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

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