AN2644 datasheet(7/64 Pages) STMICROELECTRONICS

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AN2644

The LLC resonant half-bridge converter

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In resonant inverters (and converters too) power flow can be controlled by the switch

network either by changing the frequency of the square wave voltage, or its duty cycle, or

both, or by special control schemes such as phase-shift control. In this context we will focus

on power flow control by frequency modulation, that is, by changing the frequency of the

square wave closer to or further from the tank circuit's resonant frequency while keeping its

duty cycle fixed.

The LLC resonant half-bridge converter

2.1

General overview

According to another way of designating resonant converters, the LLC resonant half-bridge

belongs to the family of multiresonant converters. Actually, since the resonant tank includes

three reactive elements (Cr, Ls and Lp, shown in Figure 3), there are two resonant

frequencies associated to this circuit. One is related to the condition of the secondary

winding(s) conducting, where the inductance Lp disappears because dynamically shorted

out by the low-pass filter and the load (there is a constant voltage a Vout across it):

Equation 1

the other resonant frequency is relevant to the condition of the secondary winding(s) open,

where the tank circuit turns from LLC to LC because Ls and Lp can be unified in a single

inductor:

Equation 2

It will be of course fR1 > fR2. Normally, fR1 is referred to as the resonance frequency of the

LLC resonant tank, while fR2 is sometimes called the second (or lower) resonance

frequency. The separation between fR1 and fR2 depends on the ratio of Lp to Ls. The larger

this ratio is, the further the two frequencies will be and vice versa. The value of Lp/Ls

(typically > 1) is an important design parameter.

It is possible to show that for frequencies f > fR1 the input impedance of the loaded resonant

tank is inductive and that for frequencies f < fR2 the input impedance is capacitive. In the

frequency region fR2 < f < fR1 the impedance can be either inductive or capacitive depending

on the load resistance R. A critical value Rcrit exists such that if R < Rcrit then the

impedance will be capacitive, inductive for R> Rcrit. For a given tank circuit the value of Rcrit

depends on f. More precisely, in [6] it is shown that for any tank circuit configuration (then for

the LLC in particular):

Equation 3

where Zo0 and Zo∞ are the resonant tank output impedances with the source input short-

circuited and open-circuited, respectively.

π Ls Cr

⋅

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

π Ls Lp

()Cr

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

crit

Zo∞

⋅

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