Power Transformer Basics

[R.G.]

The following is excerpted from the forthcoming article "The Technology of Transformers" at GEO (http://www.geofex.com) and is copyright R.G. Keen 2005. All rights reserved. It is placed here by express permission. It may not be copied, reposted, modified, served from other web pages or made into derivative works without written permission of the author. Please read the provisions of the Digital Millenium Copyright Act at the US Patent, Copyright, and Trademark web site.
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Transformers are at once one of the simplest kinds of electronic components and also most mysterious. Getting past the "mysterious" to the simple is not all that hard, but takes a little explaining.

The important concepts to grasp with transformers are few. They are:
1. The Ideal Transformer
   An Ideal Transformer (IT, since I'm a lazy typist) is a transformer that is perfect. It has infinite frequency response, DC to daylight, and converts AC voltages from a primary to a secondary perfectly in the ratio of its windings. So for a transformer with a winding ratio of ten to one from primary to secondary, if you put 10.00000 volts on the primary, you get 1.0000000 V on the secondary. If you suck out 1000A on the secondary, it's still 1.000000V, assuming that you also drive the primary with something that can provide the 10.000000V and 100A. It is perfect - no losses, just perfect transformation in the ratio of the windings.
2. Transformation ratios
   Every transformer tries, and an IT does transform voltages in the ratio of its windings, and currents in the inverse of its winding ratio. This is Mother Nature butting in again, and telling us about the First Law of Thermodynamics - energy is neither created or destroyed without nuclear or quantum reactions being involved. So the energy in and out must be either perfectly equal (for the IT case) or the energy in must be greater than the energy out plus losses to heat and radiation in the case of real, ordinary transformers which have losses.
  This lets us do some interesting things. If the input and output voltages are the same, then the currents are the same. If the output voltage is half the input voltage, then the output current is *always* twice the input current.
3. Imperfections
  Nothing in the macroscopic world is perfect, no matter what you think about that cute young lady or gentleman over there. Real transformers differ from ITs in that they have losses. This is obvious if you think about it. Wind a coil from wire, and it will inevitably have some resistance, which converts current flow to heat. That's true in transformers.

3.a. Winding resistance
The primary winding has some resistance, and so does the secondary. You can measure this with an ohmmeter. Just hook up the leads and read the resistance. Those resistances each eat a bit of the applied voltage from the winding they are part of, proportional to the current that flows.

In the primary, the winding resistance eats a bit off the primary voltage. If you have a 120Vac primary and it reads 10 ohms, then if it conducts 1A, there is only 110Vac left to transform. The resistive losses get their bite *before* you can transform anything to the secondary!!

On the secondary side the same thing happens. If you have a 120V, 10 ohm secondary, and it puts out 1A, you get only 110V, because the winding resistance eats its share before anything comes out the transformer.

In truth, both these things happen at once. If you have a 120 to 120V isolation transformer and both windings have a resistance of 10 ohms, and you pull 1A out of the secondary with 120V on the primary, here is what happens:
- The 1A out has to come from 1A in, so the primary current is 1A. That drops the effective primary voltage to 110V.
- The secondary gets its 1 to 1 voltage transformation, so it sees the 110V.
- The secondary resistance eats its 10V, too, so the output voltage is only 100V!

Dang! We lost 20V in the process! How much power did we lose? We're getting 100V*1A = 100W out.  We're putting 120V*1A = 120W in, so Mother Nature's First Law of Thermo says that we're losing 120W-100W = 20W of heat, noise, or radiation. A transformer built like I've just used for illustration will get HOT under these conditions. If it's not built to dissipate this much heat, its internal temperature will go up until it either reaches thermal equilibrium or until something breaks and we have smoke and flames.

But look what happens at lower currents. If the current is zero - that is, the secondary is open - then the primary current is zero as well, and neither the primary or secondary resistances get to eat. The primary voltage is 120V and this is transformed to the secondary as 120V. This is the no-load voltage on the secondary. At zero load, real transformers approach the perfect voltage transformation of ideal transformers.

3.b. Core Losses
Losses are even worse than wire resistance. We have to pay a toll for using the magnetic field to do voltage transformation.

To do transformation the primary and secondary coils have to be hooked together by a magnetic field. That M-field is what moves energy from one to the other. So we have to pay to set up the M-field. The magnetic field has to be supplied energy from the primary, and this is expressed as an inductive term and a resistive term. The inductive term is the amount of current that the primary windings let flow through ignoring the secondary entirely. That is, if you measure the primary winding as though it were an inductor with the secondary open, you get an inductance. The primary lets through current in proportion to that inductance by I = V/(2*pi*L).

So if the primary inductance is 10H and the applied AC primary voltage is 120V, then the magnetizing current or no-load current is I = 120/(2*pi*10) = 1.9A. That's a terrribly large magnetizing current, by the way, so I picked a bad example out of the air.

Transformer designers deliberately design transformers to have tiny magnetizing currents, as you'd guess. For a transformer with a 100ma primary current rating, you might expect to be paying maybe 1 to 3 ma of magnetizing current.

If we relate primary inductance back to our IT, the primary inductance of a real transformer looks just like an inductor of equal value connected across the primary of the IT.

Hey!! We could model the real transformer as an IT, with a resistor in series with the primary equal to the primary winding resistance and another in series with the secondary; then we put an inductor across the primary just inside the winding resistance. If we run the numbers, the model turns out voltages and currents on primary and secondary equal to the voltages and currents on the real-world transformer!!

And that's where we're headed. We're going to understand the classical model for the real-world transformer using the IT as a base.

Interestingly, the only losses from that current are in the primary winding resistance. Neither inductors nor capacitors have any heat losses, as their voltage and currents are at right angles to one another and do not overlap to cause heat losses. Only in-phase current and voltage cause heat losses.

There is one more item of loss in a real transformer, and that's core losses. The core of a transformer is being whipsawed magnetically, run magnetically from almost saturation in one magnetic direction to almost saturation on the other direction. This continual about-face of M-field causes currents to flow in the core material, which is metal (for our power and audio transformers at least). These currents are in the form of tight little short circuited loops and they eat energy just like little parasitic secondaries. That's why transformers are laminated out of thin metal - to force the eddy current loops to be loooonger than they would be in a solid metal block, so the resistance of the loop is bigger and the losses are smaller. As a rule of thumb, the higher the frequency the transformer does, the thinner the laminations should be. That's why we use ferrites for radio frequencies - the "laminations" are literally magnetic dust particles, tiny and with low losses. Not surprisingly, core loss is frequency dependent. It's also core material dependent (well, big duh!) and magnetic-drive dependent. Drive the core into saturation and the core loss skyrockets. It's also temperature and phase-of-the-moon dependent.  OK, I made up that phase-of-the-moon stuff. But it might as well be.

How do we integrate core losses into the model? The core losses are like a nonlinear resistor strapped across the primary in parallel. Good transformer design makes core loss well under 1% of the full load power of the transformer. The core losses are accounted for in the no-load current.

4. Multiple secondaries
What happens with multiple secondaries?

Well, OK, we gotta think of what happens with one secondary first.

Think of it this way. The primary voltage sets up a magnetic pool of energy. Each secondary has a straw to sip from the magnetic pool, that straw being its transformation (winding) ratio and its wiring resistance. Suck M-field from the pool and the primary instantly replenishes the pool from the energy available in the primary circuit.

Actually, what's happening at a more real level is that the primary inductance is opposing the voltage-force on the primary. If some of the magnetic energy is sucked out the secondary, the primary inductance can no longer hold the primary energy out as well, and an amount of energy equal to that sucked out by the secondary is instantly let flow in by the weakened M-field. The primary voltage and inductance have a balance set up that the secondaries unbalance. The secondary energy in effect flows through the M-field but does not change the M-field in any substantial way.

With two secondaries, both secondaries are sucking through their transformation/resistance straws from the same pool, and the primary voltage/inductance balance is making up the losses.

So to see what happens with two secondaries, we model both secondaries by their transformation ratio and winding resistance. We compute the amount of primary current that would flow if each secondary was sucking by itself, then add the two primary currents. That current plus the semi-invariant magnetizing current and core losses is what flows in the primary.

Works for as many secondaries as you care to add.

5. Power rating

How do you determine what the power rating of a transformer is?

Here's the key: the power rating of a transformer is the power it can put out when it's primary voltage and current are as designed and it's getting just hot enough that its winding insulation is just barely not being damaged by the heat and its core is not hot enough to lose its magnetic properties. In practical terms, the insulation melting is the temperature limit, and that one temperature determines how much iron and copper you have to use to keep losses down to a level that will keep the temperature below the limit.

Circular? You bet. That's why the power rating/ thermal design of transformers is **hard**.

As usual, for you, the user, there are some short cuts. You don't often design transformers, so you just want to know how much this here lump of iron and copper will do. So try it. Let it heat up. The lowest temperature class used in modern transformers is Insulation Class A, which has a limit of 105C. That's 221F, and sufficient to boil water. But that's the hot spot temperature inside the transformer where you can't get to it to measure. You can only measure the outside temperature.

Actually there are ways for you to measure the inside, but let's make this simple. It is one of those accidental goodies that Mother Nature sometimes gives us that you as a human of relatively standard design will not voluntarily keep your index finger in contact with a metal surface if the metal surface is hotter than 130F/54C. If an iron core transformer is not too hot for you to touch with your index finger pad, it's below 130F, and that implies that the core of the transformer is below 105C. Notice that it may take a largish ten pound and more transformer **hours** to heat up fully, though.

6. Little transformers

In the effects world, we deal with little power transformers. Small powers, and ideally small size and weight.  There are some special considerations with little transformers.

The number of turns needed on a primary to make enough inductance to keep excessive magnetizing current from flowing (that is, the number of turns needed to set up the magnetic balance pool to just the right depth) depends on the area of the core the wire is wound on and the length of the magnetic path through the core. Both of these are small in physically small transformers. That means that a small-power transformer has to have a lot of turns per volt of applied primary voltage to make enough inductance to keep magnetizing current down to some acceptable level.

Lots of turns in a physically small package means thin wire, and that means a lot of winding resistance. Small transformers have high turns per volt, high winding resistance, and higher losses on a percentage basis than their bigger brothers.

There is a concept in the transformer world called "regulation". This is NOT the active regulation that a voltage regulator does. It is rather a passive absence of losses. It works like this. If we put rated votlage on a transformer winding, that sets up the requisite magnetic pool. We can then measure the primary and secondary voltages and find that they are identical to the winding ratios to a high degree of precision. If we then pull enough current through the secondary to get the insides to full rated temperature at the hottest point inside, that's all the load we can non-destructively pull out, and is full load/power. At full power, the losses in the primary and secondary winding resistance get subtracted from the available voltages, so the secondary output voltage is lower than it was at no load.

"Regulation" for transformers is the percentage loss from no load to full load on a secondary.  A transformer with a 10V secondary that puts out 10.0V at no load and 9.0V at full load loses 1V, or 1/10 of its voltage. This is a 10% regulation transformer.

Sometimes it's expressed as no-load voltage and full load voltage, which is more useful. One small transformer I happened to look at recently, the Amveco 7040, had two "7v" secondaries that produced 0.714A at full load. The no-load voltage was specified as 8.3V. What the maker was telling you was that he put enough extra voltage into the winding so that by the time you had pulled full rated current through the winding, it would sag down to the specified voltage. The "regulation" in this case is 15.7% ((8.3-7)/8.3) . Regulation can be brutal on small transformers in the one to 10VA class, right where we're interested in them.

7. What's a primary?

It's a winding. The insides of the transformer don't care what winding you call a primary as long as whichever winding you use as a primary sees no more than the open circuit  voltage it's designed for.

If you put a higher voltage on any winding than it's designed for, this overdrives the internal magnetic field and the M-field can no longer balance out the external drive. HIGH  currents can and do flow in the primary, limited only by the primary winding resistance - which the transformer designer deliberately tried to keep little.

This often leads to an unintentional pyrotechnical display as the heat vaporizes the internal insulation, sets fire to the layer insulation, and melts the windings until the wall-socket AC breaker blows or some other limiting event happens.

So we won't do that. But other than that, we can use any winding as a "primary".

That's the origin of the back-to-back tube transformer. If you have a no-load 120Vac to 7Vac transformer rated at 6.3V and 1A, you can run it backwards by putting 7Vac into the "secondary" and get 120Vac no load out of the "primary". Notice that the only practical way of doing this is to drive it from another transformer secondary with its own regulation losses - but you already know how to calculate those losses.

The "120Vac" you get out  will be decreased by the regulation losses of both transformers. If one small transformer's regulation can be bad, two in series can be brutal. But is is all calculable.

To use a small power transformer, read the maker's data sheet. If you don't have that, measure the winding resistances and then the no-load voltage ratio. When you've done that, calculate the voltages and currents and you'll get a really good idea whether you can use the transformer or not. If you do, hook it up under full load and "measure" it's temperature with your finger. If it doesn't get too hot and the voltages and currents are OK, you have a working design.

[toneman]

what?
no pictures?

[Bill Bergman]

hmmmmm....enlightening

[bwanasonic]

what?
no pictures?

I know you are joking, but reading R.G.'s post made me think I am similarly  *visually oriented*. On technical topics, by brain tends to *brown out* without some visual stimuli to accompany the text. I have no problem wading through vast swaths of prose, but "left brain" stuff like this is hard for me to digest without pictures. I should put my backgound as an artist and illustrator to use, and make some diagrams from RG's wonderful post, for those of us who share this learning style.

Kerry M

[brett]

Hi.  I've just skimmed the article (I'll read it in full tomorrow at work).
Thanks RG.  

Now I'm no expert, and I rig up some terrible messes sometimes, but my experience with cheap power transformers has been very good.  They seem to be under-rated and forgiving.  Take, for example, my shameful habit of using transformers back-to back to get about 210V out from the 240V supply.  Even with little, $10 30VA transformers, I get 200V to 220V out with a 20W load.  I've never noticed significant heating in the transformers (at least not above body temperature).  I find this setup perfect for small tube amps, such as the Marshall 18W clone, and costs 1/4 (yes, 1/4 !!) what a Hammond or similar specialty transformer costs.

Anyway, thanks for the article, RG.  There's nothing like some good theory to turn experience into knowledge.

cheers

[R.G.]

Sorry about the no pictures. Like I said, it's an exerpt from the article.

The artwork for any given article takes (me at least) longer than the text. The text is always just under the surface of my conscious mind, so spinning it out is a matter of typing up what's already there. The pictures are too, but it's much slower to produce artwork that's computer ready, for me at least. Sometimes I just give in and draw it by hand. That's quicker, but messier than computer-drawing.

In reality, I see the voltages, currents and fields interacting inside my head. But there's no way I can draw that out, not having the resources of Industrial Light and Magic Inc available to me. It's like I was explaining in the polemic about magic - each person's mind makes a fully-detailed model of the external world inside their head, based on the info from the senses.

But the model doesn't have to be limited to what the senses bring in. This is the basic premise of visualization - it's a side effect/extension of the basic ability to model the external world. The visualization models are (usually) less vivid than the external-world model because they're not continually reinforced by sensual data.

It's my theory that this side-effect/extension of real-world modelling is responsible for hallucination, ghosts, ESP, etc. A person's mind under some chemical or mental stress creates an extension to the real world model that includes the extra features. It's also what makes robotic vision and operation so hard. The problem to solve is not to gather the sensory data - that's trivial. The hard problem is to make the internal world-model. We don't even know how to start describing the world model, being limited to living inside our own world-models as we are.

[Bill Bergman]

Whew!!!
That's way out there R.G.! :shock:
If you can sketch something by hand on paper, I could probably draw it up for you on the pc, athough probably not rendered in 3D or animated.

[barret77]

wonderful, as always.