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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A 4-path filter, for instance, consists in four parallel i<strong>de</strong>ntical filter cells which are<br />
cyclically sampled with a clock frequency. A bandpass filter centered at the clock frequency fc<br />
can then be used. Hence, frequency tuning means tuning the sampling frequency.<br />
Figure 183. Amplitu<strong>de</strong> response of a 4-path filter<br />
As explained in [V.3] and <strong>de</strong>picted in Figure 184.a, mixers are realized by means of<br />
switches driven by multiphase clocks. Low pass filters are simply implemented with an RC<br />
network. Since a resistor is a memory-less element, it can be shared by all paths and shifted in<br />
front of them. Furthermore, the first set of switches can also implement the function of the<br />
second set of switches, if Vout is tapped between the resistor and the switches, as illustrated in<br />
Figure 184.b and <strong>de</strong>tailed in [V.3].<br />
Figure 184. Switched-RC 4-path filter (a) and the simplified version (b)<br />
The filter bandwidth is <strong>de</strong>termined by a baseband low-pass filter. In<strong>de</strong>ed, due to the<br />
lack of reverse isolation, the passive mixer constituted by the switches frequency-translates<br />
the baseband impedance to RF. Therefore, very small cut-off frequencies can be achieved<br />
and, by up-conversion at the sampling frequency, create a highly selective bandpass filter<br />
whose central frequency is controlled by the clock frequency.<br />
In the following, simulations are run in a 4-path configuration to <strong>de</strong>scribe and quantify<br />
the impact of all parameters.<br />
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