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

APPENDIX D
D.1 MOS Differential Pair
The following study is based on computations that may be found in [D.1] and [D.2].
D.1.a Transfer Characteristic
Let’s consider the MOS differential pair depicted in Figure 205. It is also assumed that
M1 and M2 are in the strong inversion regime and in saturation mode.
Hence,
Assuming that
Figure 205. Simplified Transconductor
W
β = μCox
(D.1)
L
and the same β for M1 and M2, currents I1 and I2 are given by:
1
I1 = β
2
1 c −
1
2
2 c
2
V E E I − − = β
( ) 2
V E E −
- 212 -
th
( ) 2
1
I 1 = β 1 c −
2
th
( E − E V )
I 2 =
1
β ( E 2 − Ec
2
−Vth
)
It is also considered the differential current Imd, defined as follows:
th
(D.2)
(D.3)
(D.4)
(D.5)