Still trying to understand transformers

[MichaelJHuman]

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?

[zigzagflux]

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?

[MichaelJHuman]

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.

[star882]

Note that higher frequencies allow for smaller transformers. That's how PC power supplies pack a surprisingly high power rating into a small transformer.

[BudP]

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

[megajocke]

Originally Posted by zigzagflux

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 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.

[mige0]

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

[MichaelJHuman]

Originally Posted by megajocke

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.

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.

[megajocke]

Originally Posted by MichaelJHuman

What is the main factor which makes a wall wart put out so little power compared to a high power transformer? Copper related resistance?

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.

[MichaelJHuman]

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?