Coupling coefficient of industrial transformers

Would anybody know what is the coupling coefficient of step-down, commercial type, transformers like the ones used in shops, like a three phase 15 Kva or a 30 Kva? Thanks

Might be 0.99, or better.

Tim

-- "Librarians are hiding something." - Steven Colbert Website @

So, measure one.

I'd bet it's higher than Tim's guess. I've measured RF transformers with better coefficients than .99, and with the much higher permeability of mains-frequency cores, it should be easy to get over .

1. Admittedly, the RF transformers are wound specifically for tight coupling.

Cheers, Tom

How do I measure it? In the simulation, if the transformer has .990, it's a lot different than .995, for example. Thanks

Exactly what are you trying to calculate/simulate? Coefficient of coupling is not a useful concept when discussing power transformers; it is assumed to approach 1.

I can't speak to the size transformer you have cited, but a 3 kW single phase transformer I have on hand has a measured k of .999883

Because I am feeding it with a square wave, the shape and the amplitude of the output is very different whether the coupling coefficient is .990or .995. Thanks

Thanks for that figure!. It's the first time I've -ever- seen a real "k" quoted for power equipment. When forced to, I use an arbitrary value of 0.999 as it's physical symptoms seem to correspond well with reality but have [was!] always been leery of working with a number so near to 'perfection'.

Also, the smaller the coupling coefficient, the bigger the leakage inductance, which causes voltage spikes. Once I know the magnitude of the voltage, I can design a snubber circuit if there is a need for it. Thanks

There have been threads on this topic fairly recently.

To measure the coupling coefficient (of an iron core transformer) without making an inductance measurement, do this:

Apply rated voltage (sine wave) at one winding, and measure the open circuit voltage at the other, getting the ratio V2/V1'. V1' means that winding 1 was excited.

Now excite winding two and measure the open circuit voltage at the other winding, getting the ratio V1/V2'.

The coupling coefficient is very nearly SQRT(V2/V1' * V1/V2')

The turns ratio is very nearly SQRT(V2/V1' / V1/V2')

I just did this measurement on a 25 VA filament transformer and got k = .99767

OK, if your simulation shows different results if it's .99 versus if it's .995, that's exactly a clue how to measure it. Simulate a circuit you can measure, and trim the simulation until it matches the measurement.

One way to do this: remember that the coefficient of coupling is the fraction of magnetic field shared by two coils. If the two coils have exactly the same number of turns, and you apply 1V to L1, assuming that you load L2 very lightly, and that the resistance of L1 is low enough that there is insignificant drop in that resistance due to the current through L1 when it's excited, the voltage you'll see at L2 will be just the coefficient of coupling. But of course there's no guarantee the number of turns will be EXACTLY the same. However, if you measure L2 with L1 excited, and then measure L1 with L2 excited, you can resolve both the coupling coefficient and the turns ratio. You can add measurements to resolve other things: you can change frequency to see effects due to resistance of the windings and capacitance across the windings.

Another way: you can measure the leakage inductance and figure out the coupling from that. It likely will be important to also know the AC resistance of the windings at the frequency of measurement, though.

I don't claim to have given you a recipe here...only hints. Keep your wits about you and account for parasitic effects like winding resistance and capacitance, and possibly even nonlinearities in the core.

Cheers, Tom

How did you come up which such a precise number? Thanks

Would this method work if I don't feed the transformer at its nominal voltage, because this transformer was ment to be connected at 600 Volts on its primary side. Thanks

Because the permeability of the silicon steel core varies somewhat with flux density, k will vary a little with excitation level, but I think you will get usable results with a reduced excitation level.

Don't be fooled by the 3 leading 9's. That number only has 3 significant digits.

And with an iron core transformer, such a measurement is probably not repeatable to 3 digits, but that's the result of the measurement at the time. Temperature and magnetic history of the core can affect the measurement.

Correct me if I am wrong but I would think that it's even harder to "measure" the leakage inductance. I don't think that you could "measure" the leakage inductance without figuring it out from other measurements in some kind of test under certain condition. Thanks

Not really...short the secondary...

Tim

-- "Librarians are hiding something." - Steven Colbert Website @

As Tim wrote, short the secondary, measure the primary. That's not quite all there is to it, since you can't really short the secondary inductance; you're putting a resistance equal to the winding resistance across it. But yes, you can do it if you think about it carefully.

I think the measurement of the secondary voltage with the primary excited, and vice-versa, is a better way, though there you technically need to compensate for the drop in the resistance of the excited winding because of the current through the winding. That is, the voltage across the pure inductance is less than what's applied to the winding. I'm not sure you got a proper answer to the question about how to measure the coupling so precisely. Consider if the transformer is 1:1; you could connect the windings so that you only have to measure the difference between them to know how much lower the secondary is. You do need to account for the case where the transformer is, say, 1.001:1 turns ratio. Then when you reverse the windings, be sure that you know which winding has the higher voltage. You loose the polarity of the difference when you're only measuring an AC amplitude. If the transformer isn't 1:1, you can still do it if you use an accurate voltage divider... -- I haven't actually done this with mains-frequency transformers, so I may be missing some practical aspects...I normally work with things at 100kHz up into many MHz, where there are ways to deduce the coupling, also, and I do have some experience with those.

Cheers, Tom

Go look up the thread with the subject line:

"About Leakage Inductance in Transformers"

that I started on March 1, 2007. Read my first post and Tony Williams' response to my questions.

Each winding in the transformer has a leakage inductance associated with it, and determining the individual leakage inductances from measurements is difficult with an iron cored mains frequency transformer. Shorting one winding and making measurements at another winding gives a result that combines the effect of the separate leakage inductances, and very often this is all that is needed.