Inductor on ferrite road: determining the permeability?

Hi all,

I have a little question concerning ferrite coils I'd like to ask you.
I'd like to make a inductor based on a ferrite cylinder, sort of rod you find in a AM radio.
But the question is: what is the permeability of the ferrite ?

I have 2 methods, but I don't know which one will provide the correct answer.
because they provide 2 different results.

All are expressed in metric system (sorry for that one)
Here's the first one:

µeff=L/N²

Click to expand...

where L is the measured inductance [H] and N the number of turns []

(quoting from http://www.c-maxgroup.com/tech/antenna.php )

The second one is:

µr= L*l /(µ0*N²*S)

Click to expand...

where L is the inductance [H], l the length of the rod [m], N the number of turn [] and S the section [m²]

(quoting from http://fr.wikipedia.org/wiki/Bobine_(électricité) )

First of all, is there any mistake in any formula ?
Then, do I understand well when I say µeff = µr ?
Afterward, do I made any mistake transcripting ?

Calculation provides a µ=480 (*) for the first one and µ=200 for the second one.
What is quite annoying !

Any help would be greatly appreciated !
Thanks a lot !

Regards


Data: L= 71.9µH (measured), N=22, S is calculated with a diameter of 1.10^(-2)m

(*) mistake : 71.9µ/484=1.48µ !!!
So µeff is related to what ??

Snelling Soft Ferrites has a sub-chapter on open magnetic cores (e.g. ferrite rods). The literature suggests that none
of your simplified formulas can be correct. L/N² is simply the definition of the well-known AL value. Generally, the inductance
of a ferrite rod aerial depends among others both on coil and rod length, it's not clear how they should been related in your
second expression.

What's your motivation to calculate permeability from ferrite rod inductance, by the way?

Hi FvM, thanks for your answer !
In fact the second expression seems valable for a same length of ferrite rod and coil, but in "real life" I don't want to cut the rod or spend so much time winding thousands of turns, so I take the ferrite rod (about 13cm) and I wind about 30 to 50 turns on it.

And you're right when you said it depends among both length, because if I put the winding at the beginning of the rod, the inductance isn't the same if I wind at the middle length of the rod.

I did not find any expression synthetising the contribution of the position of the coil on a ferrite rod, that is quite disturbing.

The motivation of determining the permeability of a ferrite rod is the first step of a small project, realizing a B-field generator; ferrite will be used to keep the field lines parallels for a small axial distance, then a gap, then another coil.
This makes a kind of transformer.

Regards

The usual instrument to generate a homogene magnetic field in a extended region is a helmholtz coil

https://en.wikipedia.org/wiki/Helmholtz_coil

Click to expand...

The solution of cyclinder-symmetrical magnetostatic problems, although simple compared to general 3-D problems,
still involves elliptical integrals. Thus most people would use numerical methods (FEM solvers) those days.

True !
One other aspect related to this small project is the estimation of the B/H-field.
I discovered measurements modifies the field, I doubt about my method measuring the field.

In a normal situation, with a solenoid you generate some kind of magnetic field, quasi-constant along the symmetry of the structure, then outside the field lines loops themseves from one pole to another.
If I put a small coil on a ferrite rod inside the solenoid -or outside, the local field will be alterated, and nothing can tell me the value of the field at the coil position...
Nothing but maths ?

Seems to me like you could do some catalog shopping
at ferrite materials suppliers, looking for the dirt cheap
ones (AM radios, zero profit) and see if there is a "norm".

If you are only interested in the amount of flux in the core (most of it will come out at the end, where you need it), you can do a measurement with a 'pick-up' winding. Just put some extra turns across the solenoid, and measure the voltage generated on it. The input can be any current waveform, but probably a sinus is easiest.

Measure Iin and Vpickup with an oscilloscope, export to excel and do the maths.

This method can be used to determine magnetic properties, mostly on very low frequencies (to reduce the influence of the Eddy-currents on the BH-loop). But with Ferrite, I think eddy currents should not be a primary issue.

flux = -N dflux/dt --> flux = integrate(V*dt).

It is a bit tricky, but I used in the past to create some characteristics of the 'system' B-NI curve (not the BH-curve of only the material)