Saturation magnetic field

[neonwarrior]

How can I measure the saturation magnetic field (Bsat) and permeability on an ferrite core?
Can I use this circuit?
View attachment 12624-Figure_1.pdf

 

[Eddy_C]

Yes, this circuit can be used to obtain the hysteresis loop.
The signal from the x channel represents then the magnetic field H (calculated from the current Ux / R1 through the primary windings -
requires knowlage of number of turns, cross section of the magnetic torous).
The y channel is proportional to the resulting magnetic flux B (also winding parameters and R2,C1 values have to be taken into account
to obtain the exact value of B).

Permeability is then the slope of B vs H - may depend on operation point, e.g. if this value is of interest for saturation,
then on has to deduce it for high H values where the slope is constant.

 

[neonwarrior]

So H = N* U/R1
But I can't figure out B. Plz help

 

[Eddy_C]

With given magnetic field H, one can obtain the magnetic flux density from the relation

B = µ * H, with µ = µ0 * µr

µ0 : absolute magentic permablility, 4pi×10−7 Vs/(Am)
µr : relative magnetic permeability

The resulting total flux Φ in the core is then

Φ = B * A,

with A the core's cross section area.

If now H changes with time, then also B does and will induce a voltage U2
in the secondary windings of n turns:

U2 = -d(Φ/dt)*n

For fast changing input current (input frequency is high compared to the low pass time constanat R2*C1)
the voltage at the capacitor C1 is small, thereby nearly all the voltage appear over R2

I2 = U2/R2

I2 is stored by capacitor C1 resulting in voltage Uy, which is then the integral of
I2 over time.

Uy = integral ( U2/(R2*C1)) dt
= 1 / (R2*C1) integral (U2) dt
= 1 / (R2*C1) integral (-d(Φ/dt)*n) dt
= 1 / (R2*C1) integral (-d(B*A/dt)*n) dt
= n*A / (R2*C1) B
= n*A / (R2*C1) * µ0 * µr *H

and with H = n * I1 = n * Ux / R1

Uy = n² *A / (R2*C1) * µ0 * µr * Ux / R1

Then relative permeability is given by

µr = ( Uy* R1 ) / ( n² *A / (R2*C1) * µ0 * Ux)

As one can see,

µr ~ Uy / Ux

so the slope of trace on the scope is proportional to µr

 

[FvM]

The circuit is good to get a visual representation of the core characteristic. With a modern digital oscilloscope, the less than perfect low-pass "integrator" should be replaced by the waveform math integration feature.

If you don't rely on the nice magnetization curve, you can determine AC magnetization as a table of input current and induced voltage magnitudes for a particular frequency. In either case, you see that saturation is a continuous process for usual soft magnetical materials. There isn't a single saturation number rather than a useable B range depending on application paraneters.

 

[neonwarrior]

Thanks for your reply
And thanks Eddy_C for doing the math, that's what I was looking for!!!

 

[neonwarrior]

Hi I think in the H = N * Ux/R1 formula the magnetic length is missing. Is that correct??

 

[Eddy_C]

Correct - I missed it in the calculation above.

It must be

H = n * I / L_m = n / L_m * Ux / R1 ,

with L_m the (mean) magnetic length.

If the core is a torus, as shown in your drawing,
then the mean magnetic length is

L_m = 2*Pi*R

with R the radius from symmetry axis of the torus
(center of the "donut") to the center (geometric centroid)
of the cross section area.

For other core shapes, L_m is given by manufacturer specification.

 

[neonwarrior]

Thanks Eddy_C!!!