids, are very vulnerable. The lower primary resistance which makes them better transformers in general also makes them prone to high currents and high wire heating when they are saturated. Toroids in particular have no noticeable air gaps, so any help from an air gap in softening saturation is not present. Toroids are very sensitive to volt-time saturation.
Not knowing what was in the designer's head or the iron-bin at the factory, or how carefully the iron was jogged together, I tend to stay strictly within the lines with most trannies.
It is possible to deliberately overvolt a transformer in a test setup where you can watch the no-load primary current and thereby find how quickly it shoots up under how much over voltage on the primary. This lets you make an informed judgement about how much to abuse it. But this is not for the average Joe. It's for the expert to see how close to the edge of the cliff they can stand. And it's definitely not to be used in stuff anyone else but the risk-accepting expert to use after the expert is done with it. Fires can happen decades later.
So I stay conservative with public advice. The recommended primary voltage +/-10% is where the world lives, and I tell folks to stay there.
As a side light, the creep of AC power line voltages from 110Vac back in the 1950s to 125Vac today represents a danger to vintage amps. Many of these are always on the high edge of their power transformers' capability as designed. That's one reason I came up with the bucking transformer setup in the Vintage Voltage Adapter at Geo. It corrects the incoming AC line back down to the nominal design point for the power transformer in these amps.
Quote from: R.G. on June 12, 2010, 10:08:51 AM
The details that matter are:
- how close to the edge of saturation the trannie was designed for in the first place
- how sharp the edge of saturation is in the iron alloy of the core
- the mechanical history of the iron's rolling direction, annealing, etc.
- the stacking method and how carefully the core stack was joggled to minimize air gap; air gap does not saturate, and if the tranny was otherwise designed to cope with a sloppy air gap, it will not fail as suddenly when overvolted.
- the resistance of the primary wire; in this case, really small transformers are better because they are handicapped by a large primary resistance to start with
If you don't mind can you please explain the underlined statements. I've read your article about designing output transformers on Geofex. But I don't recall reading about those.
Quote from: panterafanatic on June 12, 2010, 11:58:59 AM
If you don't mind can you please explain the underlined statements. I've read your article about designing output transformers on Geofex. But I don't recall reading about those.
Sure. But I'll have to talk about some basic stuff first.
"B" is a term for the magnetic field flux density. You can think of this as how intense the magnetic field is. "H" is the magnetomotive force (MMF), that being a word for how hard you have to push on the material to make its field change. In transformer and other wound-core devices, H is usually expressed in ampere-turns. One amp of current in one turn is one ampere-turn. One milliamp in a thousand turns is one ampere turn. There are several units for B; most current is the Tesla, the MKS unit. I learned and am most comfortable working in kilo-Gauss. But the units don't matter much for the initial understanding.
Transformer core materials can be "pushed" by an MMF into having a flux density B higher than would happen for the same push on air, vacuum, cardboard, etc. The ratio of how much more magnetic field you get with the core material above that of vacuum is the relative permeability. So if I get 100Gauss of field intensity for a given coil and current in air, then I fill the center of the coil with iron/cobalt/nickel alloys, the field intensity will be higher because these things have internal magnetic domains which can be easily aligned by the push of an MMF. How much more flux density depends on how much of the pathway that the magnetic flux has to travel through is filled with iron and how much with air/vacuum/cardboard/etc.
This happens because the iron/cobalt/nickel core stuff is (conceptually!) filled with little bar magnets which line up with the applied MMF and concentrate all their fields together. There are a fixed number of little magnetic domains inside any bit of core material, and it's easy to move a few of them into line, but you have to apply more MMF to make more of them line up, and even harder to make all of them line up. And you hit a wall when they're all lined up already. No matter how much you push (MMF) you can't make the field intensity go up any more once the domains are all lined up already. That's saturation. The core is saturated with as much field density as its aligning domains can carry. You can push the density higher with even more MMF, but you get no "boost" from the alignment of domains, and the iron above the saturation density may as well be vacuum for how much field increases with more MMF.
Quote- how sharp the edge of saturation is in the iron alloy of the core
Look at figure 1 here: http://www.walkerscientific.com/Products/Product_Lines/Magnetic_Analysis/Hysteresisgraphs/Initial-4-Quadrant.pdf (http://www.walkerscientific.com/Products/Product_Lines/Magnetic_Analysis/Hysteresisgraphs/Initial-4-Quadrant.pdf) This is a plot of B (flux density or magnetic field intensity) versus H (magnetomotive force). Notice that down at zero MMF and zero B, B increases very rapidly as you push on it with H. It's close to linear: double the H, double the B. As you get to higher B values, you have to use more and more H to get each increment of more B. The curve stops looking like a sloped line and bends over to the right into saturation.
The shape of the "knee" of that bending over, how softly and gradually it bends to the right or how suddenly it breaks over and heads right is the sharpness of the edge of saturation I was talking about. That plot is for gradual saturation transformer iron. There are other alloys. Some alloys are "square loop" types. They have high and relatively constant slopes up to a critical B value, then suddenly change to saturated. Saturation is sudden, and intense. This is useful in some special situations, but square loop materials are intolerant of voltage input drive in the way it's done for general power transformers.
The sharpness of the knee of saturation is determined by the iron/cobalt/nickel/other junk alloy of the core, it's mechanical, and thermal history. Which leads us to:
Quote- the mechanical history of the iron's rolling direction, annealing, etc.
The magnetic properties of an iron based material are affected by what's been done to it's magnetic domains, and that can be mechanical and thermal as well as electronic. If you take soft, just cooled-off-from-the-melting iron and test its B-H curve, then pound in it or roller it flat and test it again, you can see a difference in the before and after B-H curve. If you then re-heat it to above the temperature where it loses its magnetic properties (known as the Curie point) and cool it slowly, this mostly resets the changes from the pounding. If you roll it into flat sheets, the magnetic properties go from being the same in any direction to being better in some directions and not others. This last is known as grain oriented iron.
Magnetic properties of iron tend to be somewhat linked to its mechanical hardness. Softer irons tend to be softer magnetically, and vice versa. Iron and steel work harden under stress and strain, and this tends to harden the BH curve too.
This is an extremely fast and superficial overview of what's going on with transformer iron. Tell where it confuses the issue more than illuminates it.
So using a 12V secondary wall wart to drive a 6V secondary wall wart in an attempt to get 240V un rectified would be a big No No ?
I was gonna use a 12v to drive a 9v (wall warts) with the 9v having a higher amperage rating ,would this be to outa bounds safety wise ?
Thats a 25% difference in voltage ,would having the same difference in amperage(but reversed to which wart is greater) pad the safety zone ?
Quote from: Brymus on June 12, 2010, 05:17:04 PM
So using a 12V secondary wall wart to drive a 6V secondary wall wart in an attempt to get 240V un rectified would be a big No No ?
I was gonna use a 12v to drive a 9v (wall warts) with the 9v having a higher amperage rating ,would this be to outa bounds safety wise ?
Thats a 25% difference in voltage ,would having the same difference in amperage(but reversed to which wart is greater) pad the safety zone ?
You would probably - probably - be saved by the fact that wall warts are often in the "small, high resistance primary" category. There's another thing I didn't mention earlier. When the primary saturates, the secondary voltage flattens off at the voltage where the primary saturates. The saturation of the core keeps it from transforming the primary across, so the secondary soft clips at the proportional voltage where the primary saturates.
Let's do some f'rinstances.
If you have a 120:12Vac transformer you're using for a driver, and a 9V:120 you're wanting to use for the high voltage stepup, and although we don't know it yet, the 120:12 driver has a 14V open circuit voltage on the secondary (accounting for primary and secondary resistance sag) and the 9:120 is really a 120:11, for the same reason. So with no loading at all, the best you'll get with a 120V input is 120V * (14/120)*120/11 = 120*14/11 = 153Vac. That gets you at best 153*1.414 = 216Vdc. What actually happens though, is that the driver transformer does sag to 12Vac under load, and the driven transformer sags by 18% when driven backwards just like it would driven forwards. So the 14V driver secondary sags to 12V, it drives the 11V open circuit driven transformer, probably no massive saturation there because the driver transformer can't supply enough voltage and current to make a mess. The driven transformer gets 12V on its 11V winding, and puts out (120/11) times the 12V it's getting in, or 131V open circuit, but under load that sags 18% just like it would the normal way, to get you 107Vac, and that gets rectified to 152Vdc.
So the good news is you don't get meltdown. The bad news is you don't get nearly the DC you thought you'd get because both the resistive losses and the reversal of the "anti-sag" design of the transformers work against you. It may not be as bad as I've guessed in the thought experiment, but it could also be worse, depending on the actual transformers you happen to get. And I didn't even get into the rectification to DC having even worse losses because capacitor input filters cause huge current pulses which cause even more sag in the winding resistances.
I found all this out when I was doing my first back to back transformer setup a couple of decades ago and found out that no matter what I did, I could not get more than about 130Vdc on the output. It took a while to figure out why Mother Nature was thwarting me.
It's a far better idea to get a driven transformer with a dual 120V primary. The other stuff still works against you, but the basic transform ratio now gives you more voltage. Something that works really well is to get a small dual-primary toroid for the driven transformer. You can also use a *third* tranny, a second driven trannie and series the primaries of both driven transformers.
The problem with most small transformer setups is that the winding resistance keeps killing off the voltage you're trying to get.
Transformers above - I don't know, maybe 10W? start having issues with overheating because they have lower resistances.
RG. Thank you for that. So B varies with H correct? and if so does H change with voltage, frequency and current? A higher permeability means you need less power to drive it then? Or are H and B generally independent? If so how do you choose which part of the curve you design around?
Once you saturate the core, what exactly happens? The response flattens out and can no longer produce more secondary current no matter how much current is put through the primary?
Can using flattened out sheets causing grain oriented iron in EI laminated transformers assist in better responses and less coupling into other components (in say a valve amp) by placement and rotation of the transformer?
I've covered the very basics of electromagnetics, just starting to delve further into this stuff as well as other fields of EE.
Thanks RG
If I understand correctly ?
You would Use one 120/12V with 2x 120v and 2x 12v windings to drive 2 trannies 12/120V and wire the two 120v windings from each of the driven transformers in series to get 240v?
Or could you drive two transformers from one 120/12v trns by hooking the two 12v windings in parallel (driven by the first trns 12v winding) and the 120v windings in series ? And just have the VA of the first equal the combined VA of the 2 driven or is that neccasary ?
Sorry if thats redundant or silly questions...
I just dont want to fry anything especially myself !
Quote from: Be-Kind-Rewind on June 09, 2010, 08:00:10 PM
Can you flip a transformer around to step up a voltage? ??? I ask this because I can't find a transformer that'll increase voltage so I wanted to use a 120vac to 12vac and invert it so it takes 12vac and steps it up to 120vac. :icon_idea:
Check these links below... If you have any questions about how they work let me know...
http://www.allaboutcircuits.com/vol_3/chpt_3/8.html
http://www.reuk.co.uk/Making-Voltage-Doublers-and-Multipliers.htm
http://www.aaroncake.net/circuits/inverter.asp
http://en.wikipedia.org/wiki/Voltage_multiplier
I have built a multiplier a while ago.... it took 220 AC and gave an output of 3615 Volt DC with around 10 Ampere Current...
Be extra carefull with that built and when measuring the output of it place a voltage divider in the end with 1W resistors ( value from 500K to 1M ) so that you will burn your multimeter just in case something goes wrong and gives a greater output that you would suspect it would.
Taka care,
Angelo
> use a 12v to drive a 9v ... Thats a 25% difference in voltage
12/9= 1.33, 33%, considerable over R.G.'s guideline.
Yeah, small-stuff probably won't burn the house down. May run for years.
I'm building a porch. Lumber tables say a 2x6 can run 8 feet, I need 9 feet. It will work. May not collapse for years. But why not use 2x8 instead?
> attempt to get 240V un rectified
Don't see how you will get 240V. With a 9V:120V you get 160VAC minus losses (which will be high). If you score a 9V:240V you get 320V, in excess of target.
120V:12V into 12V:240V get you very close to the 240V target.
While 120/240 split windings are now common, if you only have 120V windings, you can use the 120V:12V to 12V:120V into a Voltage Doubler to get 2*120VAC*1.414= 330V DC.
> Transformers above - I don't know, maybe 10W? start having issues with overheating because they have lower resistances.
Also surface/volume ratio. (And frankly commercial pressure.... a utility company will pay a little more for low loss over the years, first-cost is the most important thing in consumer electronics.)
>> explain the underlined statements
> extremely fast and superficial overview of what's going on with transformer iron.
More fast n superficial-
Take a nail, heat red hot, and hammer it out to a "guitar string" while hot.
You'll notice that it is fairly limp, stretches a lot, and breaks before it comes to pitch. However used as a nail, it is stronger than wood and will take lots of abuse.
Take the same iron nail, remove some impurity and add others. Roll it down smaller, then work it through smaller and smaller holes as hard as you can. This works the grain, makes the iron stronger and stiffer. It won't stretch so much and it can be brought up near pitch.
Put a kink in the wire, straighten, then try to bring to pitch. It breaks.
The magnetic properties of iron can be "massaged" similarly to its mechanical properties. You can get the mag curve to rise slow and bend gently (soft-iron nail), or rise fast and break-over abruptly (music-wire). You can make it carry flux better one way than another. And because mag-domain boundaries are weaker than atomic bonds, a highly-tuned magnetic iron can be degraded by some "gentle abuse": straightening from the roll, punching and shearing, etc.
Quote from: panterafanatic on June 12, 2010, 07:48:13 PM
So B varies with H correct?
Correct. The ratio of the change in B resulting from a change in H is permeability. It's the slope of the B-H curve at any specific point on the curve.
Permeability is not constant. It starts low, that "initial permeability" thing, gets higher, then decreases as the curve folds over.
Quoteand if so does H change with voltage, frequency and current?
It's more like the resulting B and permeability vary with changes in H. H is magnetomotive force. The nominal unit is oerstads, but I think of it in terms of ampere-turns. H is what causes the magnetic field to happen. B is a measurement of what field intensity happens for a given MMF.
QuoteA higher permeability means you need less power to drive it then?
A higher permeability means that you get a higher flux density B for a smaller MMF driving the field. Higher permeability means higher inductance per turn. So for a given physical size core and winding area, you can get more inductance, which, for a given frequency and voltage means lower magnetizing current for a given field intensity. It means the price you pay to magnetize the core so it can work as a transformer is smaller if you do everything else correctly. It's more like fewer losses and higher efficiency than lower power. The secondary power is going to be 90+% of the power into the trannie anyway. Higher permeability and as importantly, high flux density before saturation are important. Iron alloys tend to saturate between 12kG and 20kG, with conservative transformer iron designs using the 12kG end for 4% silicon grain oriented transformer steel. Ceramic ferrites - ceramic compositions of magnetic oxides and binders - have lower permeabilities and lower saturation, typically down around 3kG to 4kG. But the particles of ferromagnetic stuff are so small that the eddy current losses are much smaller at high frequencies, which is something we haven't touched on in this discussion. Yet. :icon_biggrin:
QuoteOr are H and B generally independent?
No, the B-H curve is a property of the material. It's like physical strength. Push this hard (H) and it bends this much (B). Push too hard and the material can't stand any more bend and so it deforms (saturates). You set the H by how hard you push (in ampere turns), and the material's B-H curve tells you how much B you got for that much H. Add a little more cobalt or nickel to the melt, or cold-roll the steel and the resulting B-H curve is different.
QuoteIf so how do you choose which part of the curve you design around?
Tricky question. It depends on what you're trying to do. If it's design power transformers, you use the whole B-H curve from + saturation to - saturation and work the core over the whole range. This gives you the widest range of H and B to use to funnel power through. If you're designing a signal transformer, high inductance and low hysteresis losses matter a lot. An input transformer may use only the small region around the 0,0 origin. If you're designing a power AND signal transformer - an output transformer - you're forced to compromise between using as much of the B-H curve as you can, while still not getting into even the beginnings of saturation. If you are forced, absolutely forced to use a DC offset out into the middle of one side of the B-H curve as you do in a single ended tube output transformer, you're stuck. You use as much of the B-H curve in one quadrant as you can, and make the transformer big enough to not saturate. Even then, you have to stick in a relatively big air gap to linearize things, and that drives inductance down, so you have to make the core and windings bigger yet. A single ended output trannie will be about four times bigger than a push-pull output for the same power, given semi-equivalent performance qualities.
Notice that flux density is flux per unit of core area. If you are restricted to a low B, and you have a power target to hit, you may have to use a lot of area to get the thing to pass the right amount of power with a restricted flux density.
But really, I can't possibly type enough here to give you a deep understanding. The questions you outline are about a semester's worth of perhaps junior year level stuff, taught properly.
QuoteOnce you saturate the core, what exactly happens? The response flattens out and can no longer produce more secondary current no matter how much current is put through the primary?
When you saturate the core, the flux density stops changing inside the core for part of the exciting waveform. Since voltage is proportional to the derivative of flux change, the secondary voltage quits changing. The secondary is softly clipped. Yes, I've designed a transformer soft clipper. It's not good, for reasons that will become apparent. So when saturation starts, the secondary voltage quits changing. In the primary, though, the magnetizing current is limited by the primary inductance. Saturation amounts to an actual reduction of inductance. So the primary magnetizing current, which was being limited by the primary inductance, is un-limited. The magnetizing current shoots through the roof. This doesn't hurt the core, but it does cause I-squared-R losses in the primary wire to skyrocket. This sudden heating on exceeding saturation is what kills transformers which are over-volted.
Or under-frequencied. The peak flux density is determined by the volt-time integral on the primary. For constant power line frequencies, we can talk only about the voltages. However, if the primary frequency changes, the volt-time integral is the same, so the voltage changes inversely to the frequency change. This is why 50Hz power transformers are roughly 60/50 the mass of 60 Hz transformers of the same power/temperature rating. More iron and copper windings are needed to keep the flux density down because the time (1/F) of each voltage swing has gone up.
And this is why the magnetic clipper isn't a good idea. It's clipping threshold increases linearly with frequency. Only clips the lowest bass.
QuoteCan using flattened out sheets causing grain oriented iron in EI laminated transformers assist in better responses and less coupling into other components (in say a valve amp) by placement and rotation of the transformer?
Yes, as part of a many-variable complex mix of design criteria.
Quote
I've covered the very basics of electromagnetics, just starting to delve further into this stuff as well as other fields of EE.
You're lucky! There's lots left to learn. :icon_biggrin:
> A higher permeability means you need less power to drive it then?
Losses.
"Power to drive" increases trivially. But a great transformer is 99% efficient, a good one 90% efficient. This means the great tranny heats-up like 1% of maximum output, the good one heats like 10% of maximum output. The difference is probably not in your power bill, but the good tranny will heat 10 times more than the great one.
Ultimately we want to power a load. But ponder the UN-loaded transformer. It is a choke across the power line. Pretend it could be Infinite inductance. Inductive impedance is infinite. No current flows. Now pretend it is 1 Henry. At 60Hz that is a bit over 360 ohms inductive. At 120VAC it will pass about 0.3 Amperes of current.
But in a perfect inductor, all the energy you put in comes out again. The power company gets their electrons back, not even tired-out. What's the problem?
The problem is copper loss. The 1H winding might have 10 ohms pure resistance. The 0.3 Amperes will lose 0.3^2*10= 1 Watt of power. There is additional loss in the utility power lines; not so you care for small stuff, but it Matters over a large distribution net loaded with inductors.
Very small transformers don't have much more than 1H inductance: the small cores mean more turns to get a whole Henry. They may have much more than 10 ohms resistance: more turns on small core force skinny and long wire, high resistance. Say 1H and 100 ohms, that's 9 Watts of lost power. Which in smaller transformers is a lot of heat.
OTOH, because of surface/volume, small trannies cool well relative to what they can deliver. You can find small iron running below 70% full-load efficiency. 10 Watts absorbed from line, 7 Watts to toy, 3 Watts heat in a couple-inch transformer is mighty warm but not a problem.
We can't get significantly better conductors than ordinary copper at any reasonable cost. However irons and steels can be made a lot better with extra work. Taking vacuum or air as "1", a closed loop core of soft iron gives about 100 times the inductance, motor-iron nearly 100 times more Henries, and delicate Permalloy over 5,000 times the inductance. This directly reduces no-load copper loss and heat. Of course the best stuffs are found and sell roughly by "merit". You don't buy the best stuff, but the good-enough stuff for your needs.
While good iron is almost 1,000 times better than air, when you go past "saturation" it stops working like iron and works more like air. When that happens, your "1H" tends to decline toward the 0.001H of an air-core coil, and your no-load primary current tends toward 120V/10ohms 12 Amps and 1,200 Watts heat! So you never want to get too close to saturation. I know that 5,000G used to be a good place to stop. As R.G. says, modern power iron is refined so that over 10,000G is fine. (20KG is a very special case usually reserved for very intense expensive designs.)
As you get close to saturation, the tips of the waves suck more current. While utility voltage is always sine-ish, the line current gets very peaked. Small/cheap near-saturation transformers cause horrible "distortion", but that only affects the power company and their huge total load swamps the ugly current waves.
There are also iron losses. Wrap one turn of conductor around a core. Induction makes about 0.1V across the ends. Now short the ends. That 0.1V across whatever conductor resistance makes a current and a power, dissipated in the turn. Imagine a solid iron core. The outside of the core is a "shorted turn". Iron is not a great conductor, but with normal geometry the resistance of a short broad "turn" may be 0.01 ohms. That's 0.1V at 10 Amps or a whole Watt of heat.
If you use a bundle of iron wire, you get many much-smaller "turns" and lower loss. You also get a lot of gaps, poor filling, which tends to mean longer copper and more copper loss. Slicing the iron like bologna works as good with better space utilization. It is also easier to assemble different size cores with a reasonable number of slice-sizes (stampings), and rolling is effective in further refining the magnetic alignment.
Also some simple irons, like old "Swedish Iron", have lower losses. Turns out a good spoonful of Silicon in the iron reduces its electrical conductivity a lot without great harm to magnetic property. Silicon is a natural impurity in iron, but the amount (and purity) needed raises the cost, so you have 3% and 5% Si transformer steels, depending what you will pay for lower losses. (4% Si covers a lot of uses.)
When mag domains jiggle, they rub, hysteresis, another loss......
That's all "power" transformers. Interestingly, in "audio" transformers most of this does not matter, or is interpreted differently. For full-range response and low loss and small distortion of precious signal, we design for lots of inductance and very low Gauss. Heat is almost never a problem, and saturation is mostly about how much bass distortion we can tolerate. On a power pentode amplifier we have no reserve of current and keep peak Gauss low, which means a somewhat large core with makes heat a non-issue. When driving a small telco core with a good op-amp, as in R.G.'s splitter, we may tolerate 10X load current to whack near-saturation distortion and be able to run much deeper into the bass than you might think.
> The questions you outline are about a semester's worth of perhaps junior year level stuff, taught properly.
I suspect to get some of the answers he's looking toward, with confidence, will need a 10-year apprenticeship with an old-time designer. True, power iron is about at the point that you can load your iron-grade costs into a program, input specs, and let it find the minimum-cost point. Audio could be designed the same way, though there are intangibles and also a brutal HF response problem.
But in DIY we don't count pennies, and most transformer problems can be "solved" by over-sizing. $20 more metal may save $200 of headaches and wear on the abacus.
> motor-iron nearly 100 times more Henries,
Should say: "1,000 more Henries".