Re: Current Limiting and Impedence

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: syd <tesla@xxxxxxxxxxxxxxx>

Hello Gerry,

The introduction of an air gap reduces the effective permeability of the 
core, which in turn decreases the magnetic flux density (B). B needs to 
remain below the saturation point for the core material you are using, 
typically 1.6 tesla for grain oriented silicon steel (common in 
transformers). In a current driven winding, such as in a ballast inductor, 
the volts per turn isn't so important; what IS important is the current, 
the number of turns, the magnetic path length, and the permeability of the 
core.

If you're buying the steel laminations from a supplier then you'll have 
access to their specs for magnetic path length and permeability for a given 
core. E/I cores are the best because you can very accurately introduce an 
air gap with a spacer and bolt the whole thing together. If you're using a 
'found' core such as from a transformer, then you can roughly measure the 
magnetic path length. In an E/I core there are two paths, both go through 
the center and then circle around the shells. Add both of those together 
and you have the total magnetic path length for that core in meters.

Next you need to determine the core's relative permeability. If you have no 
data on it, and it is a laminated steel core, then this figure might be 
around 40,000. That is to say, 40,000 times more permeable to a magnetic 
field than a vacuum. This would be the permeability of the core with NO air 
gap. For an example, in the ballast inductors that I'm using in CAUAC, 
without an air gap they would saturate with only one turn! Adding in a few 
millimeters of air in the magnetic path length decreases the effective 
permeability by perhaps 300 times.

Effective permeability = relative permeability/(1+ (relative permeability x 
length of gap/total magnetic path))

(and in an E/I core the gap length will be twice the spacer thickness since 
the magnetic path crosses the spacer twice.)

B = permeability of a vacuum x effective permeability x H tesla
(permeability of a vacuum is: 1.257 E -06)

H = amperes per meter (which is ampere turns divided by magnetic path length)

And ampere turns are simply the current in the winding times the number of 
turns.

Suffice to say, almost every parameter affects every other parameter and 
you end up with a balancing act (kind of like tesla coil design!). You need 
heavy enough wire to keep it from melting the insulation, and you can only 
fit so many turns in the window space of the core. When you decrease the 
effective permeability of the core, it's going to take more windings to 
give you the target inductance, which in turn will increase H. BUT! 
Fortunately the inductance increases as the square of the turns, whereas H 
increases linearly. Theoretically you could build such an inductor without 
an air gap if the magnetic path length were  enormous.

The cross sectional area of the core is indirectly important. Since the 
total flux of the core in webers = B x cross sectional area of the core, 
and since this affects the inductance, then all other factors being the 
same, increasing the cross sectional area of the core increases inductance 
allowing one to use fewer windings which will in turn decrease H.

Yes. Air gaps are good in ballast inductors. Hope that wasn't unnecessarily 
obfuscatory.

syd klinge

p.s. I have new photos and video up on my web site of CAUAC's trip to 
Australia. http://www.playahearth.com





Tesla list wrote:

> Original poster: "Gerald  Reynolds" <gerryreynolds@xxxxxxxxxxxxx>
>
> Hi Steve,
>
> Could you elaborate a little more on the lack of an air gap.  It seems to 
> me that once you set the volts per turn and the cross sectional area of 
> the core, that deterimines the margin from saturation.  If one then 
> eliminates the air gap, all that changes is the inductance goes up and the 
> ballast current  goes down.  Im thinking the reason for an air gap has to 
> do with the effective BH curve and the resulting core losses.  Would this 
> be correct??
>
> Gerry R
>
> > Original poster: Steve Conner <steve@xxxxxxxxxxxx>
> >
> > Ballast inductors without air gaps are no good whatever the core 
> > material. The one exception being iron powder which has a "distributed 
> > air gap". So you will see iron powder toroids used as filter chokes in DC 
> > power supplies and the like.