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Coupling coefficient of industrial transformers

Discussion in 'Electronic Design' started by orvillefpike, Apr 7, 2007.

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  1. orvillefpike

    orvillefpike Guest

    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?
  2. Tim Williams

    Tim Williams Guest

    Might be 0.99, or better.

  3. Tom Bruhns

    Tom Bruhns Guest

    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 .
    99. Admittedly, the RF transformers are wound specifically for tight

  4. orvillefpike

    orvillefpike Guest

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

    BFoelsch Guest

    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.
  6. The Phantom

    The Phantom Guest

    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
  7. orvillefpike

    orvillefpike Guest

    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.
  8. john jardine

    john jardine Guest

    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'.
  9. orvillefpike

    orvillefpike Guest

    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.
  10. The Phantom

    The Phantom Guest

    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 =
  11. Tom Bruhns

    Tom Bruhns Guest

    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

    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

  12. orvillefpike

    orvillefpike Guest

    How did you come up which such a precise number?
  13. orvillefpike

    orvillefpike Guest

    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.
  14. The Phantom

    The Phantom Guest

    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.
  15. The Phantom

    The Phantom Guest

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

    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.
  16. orvillefpike

    orvillefpike Guest

    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.
  17. Tim Williams

    Tim Williams Guest

    Not really...short the secondary...

  18. Tom Bruhns

    Tom Bruhns Guest

    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

    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.

  19. The Phantom

    The Phantom Guest

    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.
  20. The Phantom

    The Phantom Guest

    Are you referring here to the post where, after I gave the OP a k of
    ..999883, he said:

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

    I suspected that he saw the number .999883 and thought, six significant
    digits. I wanted him to know that that value only has three significant

    If the question is, how did I get even a three significant digit
    measurement, that's easy to do with good DVM's using the method I described
    to him (and which you are recommending).

    On the other hand, trying to get more than about 1 significant digit by
    some method involving leakage inductance will be difficult with a mains
    frequency iron core transformer.

    But if you ask me if I believe the k value of .999883 is *accurate* to 3
    significant digits, that's another question. The OP didn't ask that; he
    just asked how I got "such a precise number", and I wanted to be sure that
    he understood that .999883 is not *precise* to 6 digits. :)

    Trying to get repeatable measurements from a mains frequency iron core
    transformer is not easy. I find that if I just try to measure the
    self-inductance of a winding at 60 Hz and some excitation level, the
    reading will drift for many minutes, sometimes taking 5 minutes or more
    before the measurement is stable to 3 digits. Apparently the initial
    transient of connecting the meter tweaks the core and it takes a while to
    relax, and if the transformer has just been connected to line power, it can
    take even longer!

    I mentioned that flux density at the excitation level of the measurement,
    temperature and magnetic history of the core could affect measured k. How
    much would depend on the particular transformer, of course.

    The 1943 book I refer to in the earlier thread says it well (about a method
    for measuring leakage inductance):

    "...this method is inherently inaccurate when used with *measured* values
    of the self- and mutual inductances of iron-core transformers. The leakage
    inductance of one winding of such a transformer often may be as small as
    0.2 per cent of its self-inductance. For example, if the self-inductance
    of winding 1 is 10 henries, its leakage inductance may be about 0.02 henry.
    If the value of the leakage inductance is to be determined from Eq. 91, to
    the nearest millihenry--or within about 5 per cent of its true value--the
    value of the self-inductance must measured to the nearest millihenry, or
    within 0.01 per cent of its true value, and the mutual inductance must be
    measured with the same per cent accuracy. Such precise measurements are
    impossible with iron-core transformers."
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