[SOLVED] Iron sheet laminated gapped core inductor variation

Hello everyone,

I have a gapped (few mm of air gap) inductor wound around the E+I sheets of a laminated core Power Core M400-50A.

The problem that I see is that the inductance when measured with an LCR meter varies when the amplitude of the LCR varies.

• 56mH @50 Hz @ 50mVRMS
• 50mH @50 Hz @ 300mVRMS

The core is not saturated because it can withstand 1ARMS without saturation, so the decrease of inductance due to increase of voltage is not due to saturation.

Could this be due to the I*R drop in the series resistance ? Why could this be ?

Any comment is appreciated !

Iron core hat strong magnitude dependency of permeability. Did you calculate if the measured inductance variation can be explained by it? I*R is a linear effect and can't affect measured inductance.

My guess is that residual magnetization can take place (rather, be more perceptible) at very weak magnetic fields; did you find out if these values hold exactly as exposed above, either increasing or decreasing the voltage?

Either per Andre above - or your measurement equip is a bit suspect ... 50mV allows noise to add in error ...

LCR meter varies when the amplitude of the LCR varies...

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I assume the applied voltage is sinusoidal.

Most common machines assumes that the device under test is a pure L /C /R. What is the approx resistance of the coil?

Just for a test: make a simple air core inductor with a thin wire (say 100 turns on a paper former with a 32-40 AWG wire).

Measure the inductance at two different applied voltage and report the result. Perhaps you will see two different values.

Could this be due to the I*R drop in the series resistance ? Why could this be? ...

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Honest answer: I do not know. But much depends on the meter (and not on the coil).

Resistance measurements are usually accurate but LC measurements with series resistances are usually not.

Measure the inductance at two different applied voltage and report the result. Perhaps you will see two different values.

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Not going to.. sorry, because I know accuracy is affected by voltage applied due to different currents in the connections. Furthermore, I am using the "series measurement test". Not parallel one, as I forgot to mention in the OP.

The main problem I think it is due to the core.

Iron core hat strong magnitude dependency of permeability. Did you calculate if the measured inductance variation can be explained by it? I*R is a linear effect and can't affect measured inductance.

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From manufacturer core data, we have:
J=1T (H=199 A/m) => muA (amplitude permeability) = 5927
J=0.5 T (H=108 A/m) => muA = 5276

Without air gap, the variation on permeability means L1/L2 = muA1/muA2 = 1.12 i.e. 12% increase which turns out to be exactly the values I see... I DO NOT UNDERSTAND how can this happen since our core is gapped (E laminated sheets + I laminated sheets on top).

A gapped core is supposed to reduce the influence of core variations e.g. form the magnetic permeability.

Without air gap, the variation on permeability means L1/L2 = muA1/muA2 = 1.12 i.e. 12% increase which turns out to be exactly the values I see... I DO NOT UNDERSTAND how can this happen since our core is gapped (E laminated sheets + I laminated sheets on top).

A gapped core is supposed to reduce the influence of core variations e.g. form the magnetic permeability.

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Yes, that's why I asked if you have calculated the expectable L variation for the gapped core. The reduction is according µ_eff/µ_ungapped.

I presume however, that the test conditions are in much lower B range than the quoted spec, you didn't tell. See an example for a different core, your test conditions are probably further to the left.

andre_teprom said:

My guess is that residual magnetization can take place (rather, be more perceptible) at very weak magnetic fields; did you find out if these values hold exactly as exposed above, either increasing or decreasing the voltage?

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Yes. With very low current, might not get enough magnetic field strength ("H"), hence low mu_R... Next will try variations using high current.

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FvM said:

I presume however, that the test conditions are in much lower B range than the quoted spec, you didn't tell. See an example for a different core, your test conditions are probably further to the left.

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You presume correctly. I am in the B_peak=0.012 T range in the central leg and half that in the outer legs...

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See an example for a different core, your test conditions are probably further to the left.

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Further to the left means small µ_r => µ_eff/µ_ungapped~1 => core follows the ungapped inductance and its variations => makes useless the gap.

Will check whether the inductance varies or not at higher B_peak.

Inductance measurement done in the 0.5 T range and does not vary with changes in voltage (maintaining high magnetic density flux).

Thank you all for your help.

J=1T (H=199 A/m) => muA (amplitude permeability) = 5927
J=0.5 T (H=108 A/m) => muA = 5276

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Puzzled; I checked some unit conversion tables and 1T=798 kA/m.

You have to calculate the magnetic reluctance for the overall path (include the gap) and then use that to get B.

Or, am I missing something?

c_mitra said:

You have to calculate the magnetic reluctance for the overall path (include the gap) and then use that to get B.

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Sure. Or assume you are in the high µ_r region and neglect core recultance: R_core<<R_{air gap}. Under this assumption, the overall path has a reluctance: R_{overall path under above assumption & E+I core geometry} ≈ R_{air gap}
That is what I used to design "L".

I computed "B" assuming a "L" by design.

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Puzzled; I checked some unit conversion tables and 1T=798 kA/m.

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And what is your point ? The value you are providing is only valid for air (i.e. mu_r=1). I am providing data for the core we used i.e. its mu_r, which is very different than 1 (air).

And what is your point ?

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Ok, you should have used B, rather than H. But that is a minor point.

the overall path has a reluctance: Roverall path under above assumption & E+I core geometry ≈ Rair gap...

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Approximately correct.

If I use the graph presented in #7, the H values (199/108 A/m), the mu values you use are different. In particular, the points are to be right of the peak (undesirable).

Better to use the H value, use the mu vs H graph, then recalculate. I think there should a term like (gap length)/(total magnetic path). Please check (I may be rusted).

If I use the graph presented in #7, the H values (199/108 A/m), the mu values you use are different.

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Of course they are not the same. FvM showed typical iron core material to let me see how much the permeability varies with such material, but still not exactly mine (M400-50A).

Better to use the H value, use the mu vs H graph, then recalculate.

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Sure. Or another way is to use "B" (because it easy to compute), go to "B vs H", then to "mu vs H".

Or another way is to use "B" (because it easy to compute), go to "B vs H", then to "mu vs H". ...

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I am not so sure. The current is responsible for the magnetic field (H) and that is in turn responsible for the induction (B).

In other words, when you try to calculate B directly, you are using the constant (permeability) somehow somewhere (I do not believe you can compute B without using mu of the sample). Please elaborate.

If mu is a function of H (true for all materials except vacuum), the induced magnetism (B) is also a function of H (obviously because of the B-H curve).

Therefore when you apply 50mv RMS vs 300mv RMS (respectively) to a inductor and compute the B values and then compute the H and find H 108 and 199 A/m (respectively), I guess there is some mistake.

I wonder why you quote voltages instead of current values (because that is the causative agent for the magnetisation). Current values should be proportional to the H but not to B because of permeability variations.

c_mitra said:

Therefore when you apply 50mv RMS vs 300mv RMS (respectively) to a inductor and compute the B values and then compute the H and find H 108 and 199 A/m (respectively), I guess there is some mistake.

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Of course there is a mistake. That was the whole point of this thread. I computed theoretical inductance for high "H" and hence "mu_r", but did not tested it correctly (at few mV RMS, the current is so little that high "mu_r" is not achieved).

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In other words, when you try to calculate B directly, you are using the constant (permeability) somehow somewhere (I do not believe you can compute B without using mu of the sample). Please elaborate.

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Yes, I use the constant permeability when computing the inductance "L" and compute "B" knowing the inductance value.

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I wonder why you quote voltages instead of current values (because that is the causative agent for the magnetisation). Current values should be proportional to the H but not to B because of permeability variations.

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Sure. I quoted voltages because from the voltage you get a current. The important thing was in what order of magnitude I was testing e.g. few mV or hundreds of mV or hundres of Volts and what inductance I was expecting.

having read the above - and, as some one who regularly designs iron cored chokes and transformers - there is a lot of mis-information in the above - the simple facts are at 50mV there is too much room for noise to make an accurate measurement, even 300mV is marginal.

For a choke made out of transformer steel with a very even gap - the inductance does not change with excitation until you get to > 0.5T peak

the fact that you are exercising the core very little at low excitation does not mean the instrinsic inductance changes - especially as L is dominated by the gap

If you have a little bit of steel poking out into the gap - which really shouldn't be there - then you may get a higher L reading at low excitation - but this little bit of steel will saturate at higher levels of H and the L will then fall to the nominal air gap value.

Often times "butt stacked" chokes are welded on the sides to reduce noise and hold everything together - there is no air gap for low excitation and you get high L near the zero crossings of signals - but swamped very quickly as the signal rises and the weld is saturated for most of the operating cycle ( the weld does add heat though ).

I hope this clears the matter up ...

For a choke made out of transformer steel with a very even gap - the inductance does not change with excitation until you get to > 0.5T peak

the fact that you are exercising the core very little at low excitation does not mean the instrinsic inductance changes - especially as L is dominated by the gap

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L dominated by the gap would be also my expectation if we assume typical gap dimensions. Unfortunately CataM never managed to report the relative gap size respectively expected µeff.

L dominated by the gap would be also my expectation if we assume typical gap dimensions.

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Also mine and yes it is dominated by the gap. In fact, that is how I computed it. The inductance variation is due to low excitation value provided by the LCR ( in the mA range).

gap length = 0.23 mm

Roverall path under above assumption & E+I core geometry ≈ Rair gap

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Correction: ≈ 3/2 * Rair gap

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the inductance does not change with excitation until you get to > 0.5T peak

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Are you saying that inductance does not vary with lower than 0.5T but it does vary with higher than 0.5 T ?

Are you saying that inductance does not vary with lower than 0.5T but it does vary with higher than 0.5 T ?

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that is exactly what I said ...

that is exactly what I said ...

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How low? I understand that at higher than 0.5T most materials can start to saturate, but using a very low range of magnetic flux density also makes it vary, as you just saw from the above posts...

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You should specify the lower end of magnetic flux density the inductance does not vary... not just use "absolute" statements, as they were true always.