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20th March 2017, 12:11 PM  #1 
diyAudio Member
Join Date: Sep 2016

How to calculate transformer secondary resistance ?
Hello everybody, i wonder if there is way to calculate the secondary R of a transformer, if you know the output V, off load V, and I rating ?

20th March 2017, 01:13 PM  #2 
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Join Date: Jan 2011
Location: Iasi

You cannot calculate because it is connected to the tYpe of transformer....but if you can do some measurements you can calculate using the measurements results.

20th March 2017, 01:45 PM  #3 
diyAudio Member
Join Date: May 2007

Do you mean secondary DC resistance? If so, calculate using knowledge of the wire used and length. Or measure it.
Do you mean effective secondary resistance? If so, calculate from measured primary and secondary resistance and voltage ratio. Or from measured voltage droop at a known current. Secondary resistance is one of those things which if you know why you want the number then you know how to obtain the number. 
21st March 2017, 01:19 AM  #4 
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> you know the output V, off load V, and I rating ?
Same as any Ohms Law problem. Difference of Voltage, divided by Current. Example: Rated 12V at 1 Amp, 15V at no load. 3V difference. Caused by 1A current. 3V/1A is 3 Ohms. This is NOT the "secondary resistance", but the sum of primary and secondary resistances (and also leakage inductance). Which is usually what you really want to know: the total loss. How this splits between primary and secondary is usually only important to the transformer designer. Last edited by PRR; 21st March 2017 at 01:21 AM. 
21st March 2017, 01:32 AM  #5 
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You can make some estimate of the secondary resistance from only the onload output voltage and the open circuit output voltage. As above in PRR's post, the secondary resistance will normally be half of the resistance measured from the voltage drop. The other half is the transformed primary resistance (primary resistance divided by turns ratio squared).
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21st March 2017, 03:39 AM  #6 
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Join Date: Oct 2007

Most of a transformer's voltage drop under load comes from leakage reactance due to imperfect coupling between pri/sec. That models as an equivalent series inductance, not resistance. The same laws of reflected impedance between pri and sec apply  it's just there's a "j" in there. Little bitty five watt trafos may be dominated by resistance, but anything you really want to make an amplifier with won't be. With really big power trafos they rate them in "% reactance" because the resistive part is vanishingly small.

21st March 2017, 04:00 AM  #7 
diyAudio Moderator

i do copper loss testing aka short circuit testing of my traffo builds....
i test them in increments of 1 amperes or up to rated primary current.... i use a variac and a home brew voltage and current meters... the variac supplies low voltage to the primary, while all secondary windings are shorted together... very straightforward to use, just read the voltage at the rated current... this is a non destructive test.....
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21st March 2017, 05:48 PM  #8 
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Location: Maine USA

> i do copper loss testing
Do you (or anybody) have data about wg_ski's statement "Most of a transformer's voltage drop under load comes from leakage reactance..."? Reactance matters, why is why I edited it into my post. At 10KVA and up it becomes dominant. (In part because of the economics of large power: resistance is real loss while reactance is just sag, and useful to limit fault current into a short.( Below 1KVA, I would expect many transformers to have low reactance. However there are many ways to wind the little beasts. Primary over secondary is well coupled. Pri and Sec on separate legs is poor coupling, and often done for safety, shape, or to reduce HF noise. 
21st March 2017, 10:42 PM  #9 
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i have no data on that as i do not know how to measure it....
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22nd March 2017, 01:50 AM  #10 
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Location: Charlotte, NC

X/R ratio is related to kVA in general. Maybe not linearly, but perhaps more exponentially. The IEEE Red Book has graphs of 'typical' X/R ratios, but this is pertinent specifically to transformers that rate in the MVA's.
Point being, small dry type transformers have X/R ratios around 1 at about 15 kVA three phase, and it climbs to approx 5 when you reach 1000 kVA. From there you tend to find a limit around 2030 for the really big boys. Transformers that rate in VA are dominated by resistance, and this I have tested up to around 500 VA single phase. Anything in home audio will be mostly resistance, regardless if you are talking toroid or EI. Sure, EI will have more relative leakage, but it's still small in comparison to the resistance that contributes to overall impedance Z. 
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