# Leakage Inductance

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#### chris2

Hi everyone,

I'm building a power supply similar to the one from Carlos.

It has some snubber capacitors/resistors with std. values.

Just 4 fun, I thought I would try to optimize those values for the parts I have chosen.

I read an article here somewhere about snubbers and how to det. values for them. The article said that since the ringing of an AC/DC psu occurs when the diodes are tuning off and that this is due to the leakage inductance + stray capacitance of the transformer/diodes.

Therefore, has to det. the leakage inductance and stray capacitance and then plug those into some equations to calc them.
For example:
-snubber resistor, SR = sqrt(L/C), where L is the leakage inductance and C the stray or interwinding capacitance
-snubber capacitor, SC = 2 * Pie * sqrt(L*C) / R.

So, the first question is:
1. how to measure the leakage inductance of a transformer.
2. Do i simply short the secondaries with a good thick wire and measure the inductance of the primary, is that it?
3. Or do i need to det. all the resistances, e.g. of the short wire, my DMM when shorted, dc resistance of primaries, secondaries, turn ratio's, reflected resistance, etc.?

Sorry but I'm a little confused about how to go about this... I'm just hobbyist, so a super expensive LCR meter isn't an option for me. However I do have an oscilloscope and a function generator at my disposal.

Thanx,
Chris

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#### chris2

two equations for 2 unknowns

Is the R value in the second link's diagram, the secondary dc resistance?

Also what are the two equations he mentions?

Thanx,
Chris

#### soundchaser

Paid Member
You can measure it by putting a short across the secondary and measuring the primary inductance. We used to measure it that way when I worked at a transformer shop in high school. Wikipedia has a page on it too.

Leakage inductance - Wikipedia, the free encyclopedia

Matt

#### nigelwright7557

I supress oscillation by looking at the frequency of it then use:
1/2 pi r c to determine the components.
This has worked really well in fly-back SMPS.

#### chris2

Yes Speedskater,

one of the articles I read was from Jim Hagerman but also and article from Cornell Dubilier, which he references.

Cheers,
Chris

#### chris2

Hi,

using transistormarkj's inductance measuring techniques, e.g. det. nat. freq. of secondary with and without an "extra" known capacitance, Cx using sig. generator and oscilloscope.

resonant frequency1 = 1 / (2 * pie * sqrt(Ls * Cs))
resonant frequency2 = 1 / (2 * pie * sqrt(Ls * (Cs + Cx)))

Ls = secondary inductance
Cs = secondary stray capacitance

Therefore equation 1: (using resonant freq. equation)
Ls * Cs = 1 / (4 * pie * frequency1^2)

And equation 2:
Ls * Cs + Ls * Cx = 1 / (4 * pie * frequency2^2)

Substituting equation1 into equation2 yields:
Ls = (F2 - F1) / Cx

where F2 = 1 / (4 * pie * frequency2^2) and F1 = 1 / (4 * pie * frequency1^2)

To det. Cs, just substitute just calc. Ls value into first equation, e.g.:
Cs = 1 / (4 * pie * frequency1^2 * Ls)

That's it, i hope.....

P.S. I'm still not sure what the series resistor R is about in transistormarkj's diagram. Do I need to add some known value here when doing the above measurements?

Thanx and Cheers,
Chris

#### Mark Johnson

Paid Member
Those equations look good to me.

I'm still not sure what the series resistor R is about in transistormarkj's diagram. Do I need to add some known value here when doing the above measurements?

The external series resistor R guarantees that the signal generator always sees a well behaved, easy to drive load. Even at low frequencies, where the inductor is a very low impedance. Even at high frequencies, where the capacitor is a very low impedance. I typically use a 2Kohm, 1/4 watt resistor in this position.

Important note: You want to measure the secondary's leakage inductance, so you need to SHORT the primary. As Hagermann's white paper says, and also as member soundchaser001 says here in this thread.

You can play with the measurement technique in circuit simulation if you wish. Sweep the signal generator frequency and look for the max amplitude (or look for the phase=0 crossover). Do this with different values of Cx. Put the measured resonant frequencies into your equations. Do they yield the correct inductance and capacitance values, which you installed in your simulated circuit?

Protip: If you make Cx really really large, so large you are quite certain that Cx >> Cs, then the two resonant frequencies will be quite far apart, like maybe, f1 > (3 x f2). This will result in less numerical cancellation when you're performing the arithmetic to solve for Ls and Cs. Another way to think about it is: if (Cx >> Cs) then Cs is negligibly small compared to Cx, so (Cx + Cs) = Cx and the measured resonant frequency with known Cx gives you Ls directly. It's one equation in one unknown.

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• LTspice_example.png
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#### chris2

Thanx for the verification of my prev. post transistormarkj.

The transformer i want to measure has two primaries and two secondaries.

Both primaries are wired in series for 230v AC, so i would short the other two wires here.

For the secondaries, i would make two measurements one for each winding. I assume that the results of both measurements would be almost identical.

Also thanx for the tip on using a Cx that's a lot larger than Cs. Didn't consider that but when one looks at the equation its quite obvious.

I'll post the result here later.

Regards,
Chris

#### chris2

Btw. in your diagram i guess you meant 0.01uF for Cx.

Cheers,
Chris

#### chris2

FirstTry

I just performed a first measurment w/o the extra capacitor.

For my testing setup, i fed the signal generator directly into one channel of my oscilloscope and the other into the transformers secondary winding. See first pic.

The basic idea being that the ref signal and the measurement signal align or in phase at the resonant frequency.

Unfortunately this wasn't the case. I could see the amplitude of the meas. signal rise to a maximum at around 172kHz. See second pic.

I found another resonant frequency at around 933kHz. In this case the wave forms aligned as expected. See third pic.

Should i just accept the first measurement or is something wrong here?

Thanx,
Chris

#### Mark Johnson

Paid Member
Hm, the transformer I measured most recently was an 80 VA model, one of these: http://www.mouser.com/ProductDetail/Triad-Magnetics/VPS36-2200/?qs=1hmqIh58KVntx%2bpne6dXjQ==

and its secondary resonated at 155 kHz (Cx=0) with the primary shorted. So I am inclined to think your 172 kHz measurement is probably the one to trust. Hagerman says (page 5, paragraph 4):

Measure the voltage across the coil while varying frequency. The lowest frequency which gives a peaked reading is probably the natural frequency of the coil.

If you grab my doc (Word) file of handy electronic formulas here, the first section covers coupling and leakage. IMO, it's useful to measure coupling because that which isn't mutual inductance must be leakage inductance.

#### geraldfryjr

Here is a cool little spreadsheet for excell that I was introduced too in this thread,

http://www.diyaudio.com/forums/plan...truct-cube-louver-acoustat-3.html#post2180015

For calculating leakage inductance and stray transformer capacitance a while back.
You can also enter in the transformers natural resonate frequency and enter 0pf in the first line and then add your extra capacitance and enter the second frequency in the next.
Either way works.

This will help you from doing the long hand method of the calculations.

The only thing I find confusing is that in his instructions jelanier says to find a dip in the voltage and this is the resonate frequency of the transformer.

I typically use the peak voltage.

I have found that using the dip voltage is usually a much higher frequency and is so small that it is hard to find at times.

Either method seems to produce the same results as long as you take very accurate readings of the frequency's.

Maybe some one can clarify this for me.
I just started getting back into this since three years ago so I am a little vauge on the proper methods.

I do know that leaving the secondary open is actually shorted by the stray transformer capacitance.
Thus adding more will produce a second lower frequency to be used in the equation to find the actual secondary leakage inductance without physically shorting the winding with a wire.

Cheers.

jer #### Attachments

• Leakage indutance caculator.zip
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#### chris2

Hi jer,

I'm not 100% sure what u mean by the following:
I do know that leaving the secondary open is actually shorted by the stray transformer capacitance.
Thus adding more will produce a second lower frequency to be used in the equation to find the actual secondary leakage inductance without physically shorting the winding with a wire.

Isn't that what I'm doing?

Maybe its not clear but I'm modeling this according to the transistormarkj's sketch.
http://www.diyaudio.com/forums/power-supplies/230027-hexfred-vs-hyperfast-diode-1200v.html#post3370937

E.g. with the stray and extra capacitance connected across the secondary winding.

Regards,
Chris

#### geraldfryjr

Yes, it is actually.

jer #### chris2

Calc. now with Cx or extra cap

Thanx jer, also for the excel sheet.

It made me realize that my equations post had some error's, forgot to square pie in all of the formula's. I added now the extra capacitor with value 0,033uF. My new resonant frequency was around 105.660 kHz. This freq. was indeed lower than the measurement w/o it! I also wasn't able to discover any higher resonant frequencies with it installed, at least up to 2 MHz!

But it wasn't at least 1/3 of the nat. freq. of the transformer, e.g. of 171.239 kHz, so i used both measurements to calculate the inductance.

Here's what i got:
L Leakage = 0.00424 H or 4.24 mH (Btw. this agrees with the excel sheets calculation!)

For C, I'm still not so sure, when I plug it in I get:
C Stray = 0.00000536 uF or 5.36pF

The excel sheet calculates a value of:
20600pF

For the calculation of my C Stray value i just substituted the L value into my second equation, e.g.:
C = 1 / (freq2 ^2 * 4 * pie^2 * L) or
C = 1 / (105.660^2 * 4 pie^2 * 0.00424)

The excel sheet calculates it a bit different. Will have investigate that to fig out what its doing.

Maybe I will choose and even larger Cx and retest s.th. new resonant freq. is < 1/3 of nat. freq..

Cheers,
Chris

#### Mark Johnson

Paid Member
Chris, I would have expected that if (Ls , Cs) resonates at 172 kHz, then (Ls, (Cs || 33nF)) would resonate at about 30 kHz. Perhaps if you started your sinewave generator at a frequency of 3 kHz, and then dialled it up very slowly, you might see a resonance in the low tens of kilohertz (?)

Does your capacitance meter agree that the extra capacitor is indeed 33 nF?

By the way, you can double-check the results of your hand calculations, or your Excel spreadsheet, using LTspice. Simulate the circuit that you're measuring, and see whether it resonates at XX kilohertz with no extra capacitor. See whether it resonates at YY kilohertz with a 33nF extra capacitor. If the resinant frequencies in simulation don't match the resonant frequencies in the lab, then your calculated L and C values aren't correct.

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