AN3180 datasheet(32/39 Pages) STMICROELECTRONICS

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Electrical equivalent circuit models of coupled inductors and transformers

AN3180

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Doc ID 17273 Rev 1

inductance Lb is associated to the secondary leakage flux, the flux generated by the

secondary winding and not completely linked to itself nor to the primary winding: it is called

secondary leakage inductance and is designated by Ll2.

This choice of a is perhaps the most logical one, and is also very useful because it provides

a clear physical meaning to each element of the equivalent circuit, shown in Figure 25, but it

is not the only one that makes sense.

Figure 25.

Model of coupled inductors with a = n (a=n model)

Another possible choice, which leads to always positive values for La and Lb, is a =

This quantity, usually indicated with ne, is termed “equivalent turn ratio” and is conceptually

and numerically different from the physical turn ratio n:

Equation 27

which coincides with n if and only if Ll2 = n

2 L

l1, that is in case of symmetrical magnetic

coupling (k1 = k2 = k).

This choice is particularly useful when the physical turn ratio n is unknown, so that it is

possible to complete the model computing ne from L1 and L2, which are easily measurable.

In this case, Equation 26, considering Equation 23, takes the form:

Equation 28

It is worth noting that Lb, reflected back to the primary side, equals La, as pointed out by the

third Equation 28. Note that this property is often erroneously attributed to the primary and

secondary leakage inductances Ll1 and Ll2. It is worth stating once more that k represents

an average coupling between the windings and that the coupling k1 of the primary winding

to the secondary one is generally different from the coupling k2 of the secondary winding to

the primary one, and so Ll2 ≠ n2 Ll1. It is Ll2 = n2 Ll1 only in the special case of a winding

geometry symmetrical in such a way that the reluctance of the leakage flux path is the same

for both windings, resulting in symmetrical coupling between windings (k1 = k2 = k).

2 L1

⁄

(

)

()

⎪

⎩

⎪

⎨

⎧

−

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