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

In terms of noise, the Flicker noise which exhibits a 1/f dependency is neglected as a
first order approximation since TV bands are located above 45MHz. Hence, transconductor
input-referred noise power is proportional to 1/gm [III.4]:
Figure 108. Input referred noise power
2 ⎛ 2 2g
⎞ m3
λ ⎛ g m3
⎞
V ≈
⎜ +
⎟ ∝ ⎜ + ⎟
n,
in 8kT
1 .
2
⎝ 3g
m1
3g
m1
⎠ g m1
⎝ g m1
⎠
λ being a constant term, k being the Boltzman constant and T the temperature.
- 93 -
(III.28)
This means that the higher the transconductance (gm1) values, the lower the noise of
the Gm-cell. However, they suffer from non-linearity, as shown in Figure 109. Indeed this
figure describes the gm versus the input voltage for a same current and various transistor sizes
which increase the transconductance. From this graph it is clear that high transconductances
have to be improved using linearization techniques.
Figure 109. Transconductance non-linearity at constant current, varying the W/L ratio
Furthermore, the choice of high transconductance values means the use of high
g m
capacitances to be able to reach the low end of the TV bands since f 0 ≈ , as shown in
2πC
Figure 110. In an advanced CMOS technology, large capacitors integration are not suitable
for an optimum die area.