III. Gm-C Filtering - Epublications - Université de Limoges

one gets
for X ≤ 2 .
Hence, for small signals, the transconductance can be approximated to:
g ≈ β ( V −V
)
(D.16)
m
GS
D.1.b Linearity Computation
Normalizing the latter equation to the effective gate voltage, defined as
E md Emd
X = = ,
I V −V
0
β
GS
th
- 214 -
th
(D.17)
2
I md X
y = = X 1−
(D.18)
I
4
0
Hence, developing up to the third order, this leads to
3
X
y ≈ X − . (D.19)
8
Thus, it gives:
To compute IIP3, it is needed:
one obtains:
Given that
3
∂ y 3
= − . (D.20)
3
∂X
4
g 3
IM 3 = X
g 32
3
2
= . (D.21)
1
Vin
IIP3
= , (D.22)
IM 3
2
IIP3 = 4 ( VGS
− Vth
)
(D.23)
3