AN2450 datasheet(22/35 Pages) STMICROELECTRONICS

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Magnetic integration

AN2450

22/35

DocID12784 Rev 6

Figure 10. Transformer's APR (all primary referred) model

The problem is mathematically undetermined: there are 5 unknowns (LL1, Lµ, nt, and LL2a,

LL2b) in the physical model and only three parameters in the APR model. The simplifying

assumption that overcomes this issue is that of magnetic circuit symmetry: flux linkage is

assumed to be exactly the same for both primary and secondary windings. This provides the

two missing conditions:

Equation 52

With this assumption it is now possible to find the relationship between n and nt:

Equation 53

Figure 11. Transformer construction: E-cores and slotted bobbin

It is not difficult to find real-world structures where the condition of magnetic symmetry is

quite close to reality. Consider for example the ferrite E-core plus slotted bobbin assembly,

using side-by-side winding arrangement, shown in Figure 11.

Ideal Transformer

n : 1 : 1

Ideal Transformer

n : 1 : 1

LL2a

LL2b

LL1

---------

Lm Lr

------------------



Air gap symmetrically

placed between the

windings

Separator

Slotted

bobbin

Ferrite

E half-cores

Winding

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