Revising the power output rating of an old 25 Hz transformer

[torch]

One of my hobbies is running old model trains. One of my transformers was originally designed for 25 hz, 120v mains, and rated 100 watts (input, I would suspect).

I'm trying to figure out what the theoretical power rating is when used with the modern North American standard 60 hz, 120v supply. I know that it runs cooler than a modern 100 watt transformer. I believe the windings are more numerous but of smaller gauge than a transformer designed for 60 hz, increasing the input impedance. I have found information suggesting that the windings could handle higher input voltage, up to 240vac (with a corresponding increase in output voltage, of course).

I seem to recall reading something years ago that such a transformer could supply significantly higher power than the original rating, due to the robust construction required for 25 hz operation and the resultant cooler operation when fed with 60 hz.

But when I try to apply my limited understanding of transformer theory, I'm left to conclude that the power output will actually drop when only the frequency is increased (higher frequency = higher impedance = lower input current = lower power), which would explain why it runs cooler at 60 hz compared to 25 hz.

Applying the Ohm's Law for inductive reactance formula I=V/(2pi * f * L) and solving for the inductance of that actual transformer, assuming 100 watts at 25 hz, then reversing things to solve for I at 60 hz, I end up with a theoretical de-rating to 41 watts at 60 hz.

Am I doing this right?

[T3sl4co1l]

The current capacity is essentially constant with frequency, being limited by what size wire was used, and the temperature rating of the insulation.

Voltage capacity is proportionally higher, which means VA capacity goes up nearly proportionally.  It's not quite even, because core losses will be higher as well, raising internal insulation temperatures.  This probably won't do much, so you could safely run it at, say, 240VAC instead of whatever it was designed for (probably 117V?), and deliver twice the power (200VA).

One feature which may reduce power capacity is leakage inductance, which manifests as series inductance, acting to limit power at high frequencies.  Traditional 'shell' construction is usually okay into the 100s of Hz, so this isn't a big deal.

Today, bank wound / side-by-side construction is common, probably for cost as well as safety.  This design has significantly higher leakage inductance, so that performance is fairly marginal even at normal line frequency.  This enables small "impedance protected" transformers to exist: they get very hot, but don't catch on fire, under short circuit conditions.

Tim

[torch]

The current capacity is essentially constant with frequency, being limited by what size wire was used, and the temperature rating of the insulation

Ok, I'm having trouble wrapping my head around that. If the current is essentially constant, then the inductance (L) would have to be variable with the frequency?

[skipjackrc4]

The problem here is that you're looking at a transformer like like it behaves linear circuit theory, which it does not.

The primary inductance doesn't change with frequency (not much anyway), but with load on the secondary.  If you measure the primary inductance with an LCR meter when the secondary is open, and then again when the secondary is shorted, the latter will be much lower.

The frequency dependence of a capacitor's VA rating is due to core saturation.  This is a complex topic, but it occurs when the flux in a transformer's core extends beyond what the core can support.  This is like what happens to an amplifier when the output signal exceeds the supply voltages.  Now keeping that in mind, let's talk about magnetic permeability.

The inductance of a coil is proportional to a material parameter called permeability, which describes a material's ability to concentrate magnetic flux.  Air has a permeability of 1.  Magnetic steel has a permeability of 100-1000.  Values of over 10,000 are common for specially designed alloys.  The important thing is that the inductance of a coil with a steel core is much higher than an identical coil with an air core.  This is why steel cores are used in transformers--you get more magnetic coupling between the primary and secondary windings, which results in higher efficiency. 

OK, now let's go back to magnetic flux.  Flux is proportional to the integral of applied voltage.  In AC (like all transformers use), you are applying a positive voltage and a negative voltage in alternating cycles.  During the positive cycle of the voltage waveform, the flux in the core gets steadily higher.  During the negative portion of the waveform, the flux is removed from the core and goes negative.  In an AC system, the net flux must sum to 0.  Because flux is the integral of applied voltage, we want to make sure to remove flux from the core before it reaches the saturation point.  In other words, a positive (or negative) voltage can't be applied to the core for too long of a time without causing saturation.  The flux must be removed by an opposite polarity voltage.  In a transformer designed for 60 Hz, the core will be designed to avoid saturation at [your regional mains voltage] at 60 Hz.  At 50 Hz, however, the voltage may be applied for too long before changing polarity, resulting in too much flux and thus saturation.  If a transformer is designed to operate at 25 Hz, it will have no problem at all running at 60 Hz. 

Now, why does a 25 Hz transformer run cooler at 60 Hz?  The key to tying together everything from above is that a saturated core has a lower permeability than an permeability core.  MUCH lower.  Lower permeability means lower inductance.  Lower inductance means more current draw on the primary.  Again, MUCH more.  Current through the resistance of copper wire in the winding = heat.

Here is an experiment you can try if you have access to a variac and a mains rated transformer.  Connect the output of the variac to the primary of the transformer, and leave the transformer's secondary open.  Measure the current flowing into the primary.  Start the variac at 0 V.  You will have 0A flowing.  Now increase to 30V.  You will have some current flowing, called the magnetization current.  This is the current that flows through the inductance of the primary.  Leaving the secondary open makes the primary look like a regular inductor (If you put a load on the secondary, this is no longer the case).  At 30V, let's say the magnetization current will be 50 mA.  Now increase to 90V.  The core starts to saturate a little bit, but not much.  The current now might be 180 mA.  Now increase to 120V.  We have a little more saturation now, but it's still not too much.  Let's say we're drawing 250 mA.  Now increase to 130V, which is above the rated voltage of our transformer.  Current now is 1A!  Why?  Because the core saturated and the primary inductance became much lower.  If we go to 140V, current might be 10 A.  If the transformer is only rated for 5 A, then you have a serious safety hazard on your hands.  If the transformer is rated for 20A, it will still operate as normal, just must hotter because of the excess current draw.

Does this more or less answer your question?  This is a highly simplified overview, but I think it gets the point across.

I offer this information with the disclaimer that I'm a microwave guy and it's been a long time since I've dabbled in power magnetics. 

[calexanian]

An empirical view....

The lower the frequency of operation for a transformer the higher the primary inductance to maintain proper magnetizing force when calculated against the permeability and flux capacity of the core material.

Ok..... So a 25 HZ transformer must have a significantly higher inductance than a 60 hz one. Simple enough.

Now... With more turns we have a higher amp turn factor. There is a sliding scale between primary impedance, leakage current, magnetizing force, permeability, and output coupling.

With this being said operating at 60 hz the net impedance of that primary will be much much higher. That will narrow our operating window and actually give us less effective flux to work with. We are impedance limited rather than core flux capacity limited in this case. This is actually one of the principal methods of operation of inherently limited class 2 transformers. The other being a fuse buried in it somewhere.  In other words at the higher frequency we can only pull so much current through the primary at any given time.  True we are drawing less primary current just sitting there with no load and will have less heat rise but we struggle to deliver current under load. This is one of the reasons an audio type transformer rated at 50 watts is significantly larger than a filament or rectifier type transformer of that same 50 watts. One weighs about a pound or so, and the other if properly made about 5 pounds.

Just some ramblings.

[T3sl4co1l]

Remember, the impedance seen at the primary is the sum of magnetizing current (depends on transformer winding and core, doesn't depend on load) plus load current.  Load current does not depend on primary frequency, only on what the load draws.

Tim

[torch]

The problem here is that you're looking at a transformer like like it behaves linear circuit theory, which it does not.

The primary inductance doesn't change with frequency (not much anyway), but with load on the secondary. 

Remember, the impedance seen at the primary is the sum of magnetizing current (depends on transformer winding and core, doesn't depend on load) plus load current.  Load current does not depend on primary frequency, only on what the load draws.

Doh! I just had one of those "Why didn't I think of that?" moments. It's so obvious in retrospect. And it only took several of you to soften my thick skull with a metaphorical 2x4 before it sunk in. I was comparing apples to oranges: Input current varies with load current.

So the half-remembered claim that the power handling capability of a transformer increased by switching from 25 hz to 60 hz likely included the caveat that the input voltage was also increased at the same time. (In my defense, I was still pretty young when our area finally changed over to 60 hz).

Voltage capacity is proportionally higher, which means VA capacity goes up nearly proportionally.  It's not quite even, because core losses will be higher as well, raising internal insulation temperatures.  This probably won't do much, so you could safely run it at, say, 240VAC instead of whatever it was designed for (probably 117V?), and deliver twice the power (200VA).

We are impedance limited rather than core flux capacity limited in this case. This is actually one of the principal methods of operation of inherently limited class 2 transformers. The other being a fuse buried in it somewhere.  In other words at the higher frequency we can only pull so much current through the primary at any given time.  True we are drawing less primary current just sitting there with no load and will have less heat rise but we struggle to deliver current under load.

Ok, so there is a window of efficiency that the designer aims for, based on the design frequency. The upper limit of that window (impedance) means that the power handling capability does not double when the frequency and voltage are doubled.

In this case, dealing with an increase of tens of hz, and maintaining the input voltage, the available power may be slightly decreased, but will still likely approach the original 100 watt (or more correctly, VA) rating.

BTW: The plate indicates a 115vac input rating, although it is unlikely voltage fluctuated less than +/-10v in 25hz mains 50 miles from the hydro-electric dam in rural Ontario. And I doubt there is any sort of fuse in the windings. This thing would make any regulatory or certification agency run and hide under the bed! Mains powered, metal and die-cast construction, ungrounded, unpolarized plug, all in a children's toy -- what's not to love? 

Thanks to all for the lesson.