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

III.I Theoretical Study
III. Gm-C Filtering
III.1.a Structure of the Gm-C Bandpass Filter
As mentioned in previous chapter, the following fully-differential Gm-C bandpass
filter is considered for its analogy with a current-fed parallel LC resonator [III.1]. Indeed, it is
composed of an input transconductor gm3, which converts input voltage into an output current
and sets the voltage gain of the filter. This current then flows through variable capacitors Cb
and a gyrator synthesizing an inductance, made of transconductors gm1 and gm2, and capacitors
Ca, as depicted in Figure 97.
+
Vin
-
Vin
gm3
2Cb
2Cb
+
IinL
-
IinL
gm1
- 83 -
2Ca
2Ca
Figure 97. Proposed Differential Gm-C Filter
Considering transconductors imperfections, the capacitive parasitics of all
transconductors can be incorporated into either Ca or Cb to simplify the model. However, each
Gm-cell also has a non-infinite output impedance that will be called r0 in the following. It will
be considered r0 for gm1 and the same r0 in common for gm2 and gm3 to simplify computations.
Its RLC equivalent can be deduced and gives the following schematic illustrated in Figure 98.
Figure 98. Equivalent RLC resonator
gm2
-
Vout
+
Vout