How would design a transformer that had adjustable cores? (for saturation and de-saturation)

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You can think of the core as a resistor, if you put a gap in the core , most of the "voltage " will appear across the air gap, the core sees less voltage along Its magnetic path. Just sub in flux for voltage and you have the whole concept.

Although the gapped core will see less DC flux, it can still be magnetized.
 
The propeller heads call it reluctance but it is a term that does not come up too often, there are formulas that use reluctance but they are not really needed to design a transformer.

r = l/μA

reluctance r is equal to the length of the core divided by the cross section of the core, A, the u is permeability,

if you throw out the perm, the concept us easy to understand, the longer the lamination, the more reluctance. If you double stack the lams to give it a larger cross section, then there are more paths for the flux so the reluctance gets cut in half.

if you put in an air gap, then you are increasing the length of the magnetic path soi reluctance goes up. It only takes a tiny air gap to add a length to magnetic length to the magnetic circuit.
 
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You can think of the core as a resistor, if you put a gap in the core , most of the "voltage " will appear across the air gap, the core sees less voltage along Its magnetic path. Just sub in flux for voltage and you have the whole concept.

Although the gapped core will see less DC flux, it can still be magnetized.
The frequency-band-pass will change too, when modding the air-gap. A cut to the low-end is predictable, when introducing more air- but at the other end, measurements will have to tell the tale
 
So it 'may' be possible to have a type of band pass filter by using a transformer with adjustable core... interesting... thx
 

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