how to estimate transformer sag under load

Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.
I am developing a spreadsheet to do some requirement calculations for linear unregulated power supplies. This will take into account a variety of factors that lead to demand on the power supply, like amplifier output power, power dissipated as heat, voltage lost to the diodes of the rectifier, etc.

One thing that I have not been able to figure out, and have not found much info on, is how to estimate the voltage sag for a transformer of a given VA rating or winding resistance under load. The problem I am facing is that I can calculate the requirements for the transformer (secondary voltage and current) under full power, however, only for very well characterized transformers will these conditions be known. More likely the information that will be available for the transformer will consist of a VA/power specification and a no-load voltage for the secondary.

It would be great if I could say "the minimum required transformer for this power supply is #VA and the secondary voltage AT NO LOAD that is required will be X. What I would need to do in order to make such a statement is back calculate the no load secondary voltage from the loaded voltage requirement for the secondary, e.g. predict how the secondary voltage will sag under load.

Any ideas of how I could go about this?

Is this really feasible, e.g. are transformers so different that one model with a VA rating identical to another from a different manufacture will perform completely differently because one is under rated or over rated compared to the other???

-Charlie
 
Sounds like you are interested in the impedance of the transformer. It can be measured fairly easy. This is done by short circuiting the secondary, and measuring the voltage on the primary necessary to pull rated secondary current (a variac is needed for this test- it will be somewhere between 10 and 20V for a 120V primary).

Once you have this voltage, %Z = applied voltage/rated voltage*100.

Assuming you will want all values referred to the secondary side, you determine Zbase on the secondary:

Zbase = Voc^2/VA
where Voc=open circuit secondary voltage at rated primary voltage
and VA is rated VA

Then Zmodel = (%Z/100)*Zbase

The model of the transformer then becomes a perfect voltage source of value Voc and output resistance Zmodel.
 
Sounds like you are interested in the impedance of the transformer. It can be measured fairly easy. This is done by short circuiting the secondary, and measuring the voltage on the primary necessary to pull rated secondary current (a variac is needed for this test- it will be somewhere between 10 and 20V for a 120V primary).

Once you have this voltage, %Z = applied voltage/rated voltage*100.

Assuming you will want all values referred to the secondary side, you determine Zbase on the secondary:

Zbase = Voc^2/VA
where Voc=open circuit secondary voltage at rated primary voltage
and VA is rated VA

Then Zmodel = (%Z/100)*Zbase

The model of the transformer then becomes a perfect voltage source of value Voc and output resistance Zmodel.

OK, this is super helpful. Let me try one example calculation - Antek provides measurements of their products. For instance for model AN-1225, from the datasheet:
http://www.antekinc.com/pdf/AN-1225.pdf
We have the values:
voltage on the primary necessary to pull rated secondary* current = 8.4V
* NOTE: they measure voltage needed to reach rated primary current, so I will use that value here
%Z = applied voltage/rated voltage*100 = 8.4/115 = 7.3%
(from datasheet) Voc = 25.1 V; rated VA = 100
Zbase = Voc^2/VA = (25.1)^2/100 = 6.3
Then Zmodel = (%Z/100)*Zbase = 0.073*6.3 = 0.46 ohms

Using the model of a 25.1 V voltage source with an output (source) resistance of 0.46 ohms, if there is a demand on the transformer of 3.9 amps, there will be about 1.8V lost across the output resistance, and this should be subtracted from the open circuit source voltage of 25.1 V of the model to get the effective secondary voltage, e.g. about 23.3 V. This compares favorably to their measured value (see datasheet) of 23.2 V.

Is that correct what I have calculated above?

-Charlie
 
Sounds like you are interested in the impedance of the transformer. It can be measured fairly easy. This is done by short circuiting the secondary, and measuring the voltage on the primary necessary to pull rated secondary current (a variac is needed for this test- it will be somewhere between 10 and 20V for a 120V primary).

Once you have this voltage, %Z = applied voltage/rated voltage*100.

Assuming you will want all values referred to the secondary side, you determine Zbase on the secondary:

Zbase = Voc^2/VA
where Voc=open circuit secondary voltage at rated primary voltage
and VA is rated VA

Then Zmodel = (%Z/100)*Zbase

The model of the transformer then becomes a perfect voltage source of value Voc and output resistance Zmodel.

I've got one more question about the above procedure - what happens when you don't know the "rated VA" for a transformer? For instance, let's say I have some random transformers around that I know have about the right secondary voltage, but are lacking specs or manufacturer info, were pulled from OEM equipment, etc. How can I estimate or measure its VA rating?

Apart from that, it looks like you can do this procedure on any transformer that you can get your hands on in order to create the model of the secondary.

-Charlie
 
OK, should have searched the forum first.

It seems that there are various way to estimate (guesstimate is more like it) the VA rating of your transformer. These include:
Comments?

-Charlie
 
Well, let's back up a little bit.

Assume you don't know the VA rating of the transformer. You want to use it. How can you draw any current from the xfmr unless you make some assumptions about the rating? If you intend to use the unknown transformer at 12V, 1A, you made an assumption that it was capable of 12VA, right?

What I'm getting at is the procedure is actually independent of the true VA; it is dependent on the assumed VA. Normally, you have the ratings of the transformer, therefore the true and assumed VA's are the same, so we can load the xfmr to its full rating confidently.

Go through the math assuming a 100VA unit, then a 75VA unit. Pick any secondary voltage. You will find the method provides the same model of impedance. It's ALL based on an assumed VA and assumed primary voltage. From there, secondary is measured, and Z is measured.

That addresses the method, but doesn't answer your fundamental question, which is "how do I approximate the VA of an unknown transformer?" This is a completely different question, and one that I don't have a good answer for. You could load it down and measure temperature rise. You could get an approximation based on core size, or assume that % regulation does not exceed a certain amount based on experience with other units. Difficult to be certain, but in my mind there is no 'true' VA rating for any transformer. They reach their limit based on temperature, not math.
 
Well, let's back up a little bit.

Assume you don't know the VA rating of the transformer. You want to use it. How can you draw any current from the xfmr unless you make some assumptions about the rating? If you intend to use the unknown transformer at 12V, 1A, you made an assumption that it was capable of 12VA, right?

What I'm getting at is the procedure is actually independent of the true VA; it is dependent on the assumed VA. Normally, you have the ratings of the transformer, therefore the true and assumed VA's are the same, so we can load the xfmr to its full rating confidently.

Go through the math assuming a 100VA unit, then a 75VA unit. Pick any secondary voltage. You will find the method provides the same model of impedance. It's ALL based on an assumed VA and assumed primary voltage. From there, secondary is measured, and Z is measured.

That addresses the method, but doesn't answer your fundamental question, which is "how do I approximate the VA of an unknown transformer?" This is a completely different question, and one that I don't have a good answer for. You could load it down and measure temperature rise. You could get an approximation based on core size, or assume that % regulation does not exceed a certain amount based on experience with other units. Difficult to be certain, but in my mind there is no 'true' VA rating for any transformer. They reach their limit based on temperature, not math.

I don't follow you in the paragraphs 1 thru 3 - if I mis-estimate the VA rating, this changes the model? No?
 
transformer VA rating

1. transformer VA is temperature related, what is the temperature rise your traffo can tolerate without betting burned out...

2. transformer VA, is directly related to the copper wires used winding the coils, the bigger the cross-section more current can be drawn for a given sag....anywhere from about 300 to 700cm/ampere can be used in the design...

3. transformer VA, estimated using the cross-section area of the core:

VA = (A*5.58)^2, where A = Cl x stack x 0.95, dimensions in inches, Cl is center leg also in inches, source RDH4, chapter 5, page 235....
 
I don't follow you in the paragraphs 1 thru 3 - if I mis-estimate the VA rating, this changes the model? No?

No, the model is based off the assumed VA rating. Called 'per unit'.

Run through an example, with convenient values:

Assume 1000 VA transformer (this is your guess)
Measure open circuit voltage with 120V applied to primary, you get 100V.
This makes Zbase = 100^2/1000 = 10
Put a variac on the primary, and run it up until you get rated secondary current. Again, your assumption is this is a 1000VA xfmr, so you want to pull 10A secondary current.
Your measurement is 7.5V.
Therefore %Z = 7.5/120*100 = 6.25%
Therefore Zmodel = 6.25/100 * Zbase = 0.625 ohms
Your model is a 100V voltage source with output impedance 0.625 ohms.

Now, let's say you actually thought this was a 2000VA transformer. Whether you are correct or not is out of scope of this specific discussion. But you will be testing the exact same transformer.

Measure open circuit voltage, you get 100V. No secret there, right?
Zbase = 100^2/2000 = 5
Run the short circuit test, whereby you are looking for 20A secondary current - that is your rated current based on your assumed 2000VA rating.
Your measurement will be 15V.
%Z = 15/120*100 = 12.5%
Zmodel = 12.5/100 * 5 = 0.625 ohms
Your model is identical, even though you assumed different VA's.

Obviously, you can't go nuts with the testing and expect perfect results. If you have a 50 VA xfmr and attempt to call it a 1000 VA unit, your short circuit test will run into problems, as you are running secondary current significantly higher than what it is rated for, and surprise! your %Z ends up at 30-50%. That is a good sign your transformer is overloaded; only the tiniest units actually run at %Z above 15%.
 
I am developing a spreadsheet to do some requirement calculations for linear unregulated power supplies. This will take into account a variety of factors that lead to demand on the power supply, like amplifier output power, power dissipated as heat, voltage lost to the diodes of the rectifier, etc.

One thing that I have not been able to figure out, and have not found much info on, is how to estimate the voltage sag for a transformer of a given VA rating or winding resistance under load. The problem I am facing is that I can calculate the requirements for the transformer (secondary voltage and current) under full power, however, only for very well characterized transformers will these conditions be known. More likely the information that will be available for the transformer will consist of a VA/power specification and a no-load voltage for the secondary.

It would be great if I could say "the minimum required transformer for this power supply is #VA and the secondary voltage AT NO LOAD that is required will be X. What I would need to do in order to make such a statement is back calculate the no load secondary voltage from the loaded voltage requirement for the secondary, e.g. predict how the secondary voltage will sag under load.

Any ideas of how I could go about this?

Is this really feasible, e.g. are transformers so different that one model with a VA rating identical to another from a different manufacture will perform completely differently because one is under rated or over rated compared to the other???

-Charlie

once you determine the full load voltage and currents required by your amplifier, you can then draw up the Thevenin ideal voltage source so that the impedance required for a given set of no load voltage can be known....

it is this impedance that is critical, once you have it figured out, you can then look for a suitable transformer or design one that meets your impedance criteria...

yes, different manufacturers will have different sets of impedances in their transformers...
 
Now if you want a little more accuracy, you model the impedance more accurately, as inductive and resistive impedances which are orthogonal to one another. We can look at the Antek transformer you referenced.

The load losses are given for you as 7W. On the basis of nameplate 100VA, %R = 7%

Impedance voltage is given as 8.4V, which gives %Z = 8.4/120*100 = 7%

Set up your impedance triangle, %Z^2 = %X^2 + %R^2
For this unit, you get a very unexciting result of %X=0. Therefore X/R=0.
What this implies is the vast majority of transformer impedance is due to winding resistance, not leakage reactance. This is not too surprising for a toroid, which are purchased specifically for the low leakage.

Had you measured a larger and/or EI core transformer, your leakage reactance becomes measurable, and begins to increase the X/R ratio of the transformer. This needs to be modeled as such when you want accuracy. However, for diyAudio purposes, assuming pure resistance is more than adequate.

It's not until you get to around 50 kVA that X/R ratios increase to 2, and by 3000 kVA they are near 6. At that point the majority of impedance is reactance, not resistance. Between 100VA and 50kVA the X/R ratio is somewhere between 0 and 2. Whether you want to simulate it or not is up to you; for most purposes just measuring %Z is sufficient.
 
No, the model is based off the assumed VA rating. Called 'per unit'.

Run through an example, with convenient values:

Assume 1000 VA transformer (this is your guess)
Measure open circuit voltage with 120V applied to primary, you get 100V.
This makes Zbase = 100^2/1000 = 10
Put a variac on the primary, and run it up until you get rated secondary current. Again, your assumption is this is a 1000VA xfmr, so you want to pull 10A secondary current.
Your measurement is 7.5V.
Therefore %Z = 7.5/120*100 = 6.25%
Therefore Zmodel = 6.25/100 * Zbase = 0.625 ohms
Your model is a 100V voltage source with output impedance 0.625 ohms.

Now, let's say you actually thought this was a 2000VA transformer. Whether you are correct or not is out of scope of this specific discussion. But you will be testing the exact same transformer.

Measure open circuit voltage, you get 100V. No secret there, right?
Zbase = 100^2/2000 = 5
Run the short circuit test, whereby you are looking for 20A secondary current - that is your rated current based on your assumed 2000VA rating.
Your measurement will be 15V.
%Z = 15/120*100 = 12.5%
Zmodel = 12.5/100 * 5 = 0.625 ohms
Your model is identical, even though you assumed different VA's.

Obviously, you can't go nuts with the testing and expect perfect results. If you have a 50 VA xfmr and attempt to call it a 1000 VA unit, your short circuit test will run into problems, as you are running secondary current significantly higher than what it is rated for, and surprise! your %Z ends up at 30-50%. That is a good sign your transformer is overloaded; only the tiniest units actually run at %Z above 15%.

Right on! I get it now!

I forgot that one's assumption about the VA of the transformer will determine the "rated current" that you apply when you do the "short circuit" test. I see how it will all work out now. Thanks! This was very helpful.

I just bought a variac, so this is going to be a great way to put it to use right away.

-Charlie
 
Roughly, VA rating tells you how hot it will get and how well it will cope with being hot. You can increase VA rating a little by blowing air over it with a fan.

Effective secondary resistance tells you about voltage droop. There is no direct connection between these two concepts, except that many transformers droop around 5% under full load. However, two 300VA transformers could droop by quite different amounts: one might be 3% and the other 6% (might depend on price). You need to measure or find a datasheet. Smaller transformers tend to droop more.
 
also, consider that the open circuit(core and eddy current loss) test, and the short circuit(copper loss) test assumes sinusoidal voltages and currents.....

with a rectifier circuit, currents and voltages are nowhere near sinusoidal....

Yes, but the impedance model still holds- no need to get too particular about skin effect and increased core loss with nonsinusoidal waveforms. All rectifier-capacitor filters do is increase the crest factor, which is accounted for by calculating the true rms current. You wouldn't want to modify the impedance model for any transformer less than say 5 kVA.
 
IMHO a resistor load on the secondary of a transformer and another after a rectifier/filter combo drawing the same power produces different heating effects....

i do not do simulations but i believe this is worth looking into....

I'm not interesting in basing VA on heating effects, even if that is strictly how VA is assigned. I do not expect to be using the transformer to that level, and as many people have pointed out, it only applied to continuous resistive loads anyway. This is also a very impractical thing for a hobbyist to measure.

-Charlie
 
  • Like
Reactions: 1 user
Status
This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.