AN2644 datasheet(50/64 Pages) STMICROELECTRONICS

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Resonant transitions of half-bridge midpoint

AN2644

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Appendix B

Resonant transitions of half-bridge midpoint

To analyze the transitions of the half-bridge midpoint node HB when either Q1 or Q2 is

turned off, it is necessary to schematize the equivalent circuit during the transient. For

simplicity only the turn-off of Q2 will be considered, being obvious that the turn-off of Q1 will

be exactly mirror-symmetrical. Different circuits need to be considered, depending on

whether the converter is operated in a DCM mode or a CCM mode. These equivalent

circuits are shown in Figure 30.

Figure 30.

Equivalent circuit to analyze the transitions of the half-bridge midpoint

node when Q2 turns off

In fact, in the case of DCM operation, since the secondary windings are open, Lp is part of

the circuit and is effectively in series to Ls to form a single inductor Ls+Lp. In CCM

operation, instead, since the secondary windings are conducting there is a constant voltage

equal to ±a·(Vout+VF) across Lp and then this can be replaced by a voltage generator

(placed as shown in Figure 30 in the case under consideration). In either circuit, Q2 is

replaced by an ideal switch that opens at t=0.

Resonant tanks are again involved during the transitions, hence the denomination "resonant

transitions" given to the swings of the node HB. Considering the operation of the LLC

resonant converter in its entirety, then, there are four associated resonant frequencies.

CHB is the total parasitic capacitance of the node HB already discussed in Section 2.2: The

switching mechanism and illustrated in Figure 8 and that will be the topic of the next section.

Note that during the transient Cr and CHB are effectively in series. However, since normally

Cr>>CHB (typically, two orders of magnitude), the combined capacitance will be ≈CHB and

the changes of the VC voltage during the transient can be neglected, so that it is possible to

assume VC = VC(0) during the transient and replace Cr with a constant voltage generator

VC(0).

The value of VC(0) can be determined on the basis of the following considerations. The

value of at the end of the conduction cycle of Q1, VC(Ts/2), is given by:

Equation 26

t = 0

OFF

t = 0

OFF

a·(Vout+V

VLs

VHB

DCM operation

CCM operation

t = 0

OFF

t = 0

OFF

a·(Vout+V

VLs

VHB

t = 0

OFF

t = 0

OFF

t = 0

OFF

a·(Vout+V

VLs

VHB

DCM operation

CCM operation

-------

⎝⎠

⎛⎞

C 0

()

------

R t

() t

-------

∫

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