233
MOSFET Capacitance Models
Note that C GB = 0 in the strong inversion is expected since the inversion
charge in the channel from S to D shields the gate from the bulk and, therefore, prevents any response of Q G due to substrate bias V bs . Let us define
V gt = V gs − V th ; then using V gs − V ds = V gd (Figure 6.2b), Equation 6.19 can be
expressed as
C
Q
V
WLC
V V
V V
C
GS
G
gs
ox
gt
ds
gt
ds
GD
=
∂
∂
=
−
−
−
=
∂
2
3
1 2
2
Q Q
V
WLC
V
V V
C
Q
V
G
gd
ox
gt
gt
ds
GB
G
gb
∂
=
−
−
=
∂
∂
=
2
3
1 2
0
2
(6.20)
In the saturation regime, we can obtain the expression for Q G by replacing
V ds in Equation 6.18 by V dsat . We know that for a long channel device in saturation, V dsat = V gs − V th , and from Figure 6.2b, we get: V ds = V gs − V gd = V dsat
(=V gs − V th ). Therefore, in the saturation region, V gd = V th . Then, substituting
for V gd = V th in Equation 6.18, we get
Q
WLC
V V
V V
V V
V V
G
o x
th
th
gs
th
th
th
gs
th
=
−
(
) − −
(
)
−
(
) − −
(
)
2
3
3
3
2
2
−
=
−
(
) −
Q
WLC V V
Q
B
ox
gs
th
B
2
3
(6.21)
From Equation 6.21, we get the saturation region intrinsic capacitances at
V ds > V dsat
C
Q
V
WLC
C
Q
V
C
Q
V
GS
G
gs
ox
GD
G
gd
GB
G
gb
=
∂
∂
=
=
∂
∂
=
=
∂
∂
=
2
3
0
0
(6.22)
Note that the saturation region capacitances are independent of V ds . Since,
in saturation, the channel is pinched off at the drain end, it is electrically
isolated from the drain. Thus, Q G is not influenced by a change in V ds and the
capacitances are independent of V ds .
MOSFET Capacitance Models
Note that C GB = 0 in the strong inversion is expected since the inversion
charge in the channel from S to D shields the gate from the bulk and, therefore, prevents any response of Q G due to substrate bias V bs . Let us define
V gt = V gs − V th ; then using V gs − V ds = V gd (Figure 6.2b), Equation 6.19 can be
expressed as
C
Q
V
WLC
V V
V V
C
GS
G
gs
ox
gt
ds
gt
ds
GD
=
∂
∂
=
−
−
−
=
∂
2
3
1 2
2
Q Q
V
WLC
V
V V
C
Q
V
G
gd
ox
gt
gt
ds
GB
G
gb
∂
=
−
−
=
∂
∂
=
2
3
1 2
0
2
(6.20)
In the saturation regime, we can obtain the expression for Q G by replacing
V ds in Equation 6.18 by V dsat . We know that for a long channel device in saturation, V dsat = V gs − V th , and from Figure 6.2b, we get: V ds = V gs − V gd = V dsat
(=V gs − V th ). Therefore, in the saturation region, V gd = V th . Then, substituting
for V gd = V th in Equation 6.18, we get
Q
WLC
V V
V V
V V
V V
G
o x
th
th
gs
th
th
th
gs
th
=
−
(
) − −
(
)
−
(
) − −
(
)
2
3
3
3
2
2
−
=
−
(
) −
Q
WLC V V
Q
B
ox
gs
th
B
2
3
(6.21)
From Equation 6.21, we get the saturation region intrinsic capacitances at
V ds > V dsat
C
Q
V
WLC
C
Q
V
C
Q
V
GS
G
gs
ox
GD
G
gd
GB
G
gb
=
∂
∂
=
=
∂
∂
=
=
∂
∂
=
2
3
0
0
(6.22)
Note that the saturation region capacitances are independent of V ds . Since,
in saturation, the channel is pinched off at the drain end, it is electrically
isolated from the drain. Thus, Q G is not influenced by a change in V ds and the
capacitances are independent of V ds .