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4th October 2012, 12:19 AM  #1 
diyAudio Member
Join Date: Mar 2007
Location: California

how to estimate transformer sag under load
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 noload 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 
4th October 2012, 02:38 AM  #2 
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Join Date: Oct 2006
Location: Charlotte, NC

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. 
4th October 2012, 04:22 AM  #3 
Banned

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 
4th October 2012, 04:35 AM  #4  
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Join Date: Mar 2007
Location: California

Quote:
http://www.antekinc.com/pdf/AN1225.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 

4th October 2012, 12:29 PM  #5 
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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.

8th October 2012, 10:16 PM  #6  
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Quote:
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 

8th October 2012, 10:38 PM  #7 
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Join Date: Mar 2007
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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:
Charlie 
8th October 2012, 10:43 PM  #8 
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Join Date: Oct 2006
Location: Charlotte, NC

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. 
8th October 2012, 11:02 PM  #9  
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Quote:


8th October 2012, 11:39 PM  #10 
diyAudio Moderator

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 crosssection 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 crosssection 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....
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