AN4461 datasheet(17/70 Pages) STMICROELECTRONICS

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AN4461

ZVS LC resonant stage description

4.1

LC stage customization

4.1.1

Resonant Cell ZVS design

In order to maintain the zero voltage switching condition Equation 5 needs to be met.

Equation 5

When the half-bridge switching frequency (fs) is close to the resonance frequency (fR) then

the shape of the resonant tank current is piecewise sinusoidal. Otherwise, when fs >> fR

then the shape of the resonant tank current is piecewise linear.

For the purpose of the analysis both the magnetizing current and the AC voltage across the

tank capacitor Cres are negligible.

Considering that the square wave voltage applied to the resonant tank has 50% duty cycle,

it is possible to state:

Equation 6

Furthermore the output current is given by the superposition of the currents through the

secondary rectifier (Dout) and is a series of contiguous triangles. The DC output current is

equal to half of the resonant current peak value multiplied by transfer ratio (n = NPRI /

NSEC).

Equation 7

It can be demonstrated that the switching frequency of the converter is represented by

Equation 8:

Equation 8

The half-bridge frequency depends directly on the input voltage and inversely on the LED

current and depends on the difference between the square of the input voltage and the

reflected value of the output voltage.

It should be noted that the half-bridge frequency has a hyperbolical behavior depending on

the output power (ILED, VLED). This behavior is the main difference when compared to

an LLC or LCC resonant converter (see AN2644 and AN2450 on www.st.com).

The LC minimum operating frequency is obtained at the maximum output current, maximum

output voltage and minimum PFC output voltage. The maximum frequency is, instead,

obtained at the minimum output current (ILED, min), minimum output voltage (consider

short-circuit if required) and maximum input voltage.

(

)

Vpfc

Vdout

VLED

⋅

(

)

Vpfc

Cres

⋅

≈

Ires,

ILED

⋅

≈

(

)

[

]

Vpfc

Vdout

VLED

Vpfc

Lres

ILED

⋅

−

⋅

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