# Three legged transformer with only one winding

Discussion in 'Homework Help' started by greenheck1, Apr 4, 2011.

1. ### greenheck1 Thread Starter New Member

Mar 29, 2011
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0
Hi ...
Lets say we have 3 legged core with only one winding around the middle core and no windings around the outer legs .. just like the picture below

then, the permeance (inverse of reluctance) of the center leg would be = (Mu*A1) / (L1) .. and the permeance of the other two legs would be = (Mu*A2) / (L1 +L2) .. where L1=6, L2=8, A1 = cross sectional area of center core and A2 area of each of the outer leg.

BUT ... if the winding was on one of the outer legs, how would the value of the permeance change for both the core and outer legs? and would the total inductance increase or decrease from before?

THanks

Last edited by a moderator: Apr 4, 2011
2. ### greenheck1 Thread Starter New Member

Mar 29, 2011
3
0
I uploaded a sketch of the transformer made by myself since the mod removed the original picture. here's a link

Mar 29, 2011
3
0
4. ### t_n_k AAC Fanatic!

Mar 6, 2009
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784
While your assumptions for the excitation being on the center leg are OK you have overlooked the permeances (or reluctances) of the top and bottom sections.

The usual approach is to find the equivalent reluctance of each major section of the magnetic circuit and then draw a total equivalent magnetic circuit comprising series / parallel reluctances with the mmf centered on the particular leg being driven. The magnetic circuit is 'solved' in a similar manner to that used for solving a DC series / parallel electric circuit.

The equivalent reluctance seen by the driving mmf will be different but the individual section reluctance values will remain unchanged - assuming of course that the magnetic material is ideal.

Perhaps you know this already but to re-iterate the duality ....

MMF <=> EMF
Reluctance <=> Resistance
Flux <=> Current

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