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

V. A Perspective for Future Developments
V.1 N-path Filtering Principle
N-path filtering is a method, already described in the sixties and in the eighties [V.1
and V.2], which uses the lack of reverse isolation of passive mixers to perform impedance
transforms. A revival of interest for this technique occurs in 2010-2011 and exhibits
promising results for the full integration of RF filtering.
To explain the principle of N-path filtering, let’s consider a switched capacitor lowpass
filter, whose cut-off frequency is called fLP. Such filter consists in sampling the signal at
a given sampling frequency fc. Figure 181 depicts its amplitude response ASCLP. Aliasing at fc
suggests using a low pass filter to create a bandpass one. However, Nyquist theorem prevents
sampled-data filters from processing input signal whose frequency is higher than half the
sampling frequency.
Figure 181. Amplitude response of an SC low-pass filter
It is then only possible to use the bandpass characteristic when the Nyquist range,
depicted in red on Figure 181 and on Figure 183, is large enough. Hence, the number of
samples per period has to be increased. This is possible introducing additional paths, as
illustrated in Figure 182 for a 4-path configuration. N similar time invariant lowpass networks
and 2N mixer driven by time/phase shifted versions of clock p(t) and q(t). This architecture
allows transferring a lowpass characteristic to a bandpass with the center frequency
determined by the mixing frequency.
Vin
p(t) q(t)
p(t-T/4) q(t-T/4)
p(t-2T/4) q(t-2T/4)
p(t-3T/4) q(t-3T/4)
Figure 182. 4-path structure
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