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Background

I have a step-down isolated power transformer (EI-66x36) designed for 60Hz with one primary input Vp=110V and three secondary outputs : Vy=10V, Vb=26V, Vr=30V.

Unfortunately I don't know which wires is what. I DON'T want to connect the transformer to the main line (not even in-series with a current limiter resistor) in order to figure out which coil is linked to what. I would rather try an invasive method using the theoretical knowledge, if possible.

By using the coils turns ratio equation E: Np/Ns=Vp/Vs=SQRT(Rp/Rs), where Np/Ns is the primary-to-secondary coil turns ratio, Vp/Vs is the primary-to-secondary coil voltage ratio, I deduced that on a step-down transformer the primary coil impedance is greater than any secondary coil impedance, ie. Rp/Rs > 1.

By measuring each coil impedance I found 4 pairs of wires as following:

  • thick red wires with impedance of Rp=14.9 Ohm
  • thin red wires with impedance of Rr=10.6 Ohm
  • thin yellow wires with impedance of Ry=3.95 Ohm
  • thin blue wires with impedance of Rb=1.67 Ohm

I concluded that the thick red wires must be connected to the primary coil and the others represents the secondary coils.

I've checked that there is no continuity (infinite resistance) between the secondary coils, which means that the secondary coils are completely isolated of each other.

The problem

What bothers me is the fact that the above equation (E) doesn't seem to apply to this transformer and I don't understand why.

For instance the ration between the primary coil and the secondary coil identified by the thin red wires is: Vp/Vr=110/30=3.7 while the SQRT(Rp/Rr)=SQRT(14.9/10.6)=1.19, which is not as expected (ie. 3.7).

The same applies to the other ratios:

  • Vp/Vb=110/26=4.23 while SQRT(Rp/Rb)=SQRT(14.9/1.67)=3, which is not as expected (ie. 4.23).
  • Vp/Vy=110/10=11 while SQRT(Rp/Ry)=SQRT(14.9/3.95)=1.9, which is not as expected (ie. 11).

What am I doing wrong?

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  • \$\begingroup\$ Also keep in mind that frequency matters in transformers. A "black box" transformer could operate only around 50hZ, 60Hz, 1khZ, 100kHz, 10MHz... Now there are some physical cues which allude to frequency of operation (thickness of laminations, ferrite, etc.) But we digress. \$\endgroup\$ – rdtsc Jul 27 '17 at 0:46
  • \$\begingroup\$ Why don't you want to connect to the mains? It's like saying what is the quickest way to swim across a river without getting my feet wet. \$\endgroup\$ – Andy aka Jul 27 '17 at 8:27
  • \$\begingroup\$ Using the main sometimes is not an option (a 110V@60Hz transformer when the main is 230V@50Hz). My question was rather about finding an invasive testing method (like idiot-proof method) that would work without the need of using HV power supply. So finding the coils inductance is just a matter of using a DMM or an oscilloscope (non-invasive method). Then using a simple equation one can calculate the primary/secondary coil voltages. However, the method suggested by @petter-bennet or by you would definitely work (although one must be careful with HV AC). \$\endgroup\$ – Eugen Mihailescu Jul 27 '17 at 8:48
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I think the "impedance" measurement is misleading the results. The formula you are using relates the ratio of voltage to the square of the ratio of inductance, not impedance. And you have not calculated the inductance of the individual coils. This impedance is the vector of the inductance and series resistance. Try taking some measurements and calculating the inductance and resistance independently, if their vector becomes your impedance measurement, my hypothesis is correct.

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  • \$\begingroup\$ You are right. In this case the "impedance" should actually be "inductances" of the coils. Thanks for pointing this out. \$\endgroup\$ – Eugen Mihailescu Jul 27 '17 at 5:11
  • \$\begingroup\$ So my idea of identifying an unknown transformer works. By measuring each coil magnetic inductance (not impedance, thanks user55924) you find the turns ratio between primary-secondary coils. Since you are supposed to know the primary coil designed voltage (eg. 110V, 230V) and since you already know the primary-secondary turns ratio you can calculate the induced voltage in the secondary coils. \$\endgroup\$ – Eugen Mihailescu Jul 27 '17 at 6:36
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If you know that the lowest voltage winding is 10 volts, I'd find a transformer providing 10 volts or less, and apply its output to one of the windings (carefully ensuring the ends of the other windings can't contact each other), then measure the voltages on the other windings - this should quickly (and safely) allow you to determine which winding is which.

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  • \$\begingroup\$ I agree. Sometimes calculation is warranted, and other times it just makes more sense to quickly and safely test. The resistance of each winding is not a good measure of turns ratio or anything else. Think about it - two windings could be both "6 Ohms" - but one is many more turns of thicker wire, say, 30vAC @ 1A, while the other is fewer turns of thinner wire, say 12vAC @ 0.25A. Hence, it's far simpler to safely test. \$\endgroup\$ – rdtsc Jul 27 '17 at 0:33
  • \$\begingroup\$ Your solution would definitely work, no doubt about it. I just wanted to know what was wrong in my approach. The mistake I made (as pointed out by @user55924) was to use an equation that refers the coil inductance while I measured coil impedance. \$\endgroup\$ – Eugen Mihailescu Jul 27 '17 at 5:14

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