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AN2644 Datasheet(PDF) 56 Page - STMicroelectronics

Part # AN2644
Description  An introduction to LLC resonant
PDF  64 Pages
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Manufacturer  STMICROELECTRONICS [STMicroelectronics]
Direct Link  http://www.st.com
Logo STMICROELECTRONICS - STMicroelectronics

AN2644 Datasheet(HTML) 56 Page - STMicroelectronics

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Power MOSFET effective Coss and half-bridge midpoint's transition times
AN2644
56/64
Figure 35.
Simplified schematic to analyze transition times of the node HB when Q2
turns off
Assuming that VHB
|
t=0 it is possible to write:
Equation 46
Note that the left-hand side is the total charge Qoss(VHB) supplied to Coss(VHB) to raise its
voltage up to the level VHB. Substituting (Equation 44) in (Equation 46) and developing, it is
possible to find:
Equation 47
Considering again the turn-off of Q2, as a consequence of the discussion of the previous
section, the equivalent schematic of the circuit during the turn-off of Q2 is illustrated in
Figure 35, where the tank circuit is then replaced by a constant current source equal to the
switched current IR0. Additionally, the turn-off of Q2 is assumed to be linear in time:
Equation 48
where Tf is the time the current IQ2 takes to become zero. The total capacitance of the node
HB will be:
Equation 49
CHB will be charged by the current ICHB = IR0 - IQ2 until VHB equals the input voltage Vin and
DQ1 turns on, thus clamping VHB at Vin. Let us assume that the time TT needed for the
voltage of the node HB to reach Vin is greater than Tf. The main quantities during the
transient are illustrated in Figure 36. The total charge QT delivered to CHB in the interval
(0, TT) will be:
Equation 50
=
IR0
CHB (VHB)
IR0 –IQ2
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
f
0
R
2
Q
T
t
1
I
I
Vin
IR0
CStray
Coss1
Coss2
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
f
0
R
2
Q
T
t
1
I
I
DQ1
=
IR0
CHB (VHB)
IR0 –IQ2
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
f
0
R
2
Q
T
t
1
I
I
IR0
CHB (VHB)
IR0 –IQ2
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
f
0
R
2
Q
T
t
1
I
I
Vin
IR0
CStray
Coss1
Coss2
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
f
0
R
2
Q
T
t
1
I
I
DQ1
Vin
IR0
CStray
Coss1
Coss2
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
f
0
R
2
Q
T
t
1
I
I
DQ1
I
C
oss
τ
() τ
C
oss V
() V
d
0
V
HB
∫
=
d
0
tf
∫
Qoss V
HB
()
10
V
HB
V
in
V
in
V
HB
–
–
+
()C
oss25
=
0t T
f
≤≤
tT
f
>
I
Q2
I
R0 1
t
T
f
-----
–
⎝⎠
⎛⎞
0
⎩
⎪
⎨
⎪
⎧
=
C
HB VHB
()
C
Stray
C
oss VHB
()
+
=
Q
T
1
2
---I
R0Tf
I
R0 TT
T
f
–
() I
R0 TT
T
f
2
-----
–
⎝⎠
⎛⎞
=
+
=



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