how to estimate transformer sag under load

[CharlieLaub]

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

[zigzagflux]

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.

[fas42]

Sounds as if you need to have a good read of this thread, Power Supply Resevoir Size, especially the posts by Terry Given, and gootee, and, especially at the end of thread-- unless you've already done so ...

Frank

[CharlieLaub]

Originally Posted by zigzagflux

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

[zigzagflux]

You got it. I can make the modeling more accurate (with marginal benefit) by getting into X/R ratios, but this existing model will work darn well.

[CharlieLaub]

Originally Posted by zigzagflux

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

[CharlieLaub]

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:

• By mass: 100va per kilo, or 2.25lbs per 100VA
• By secondary winding wire diameter: 3.1A/sqmm
• By regulation/voltage drop: apply resistive load(s) to secondary. Decrease load resistance until secondary voltage drop by between 3% (for 500VA and above) and 5% (for less than 500VA). Measure current to get VA using I^2R

Comments?

-Charlie

[zigzagflux]

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.

[CharlieLaub]

Originally Posted by zigzagflux

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?

[Tony]

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....