AN2450 datasheet(9/35 Pages) STMICROELECTRONICS

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AN2450

Voltage gain and input impedance

Starting from Equation 18 we can obtain the expression of the voltage gain:

Equation 20

with the following parameter definitions:

resonance frequency:

characteristic impedance:

quality factor:

inductance ratio:

normalized frequency:

Under no-load conditions, (i.e. Q = 0) the voltage gain assumes the following form:

Equation 21

Figure 3 shows a family of plots of the voltage gain versus normalized frequency. For

different values of Q, with

 = 0.2, it is clearly visible that the LLC resonant converter

presents a load-independent operating point at the resonance frequency fr (fn = 1), with

unity gain, where all the curves are tangent (and the tangent line has a slope -2

).

Fortunately, this load-independent point occurs in the inductive region of the voltage gain

characteristic, where the resonant tank current lags the input voltage square waveform

(which is a necessary condition for ZVS behavior).

The regulation of the converter output voltage is achieved by changing the switching

frequency of the square waveform at the input of the resonant tank: since the working region

is in the inductive part of the voltage gain characteristic, the frequency control circuit that

keeps the output voltage regulated acts by increasing the frequency in response to a

decrease of the output power demand or to an increase of the input dc voltage. Considering

this, the output voltage can be regulated against wide loads variations with a relatively

narrow switching frequency change, if the converter is operated close to the load-

independent point. Looking at the curves in Figure 3, it is obvious that the wider the input dc

voltage range is, the wider the operating frequency range will be, in which case it is difficult

Mfn  Q







-------

–





 2

2 f

----

–



 2

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

 L

rCr

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

------

f

rLr

f

rCr

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

Rac

---------

oac

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



------

Pout

out

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



-------

fsw

-------

MOL fn 







-------

–

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

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