Mutal inductance depending on current

[debelino]

Homework Statement

Why is mutal inductance rising with the rise of current?

Relevant Equations

M=N2*Ф12/I1

My frient had an experiment in lab. They measured the mutal inductance on two coils wraped around one feromagnetic core.
When the current of the first coil was 1, 2, 3, 4, 5 mA the mutal inductance was 94 mH. Then they were told to rise the current to 10 mA, the mutal inductance went to 160 mH. The frequency was 50 Hz all the time.
Why did the mutal inductance rise?

 

[berkeman]

Sounds like an error. Can you post the full circuit that was used in the experiment, and details of the test equipment used?

 

[debelino]

It is not an error. Everyone got the same results. In the paper explaining the experiment they said it would happen and asked a question why? The secondary coil was open. They measured the voltage on it and calculated the mutal inductance. My only guess is it happened because of the hysteresis nonlinearity. For small currents the permeability is modeled as one number, but as the current grows the dependence of B and H changes and another, bigger number is required to model the B and H dependance. The higher harmonics are not so visible because of the big inductances.
Is this possible? I am only familiar with electromagnetism in theory...

 

[berkeman]

Can you post the full circuit that was used in the experiment, and details of the test equipment used?

 

[Babadag]

If we'll neglect the leakage magnetic flux L=B*SteelArea/I B/I=K*B/H
L5mA/L10mA =B10/B20
From magnetic curve B=f(H) of an usual silicon-steel laminate for transformers: H=magnetic field[magnetizing force] B=magnetic flux density[or induction]
If H=10A/cm B=0.9Wb/m^2
If H=20A/cm B=1.5 Wb/m^2
The ratio 1.5/.9[Wb/m^2]≈160/97 [H]

 

[Babadag]

I'm sorry. Wrong part of the B_H curves. For small H [less than 3 A/cm] the B-H curve is parallel with abscise. Let’s say for 5mA supply current H= 1.6 A/cm and for 10mA[ 2 times]= 3.2 A/cm. According to attached curve for 1.6 A/cm B=0.075 Wb/m^2 then μ=0.075/1.6=0.046875 and for 3.2 A/cm B=0.25 Wb/m^2 μ=0.25/3.2=0.078125
L=K*μ
L10mA/L5mA=μ3.2/μ1.6A/cm=0.078125/0.046875≈160/97

 

[berkeman]

Is this a steel power transformer thing? I've never noticed any small signal distortion in my ferrite communication transformers...

 

[Babadag]

I think the above B-H curve is for low carbon steel and not for silicon-steel laminate[my mistake!].In the book these curve lines are similar.
Here attached it is another B-H curve for Low Carbon Steel as per
https://magweb.us/free-bh-curves/

 

[rude man]

M = $N_2 \phi_{21}/i_1$ assuming zero secondary current. $\phi_{21}$ = flux thru secondary due to primary current $i_1$.
so it's essentially dB/dH since H ∝ $i_1$.
B vs. H in your last diagram clearly shows dB/dH starting out low, then rising to a max., then receding again.
So as you increase current, flux will be lower at first, then rise, then drop. You seem to have operated in the lower→higher region.