Can you flip a transformer around to step up a voltage?

[R.G.]

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.

and 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.

A 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. 

Or 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.

If 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.

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?

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.

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?

Yes, as part of a many-variable complex mix of design criteria.

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. 

[PRR]

> 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.

[PRR]

> motor-iron nearly 100 times more Henries,

Should say: "1,000 more Henries".