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