III. Gm-C Filtering - Epublications - Université de Limoges
III. Gm-C Filtering - Epublications - Université de Limoges
III. Gm-C Filtering - Epublications - Université de Limoges
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The equivalent impedance of a parallel RLC circuit can be computed. Neglecting<br />
drain-source capacitances at first or<strong>de</strong>r, one gets:<br />
L<br />
R<br />
C<br />
R<br />
eff<br />
s<br />
p<br />
p<br />
C<br />
=<br />
g g<br />
= C<br />
m1<br />
m1<br />
gs1<br />
1<br />
=<br />
g<br />
02<br />
gs2<br />
g01<br />
=<br />
g g<br />
This structure resonates with the following parameters:<br />
ω =<br />
0<br />
Q =<br />
g<br />
g<br />
g<br />
m1<br />
m1<br />
m2<br />
1<br />
C<br />
m2<br />
m2<br />
g<br />
C C<br />
C<br />
m2<br />
2<br />
gs 2<br />
gs 1<br />
- 62 -<br />
(<strong>III</strong>.47)<br />
(<strong>III</strong>.48)<br />
(<strong>III</strong>.49)<br />
(<strong>III</strong>.50)<br />
(<strong>III</strong>.51)<br />
(<strong>III</strong>.52)<br />
From these formulas, it comes out that M1 and M2 parameters are subject to a<br />
compromise. In<strong>de</strong>ed, to obtain a sufficiently high resonant frequency and to ensure a high<br />
quality factor, gm2 is required to be high while gm1 is kept at a relatively low value. However,<br />
in [II.8], a noise analysis is performed and <strong>de</strong>monstrates that noise voltage is proportional<br />
g m2<br />
to . The tra<strong>de</strong>-offs and the optimizations of the gyrator are discussed more <strong>de</strong>eply in next<br />
g m1<br />
chapter.<br />
A similar structure is <strong>de</strong>scribed in the literature. It actually relies on the same principle<br />
but uses a common source MOS transistor associated to a common gate one, as <strong>de</strong>picted in<br />
Figure 76. This solution aims at obtaining different formulas for Rp and Rs of the equivalent<br />
mo<strong>de</strong>l, which may be useful to reach another tra<strong>de</strong>-off. In<strong>de</strong>ed, the formulas are then given<br />
by:<br />
R<br />
R<br />
p<br />
s<br />
1<br />
≈<br />
g<br />
=<br />
g<br />
m1<br />
g<br />
m1<br />
ds1<br />
g<br />
m2<br />
(<strong>III</strong>.53)<br />
(<strong>III</strong>.54)