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

II.4.c Second Order Bandpass Filters
There are several different ways to synthesize a second order bandpass transfer
function with Gm-cells. Two first topologies are discussed before presenting the one that will
be more detailed later.
II.4.c.i The different possible topologies
In Figure 85 is depicted a first filter [II.17]. The filter transfer function is given by:
H ( ω)
V
jg
out
m3
1
= =
2
(III.64)
Vin
g m1g
m2
+ jg m3C1ω
− C1C2ω
- 69 -
C ω
Figure 85. Constant-bandwidth and constant-gain frequency tunable bandpass filter
This leads to the following parameters, assuming gm1 = gm2 = gm.
Thus,
ω =
0
Q =
BW
g
g
g
C C
m
m3
1
m
g
2
C
C
2
2
1
(III.65)
(III.66)
m3
= (III.67)
C
Thus central frequency tunability is achieved, tuning C1 or gm values, while keeping a
constant bandwidth. However, this structure needs to tune both transconductances and
capacitances. That is why it has not been studied more deeply in the following.