AN2450 datasheet(21/35 Pages) STMICROELECTRONICS

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AN2450

Magnetic integration

The LLC resonant half-bridge is well suited for magnetic integration, i.e. to combine the

inductors as well as the transformer into a single magnetic device. This can be easily

recognized looking at the transformer's physical model in Figure 9, where the topological

analogy with the inductive part of the LLC tank circuit is apparent. However, the real

transformer has leakage inductance on the secondary side as well, which is completely

absent in the model considered so far. To include the effect of secondary leakage in the FHA

analysis, we need a particular transformer model and a simplifying assumption.

It is well known that there are an infinite number of electrically equivalent models of a given

transformer, depending on the choice of the turn ratio of the ideal transformer included in the

model. With an appropriate choice of this “equivalent” turn ratio n (obviously different from

the “physical” turn ratio nt = N1/N2) all the elements related to leakage flux can be located

on the primary side.

This is the APR (all primary referred) model shown in Figure 10, which fits the circuit

considered in the FHA analysis. It is possible to show that the APR model is obtained with

the following choice of n:

Equation 51

with k transformer's coupling coefficient, L1 inductance of the primary winding and L2

inductance of each secondary winding. Note that Lr still has physical meaning: it is the

primary inductance measured with the secondary windings shorted. Note also that the

primary inductance L1 must be unchanged. It is only differently split in the 2 models of

Figure 9 and Figure 10, hence, Lm will be the difference between L1 and Lr.

In the end, the analysis done so far is directly applicable to real-world transformers provided

they are represented by their equivalent APR model. Vice versa, a design flow based on the

FHA analysis will provide the parameters of the APR model; hence, an additional step is

needed to determine those of the physical model. In particular this applies to the turn

number nt, since Lr and Lm still have a connection with the physical world

(Lr + Lm = LL1 + Lµ = L1).

Figure 9. Transformer's physical model

------

Lμ

Ideal Transformer

t : 1 : 1

Magnetizing

inductance

Sec. leakage

inductance

L2a

L2b

Sec. leakage

inductance

Prim. leakage

inductance

Lμ

Ideal Transformer

t : 1 : 1

Magnetizing

inductance

Sec. leakage

inductance

L2a

L2b

Sec. leakage

inductance

Prim. leakage

inductance

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