AN2644 datasheet(52/64 Pages) STMICROELECTRONICS

52 / 64 page

Resonant transitions of half-bridge midpoint

AN2644

52/64

The expression of the tank current will be:

Equation 34

Equations (Equation 30) to (34) apply in the time interval (0, TT), where TT is the time

needed for the voltage VHB to reach Vin. TT can be calculated from (Equation 32) taking (33)

into account; the result is:

Equation 35

To achieve ZVS, the value of TT given by (Equation 35) must not exceed the deadtime TD to

make sure that Q1 is turned on with zero drain-to-source voltage.

Note that in CCM operation there may be an additional constraint on the time interval where

equations (Equation 30) to (34) are applicable. The current IR(t) will be described by

Equation 34 either until TT or until it equals the current flowing through Lp (see Figure 9),

whichever condition occurs first. We will assume that IR(t)=I(Lp) occurs after TT.

With the usual values of all the involved quantities, the phase angles

CC and

DD are both

considerably less than unity, then it is possible to use the approximation

≈ sin ϕ ≈ tan ϕ

for both of them. With this simplification (Equation 35) can be expressed as:

Equation 36

for both CCM and DCM modes, which is equivalent to considering CHB charged by a

constant current IR(0).

Considering that in CCM operation above resonance it is Vin > 2·a·(Vout + VF) and, again,

that VC(0) ≤ Vin/2, ϕCC is always negative. As a result, IR(t) has its peak for negative t values

and decays in (0, TT). In DCM operation, if the input current is lower than a critical value, it is

VC(0) > 0 and, then, ϕDD positive. Thereby, IR(t) has its peak for positive t values, thus it

initially increases and then decays in (0,TT). In this case, which happens at light load and

with no load, the approximation IR(t) = IR(0) is excellent. Still in DCM operation, but with an

input current exceeding that critical value, it is VC(0) < 0 and, then, ϕDD negative, which

happens below resonance at heavy load. However, as compared to what happens in CCM

operation, the associated resonance period is longer, thus the change in IR(t) is lower and

the approximation IR(t) = IR(0) is still good. This is illustrated in Figure 31 and 32.

R t

()

HB t

()

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

DDt

–

()

R 0

()

cos

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

DDt

–

()

cos

⋅⋅

⋅

CCt

–

()

R 0

()

cos

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

CCt

–

()

cos

⋅⋅

⋅

⎩

⎪

⎨

⎪

⎧

DCM

CCM

-----------

–

C 0

()

–

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

⎝⎠

⎛⎞

sin

-----------

–

C 0

()

–

out

()

⋅

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

⎝⎠

⎛⎞

sin

⎩

⎪

⎨

⎪

⎧

DCM

CCM

R 0

()

-------------C

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