About leakage inductance in transformers

Insufficient data....(?) my guess

X = R1 + M.SQRT(L1/L2)R2 + sLleak

DNA

If I say it is and state the conditions. Large signal/different excitation frequency conditions.

DNA

Assuming a steel cored transformer. I've yet to find -any- LCR meter that will measure the inductive component. They're good at measuring R (so is any cheap dvm) but are magnificently inaccurate in any guesstimate of inductance. A better guess is to multiply the offered value by 10, or even just pluck a value out of thin air. john.

How do you know that the LCR meter is giving you a wrong value for the inductance unless you have another method which you are convinced is giving the correct value? What is that other method that you trust?

inductance?

giving

Essentially by comparison to direct measurement at normal working voltage and frequency (eg 240Vac 50Hz). For a Q meter design, I'd noticed all my steel cored test transformers and chokes were giving weird inductance and loss value readings that varied nearly directly with the AC test level, running upto a couple of volts. (L up, R down). Not my usual 10-20% errors (my kind of precision!) but up in the 1000s%. Only semblence of reasonable values started to turn up at the 40V~50V drive level. Move the frequency up a tad and even these readings turned to mush.

I thought this was what you were talking about, and it's well known.

It's an interesting topic in its own, but in this thread I'm talking about the inductance of one winding with the other winding shorted. Under that condition the phenomenon you're referring to doesn't happen.

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mush.

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Yes. I was on a flyer there.

Open secondary

What you are seeing here (the open circuit numbers) is the magnetizing loss. It is highly non-linear and only approximately modeled by an L and R. It is due to core losses and hysteresis and it increases dramatically as the core approaches saturation (as your numbers indicate).

This is the primary (no pun intended) reason that leakage impedance measurements are best taken with a shorted winding. The voltages are lower and the contribution of the magnetizing loss is minimized.

Would cheating do? Open Prof Wm Frazer's book, "Telecommunications", to page 80, "Inductively- -Coupled Circuits with a Resistive Load on the Secondary.". Read off eqns 4.19 and 4.20......

w^2.M^2.(Rl+Rs) Effective Rpri = Rp + -------------------- (Rs+Rl)^2 + (w.Ls)^2

( (w^2.M^2).Ls ) Effective Xpri = j.w.( Lp - -------------------- ) ( (Rs+Rl)^2 + (w.Ls)^2 )

For a short circuit secondary set Rl to 0.

Interesting that the effective primary resistance is increased as Rl reduces in value. Slightly counter-intuitive, (to me anyway).

Yes, you cheated! But, you could have derived them if you had to, right?

Anyway, those are correct. If you leave the j.w. off the second expression, you will have a formula for Effective Lpri.

It's even stranger than that. If the secondary resistance (Rs+Rl, or just Rs if you set Rl to zero) is less than w*Ls, then the Effective Rpri will decrease with decreases of Rs. If the secondary resistance is greater than w*Ls, then Rpri will *increase* with decreases of Rs.

Just take the derivative (with respect to Rs) of the first formula you gave above to see this.

Now that we've got the formulas I was asking for, use these typical values for a small 60 Hz 120 volt to 12.6 volt transformer:

L1 = 12.5 mH R1 = 32.7 ohms L2 = 938 uH R2 = 1.72 ohms m = 2.8 mH

and plot the Effective Lpri vs frequency from 60 Hz to 10 kHz.

Then answer my question:

"Is this really the leakage inductance? Under what conditions might it not be a good value for the leakage inductance?"

With 120 volts applied.

John

With the secondary shorted, the core has essentially no effect, and the measured value of Lpri is independent of the excitation level. See John Jardine's latest post where his measurements confirm this.

Of course, with 120 volts applied, the resistance of the windings will be increasing rapidly due to heating and it will be difficult to get a steady measurement. :-)

I think the leakage inductance still depends on permeability.

But he didn't apply enough excitation to substantially change permeability.

With 120 volts applied, the permeability of the iron will be seriously different from the low-flux value, so the leakage inductance will indeed be different. You can of course define leakage inductance any way you like, but if you care about things like charging caps through bridge rectifiers, or any of the other things power transformers usually do, leakage inductance measured at low level may not be predictive.

John

I don't define it myself; I accept the definition found in the textbooks. It is well known that the E-I iron core of a standard transformer (and not the tricky geometry you proposed in another thread) has a small effect on leakage inductance. It *does* have an effect, but it's small. The leakage inductance is mostly due to flux in the air space between the windings, and therefore scarcely affected by the core.

I cite from "Magnetic Circuits and Transformers", by members of the Staff of the MIT Department of Electrical Engineering, a book well worth having.

They say "Since the leakage fields are not greatly affected by the core, the effect of the iron core is sometimes entirely neglected and the leakage inductances are computed as in Eqs. 91 and 92 from formulas giving the self- and mutual inductances of air-core coils."

One way to convince yourself of this is to get a transformer that hasn't been varnished so that you can remove and re-insert the laminations. If the leakage inductance is greatly affected by the core, then it should change substantially when you remove the core. The permeability of ordinary transformer laminations is about 1000 with low flux, increasing to a peak of maybe 6000 at about 8000 gauss, then decreasing again as the flux density approaches saturation. Inserting the laminations will put material of permeability of 1000 in the bobbin. Increasing the flux to the point of maximum incremental permeability will only increase the permeability by another factor of maybe 10, maximum.

Surely replacing the air in the center of the bobbin with a material of permeability 1000 will have a greater effect than increasing the permeability by another factor of 10.

So, just take a transformer with removeable laminations, short the secondary and measure the inductance at the primary with the laminations in place. Then remove the laminations and measure Lpri again. If the measured inductance doesn't change much with a change of 1000 times in the permeability of the space inside the bobbin, then it probably isn't going to change much with another factor of 10 increase.

The measurements also depend on whether the winding you short is the inner winding on the bobbin, or not. I'll post some measurements later.

If this experiment doesn't convince you, then propose one of your own.

My purpose in this thread is to raise awareness that sometimes measuring the inductance of a winding with the other winding shorted may not accurately reflect the leakage inductance. It would be good to know when it does, and when it doesn't. Tim Williams is going in the right direction.

It probably will, but not much, since the shorted secondary is doing its damnedest to keep flux out of the core.

robert

Either you are being obtuse or you are being stupid.

Of course you might be being both.

DNA

I said "I think", not that I was sure. Of course, some people will always object to thinking, or taking a risk of being wrong.

What about a non-classic, non-concentric transformer? Like a toroid with windings on opposite sides, or a super-CE-insulated transformer with windings in different places, not on top each other? With no core, primary flux will barely brush the secondary... for the toroid, maybe 5% will couple. Add the core, and a lot more primary flux is directed through the secondary, and how much depends on the permeability.

Feel free to call me stupid again. You don't matter, you know.

John

FWIW, I can confirm that the case of the toroidal core produces much different results: leakage flux is much lower than for air core coils in the same geometry. I occasionally use ring-decay and voltage step methods to measure leakage inductance. In the latter, you simply switch a voltage step and measure current slope, solving L = V/(di/dt). The ring decay method has been discussed extensively in this group. In both cases, secondary is shorted. In some cases, it may make more sense to measure secondary leakage inductance and calculate it for the primary based on turns ratio. Using a bridge, use must use an excitation frequency high enough that the impedance of the leakage is significant compared to secondary resistance multiplied by the square of the turns ratio. This makes 1 kHz bridges useless for many high freq transformers. It also means that the method of shorting the secondary can become critical. Short the secondary with as short and stout a link as possible. Paul Mathews

Some great sage said, "Stupid is as stupid does!" ;-)

...Jim Thompson