AN2644 datasheet(23/64 Pages) STMICROELECTRONICS

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AN2644

The LLC resonant half-bridge converter

23/64

negative, i.e. it is returned to the input source. D1 keeps on conducting and the

voltage across Lp is a·Vout, so that Lp is not participating in resonance and Cr is

resonating with Ls only. IR is a portion of a sinusoid having a frequency f = fR1.

This phase ends when IR=0 at t=t6 and another switching cycle starts.

Remarks

Parallel inductor Lp never resonates and its current is essentially triangular (note: the

real magnetizing current is sinusoidal and cannot be seen on the oscilloscope). The

LLC converter, then, can be regarded as a series LC resonant half-bridge (composed

by Ls and Cr) that supplies a reactive RL load (composed by Lp and Rac, the equivalent

ac resistor loading the converter, as defined in [2] and reflected back to the primary

side). This standpoint provides considerable insight into the operation of the converter,

as shown in some of the following remarks.

In a resistively loaded series LC tank operating at resonance, the impressed voltage

and the tank current are exactly in-phase, hence the switched current is zero and,

thereby, ZVS cannot be achieved. The effect of adding an inductor (Lp) in parallel to

the resistive load is to provide tank current with the phase shift (lagging) necessary to

switch a current greater than zero, so that ZVS becomes now possible at resonance.

As shown in the diagrams of Figure 16, the tank circuit current lags the impressed

voltage by an angle

ϕ equal to:

Equation 5

so that they have the same sign at half-bridge leg transitions. Furthermore, the

switched currents IR(t1) and IR(t4) are large enough to complete the HB node swing well

within the deadtimes (t1, t2) and (t4, t5) respectively. It is not difficult to recognize that

the angle

ϕ is the phase of the input impedance of the loaded resonant tank evaluated

at f=fR1. Additionally, since the impedance of a series LC tank operating at resonance

is zero, it is possible to state that the input impedance of the LLC resonant tank at

resonance equals the impedance of the RL load.

Generally speaking, in a series LC tank operating at resonance, the voltage drop

across L is equal in module and opposite in sign to the drop across C at all times (this

is why its impedance is zero). In our specific case the drop across the series Cr-Ls will

be zero, so that it is possible to write the following voltage balance equations:

Equation 6

both of them resulting in the following relationship:

Equation 7

This is a fundamental property of the LLC resonant half-bridge: operating at f=fR1

implies that input and output voltages fulfill (1) and, vice versa, if input and output

voltages meet Equation 7 the converter is operating at f=fR1. Then, the fact that the

converter operates at resonance or not, for a given output voltage Vout and a given turn

ϕ 2π

–

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

--------

⋅

out

–

--------

–

⋅

out

–

Q1 ON, Q2 OFF

Q1 OFF, Q2 ON

--------

out

⋅

AN2644 Datasheet(PDF) 23 Page - STMicroelectronics

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