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

III.1.e Introduction to Transconductors Optimizations
As discussed previously, the dynamic range of the filter is directly related to the
dynamic range of its inner transconductors. Hence, all three transconductors have to be
optimized. This section studies the Gm-cells limitations to find an optimal trade-off in terms
of linearity and noise. This study has to be performed to reach the specifications both in terms
of frequency tuning range and of selectivity.
To optimize the Gm-cell bloc, it is considered a simplified Gm-cell with an active
load, regulated by a common-mode feedback (CMFB) [III.3], as described in Figure 107. The
bias of the differential pair ensures that gm1 = gm2 and gm3 = gm4. Hence, the transconductance
gm of this Gm-cell is given by:
g = g = g . (III.25)
m
m1
m2
Figure 107. Differential transconductor
As detailed in APPENDIX D, the transconductance gm of such a differential pair is
given by:
I 0
g m ≈ β ( VGS
−V
th ) = , (III.26)
V −V
( )
with VGS-Vth being the input voltage on either T1 or T2, and with
GS
- 92 -
th
W
β = μCox
. (III.27)
L