Page 105 - Rashid, Power Electronics Handbook

6 The Power MOSFET 91

V DD V
DD

I O D i
O

+ V -
DD

+
i =
i G
G V =V 0
i DS
D
R DD R
G G
-
V GG =0 V GG =0

(c) (d)
FIGURE 6.22 Equivalent circuits: (a) t 0 t < t 1 ; (b) t 1 t < t 2 ; (c) t 2 t < t 3 ; and (d) t 3 t < t 4 .

Assuming i constant at its initial value at t ¼ t , that is, At t ¼ t , the drain-to-source voltage becomes equal to
2
1
G
V , forcing D to turn-on as shown in Fig. 6.22c.
DD
v ðt Þ 1 I 0
GS 1
i ¼ ¼ þ V Th The drain-to-source current is obtained from the transfer
G
R G R G g m characteristics and given by
Integrating both sides of the preceding equation from t to t i ðtÞ¼ g ðv ÿ V Þ
1
with v ðt Þ¼ÿv DSðONÞ , we obtain DS m GS Th
DS 1
Where v ðtÞ is obtained from the following equation:
1 I 0 GS
v ðtÞ¼ v DSðONÞ þ þ V Th ðt ÿ t Þ ð6:34Þ
DS
1
R C g
G GD m v GS dv GS
i ¼ÿ ¼ðC GS þ C GD Þ ð6:35Þ
G
hence v charges linearly until it reaches V . R G dt
DS DD