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

Hence, the combination of the exponential current from the PDA, which has a positive
third order term, with the current from the FDA may lead to a cancellation of the third order
terms under specific conditions. The output current of the transconductor is then linearized, as
it may be observed in Figure 118.
The drain current Id of a MOS biased in weak inversion and in the saturation region is
given by:
d
≈ 2β U
where VGS − Vth
is the input voltage and UT the thermal voltage.
I
2
T
e
V
GS
U
−V
T
th
- 101 -
(D.39)
This equation highlights a strong dependency of the current versus the gate-source
voltage. The biasing of the PDA should then be very accurate. The presence of β in the
equation also underlines the importance of the W/L ratio on the current. Thus, the impact of
process and mismatch variations will have to be studied more accurately later.
However, power consumption remains the same since almost no current is added by
the PDA stage, biased in the sub-threshold region. The resulting transconductance of these
two parallel pairs is equal to the FDA one but it is linear on a wider range, as depicted in
Figure 118. Hence, noise and gain stay unchanged.
In the example below, the FDA MOS size is 16µm/0.28µm, minimal gate length is not
used to limit Flicker noise, while the PDA MOS size is 50µm/0.28µm. The corresponding
currents are 1mA for the FDA while the PDA draws about 6µA. Thanks to this technique it is
possible to get a high gm to minimize noise and to optimize linearity. Currents and gm of both
amplifiers and of the sum are plotted on Figure 118.
Figure 118. Transconductance linearization by MGTR