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

Indeed, this phenomenon is due to a peaking voltage Vpeaking at the internal node of the
gyrator, which depends on gm1 voltage gain. Increasing r0 leads to an increase of the voltage
gain of gm1 and so the peaking. This finally reduces the linearity of the filter since gm2 has then
to handle a strongly amplified signal.
Linearity performances depend on gain distribution gm1/gm2. Indeed, one can enhance
linearity amplifying more on gm2 and less on gm1, for a gm1.gm2 product kept constant, in order
to decrease gm1 voltage gain for a given r0 value. However, according to Friis formula, this
results in higher noise, which is also critical in such a structure. Thus gm1=gm2 in the
following.
The peaking transfer function can be computed and this gives the following equation:
V
g g r
= (III.21)
C C
2
H a ( jω)
peaking
Vin
m1
m3
0
=
2
2 2
1 + g m1g
m2
r0
+ jr0
( Ca
+ Cb
) ω − r0
ω
Based on the latter equation, Figure 101 illustrates that amplifying more on gm2 would
lead to a lower peaking voltage at the internal node. Though linearity is enhanced, as it may
be observed in Figure 102, noise is thus degraded. Indeed, amplifying less on the first stage
means being more subject to noise for the signal (Friis’ formula in APPENDIX A).
Figure 101. Voltage Peaking at the Gyrator Internal Node
- 88 -
a
b