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

II.4.b Gm-C filtering
Gm-C and OTA-C filtering are both based on a similar principle which consists in
synthesizing a transfer function by means of integrators built with Gm-cells or OTAs. As
said, Gyrator-C filters consist in emulating an inductive behaviour.
II.4.b.i From Integrators to Transfer Function Synthesis
In the literature, it has been shown [II.15 and II.16] that all continuous time filters can
be decomposed into an association of integrators. Thus, combining a few Gm-cell and
capacitors, several different filters can be obtained. For instance, a possible way is to
transform the circuit in an equivalent LC ladder and to replace inductors by gyrators.
A way to create an integrator is to associate a capacitor to the transconductance.
Indeed, the computation of the transfer function has an integrator form:
Vout g m
= . (III.62)
V jCω
in
Assuming the transconductor non-infinite output resistance r0, this leads to a lossy
integrator as depicted on Figure 81, having the following transfer function.
V
Figure 81. Lossy Integrator
Vout m
in
g r0
= (III.63)
1 + jr Cω
0
Hence, the basic cell of these integrators, and so of Gm-C filters, is the Gm-cell. It is a
transconductance amplifier which is able to convert an input voltage into an output current
with a given gain gm, called transconductance. The literature deals with both OTAs and Gmcells
when describing integrators. However, an OTA, which stands for Operational
Transconductance Amplifier, is regarded as an operational amplifier whose output impedance
is very low. As mentioned in [II.15], OTAs transconductance value is almost irrelevant as
long as its voltage gain is high. On the contrary, a Gm-cell is a more general term, referring to
a voltage-controlled current-source having a well determined transconductance value. That is
why the term “OTA-C” filters will be avoided in the following.
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