Re: Current Limiting and Impedence

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Mark Dunn" <mdunn@xxxxxxxxxxxx>


My gapped MOT worked great as a current limiter for my MOT based power
supply.  I ended up with 60Turns and a gap of .036".  This gave me an L
= ~5 mH.  The Inductor voltage drop was 30 volts and a current of 16.7
amps.

In analyzing the math I still get messed up in the permeability.  I was
hoping someone would clarify for me from my earlier posts.  I think the
permeability subscripts are not universal so bear with me and lets go
through the math.  Then we can discuss something extremely
interesting(to me anyway) after we are all on the same page and we
clarify any math errors that I make.

First, lets consider an inductor where we know the characteristics of
the core from the mfg(Note-since I salvage everything I can't do it this
way and that's where it gets interesting).  Note: Terms were defined in
5/11/05 1:05 PM Post.

So we have a core and we know from the Mfg:
Ve(mm^3), Ae(mm^2), Le(mm)
C(mm^-1) = ~ Le/Ae(This will be used later).
Inductance Factor - AL(nH)
Initial Permeability - Ui(dimensionless, relative to Uo)

Uo = 4*Pi*10^-7 H/m (Magnetic Constant)

Let's propose a # turns N for the coil.

Then the Inductance with NO Gap is  L = AL * N^2 * 10^-9 H  (equ 1)

The Core Flux Density is B = Vp*10^6/(4.44*Ae*N*F) Tesla  (equ 2)
(Note: sine wave formula for B)
Vp = Peak Voltage(volts)
F =  Freqency(Hz)
Compare B to Bpk and Bsat limits to be sure not saturated.
(Note: We get Bpk and Bsat from the characteristics of the core
material-again data from the mfg)

The Magnetic Field Strength is H=(10^3)*I*N*1.414/Le A/m  (equ 3)
I = Current(amps) Should this be peak current???

Absolute Permeability required U = B/H Henries/meter

Relative Permeabilty required Ur=U/Uo
(is this also called Equivelent Permeability Ue??)

So then the required Gap can be computed as:

Total Gap = G = ((Ui/Ur-1)Le/Ui)/25.4 inches     (equ 4)
So the Spacer would be 1/2 of this Gap.

Pls comment on this math as if it is not correct then everything from
her on is garbage.

So now consider the case of a salvaged core with no know properties.
We can physically measure the core to get Ve, Ae, Le and compute
C = Le/Ae.

We can make a coil with a given number of turns and apply a series of
voltages(V) and measure current(I) with NO GAP.  The we can compute Z =
V/I for this set of data.  Z should be constant if we are not
saturating.
Then L = Z/(2*Pi*F) Henries (Assume R (Ohms) is negligible.
So then working backwards we get:
AL = L/(10^-9 * N^2) nH
For my MOT core I computed AL = 10,500 nH(can anyone else confirm?) from
my testing.
So then I computed B & H from the data and subsequently U and Ur.
Ur = 800 for my un-gapped case(Seems kinda low?)
So in theory Ui = Ur(no Gap) = 800 (Is this right?)

Now I can repeat the tests for a gapped core.  I know AL already from
the un-gapped case.

This is where things get interesting.  From the test data I can compute
B and H and subsequently U & Ur for each case.  I know the Gap that I
used so if we re-arrange equation #4 above we get:

Ui=1(1/Ur-25.4*G/(Le))
(Note: G is total gap - 2 X spacer)

Upon tabulating the data I get Ui ranging from -1700 to 22000.  I have
about 30 data points.  A few of the data point give a Ui = ~ 800(Recall
that is what I got for the un-gapped core).

It appears that Ui is extremely sensitive to small measurement errors in
the data and that this renders this method somewhat useless.

Interestingly, somewhere I picked up a formula that the permeablity of
an ungapped core is:
Ur = AL x C/Uo = ~AL*Le/(Ae*Uo)
Anybody know if this is true and how it is derived.  It does work out to
~800 for this case.

Did anyone follow all this?
Comments please.

Thanks.
Mark