(distributed) air gap

[romy]

i understand b-h curves (to a certain extend), the hanna curve and appreciate how toroids are chosen as a function of LI^2. after reading and watching vids quite a bit i still cant really, really grasp the "paradox", that first we invent materials of high permeability and then have to dillute/mitigate permeability with air gaps.

can somebody please point me to a good read on this or even put it in a way, so that it all finally falls into place?

[klugesmith]

Reduced permeability, such as with discrete or distributed air gaps, is never good in a true transformer.
Transformers don't store energy; power goes into primary winding at the same time power goes out from secondary winding.

Air gaps are useful when we need to store energy in a magnetic field, as in a flyback converter or other SMPS converter.
The ferromagnetic core is useful for guiding the magnetic flux, so wire turns in one or more coils can be well coupled. (The turns mostly encircle the same magnetic flux.)
But the core saturates at some flux density, around 2T for iron or a fraction of 1T for ferrite.

For a given winding, and given core dimensions, an air gap reduces the inductance but increases the saturation current, in same proportion.
That increases the energy storage, which is proportional to L and to square of current.

In a traditional flyback core with air gap in middle of HV coil, the magnetic "reluctance" of airgap is much more than total reluctance of the flux path in ferrite.
Magnetic energy density at a place, in joules per cubic meter,  is (B * H / 2).
Flux density is about the same within core and inside the air gap, but H is vastly higher in the air gap.   The air gap volume holds more magnetic energy than the whole solid core (and the space outside the core, which has some leakage flux).

[romy]

thank you. yes, im rather concerned with storage chokes (for now). i see how 1/2 x L x I^2 works out and obviously the gap helps storing magnetic energy but the original fuzziness remains: why not use lower permeability material in the first place. what is the difference?

im seeing flatter b-h (hysteresis-) curves with distributed air gaps which means lower permeability, right? maybe i should take a step away from these diagrams and look at it from another point of view?

today i want to find out how to get from 1/2 x L x I^2 to B x H. both stand for potential energy, yes?

(i wrote this several days ago, somehow it didnt get posted.)

[davekni]

why not use lower permeability material in the first place.

Because there are few such materials, and none AFAIK with sufficient saturation flux density and low hysteresis.  That is why lower permeability materials are artificially constructed by adding air (or epoxy...) gaps.