# 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?

• 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. Commented Jul 27, 2017 at 0:46
• 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. Commented Jul 27, 2017 at 8:27
• 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). Commented Jul 27, 2017 at 8:48