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

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