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

In reference [V.5] is presented the computation of the equivalent input impedance of
the N-path filter. Hence, from the formula it is clear that when the duty cycle is smaller than
1/N, all switches are OFF periodically for some time and the output signal of the filter then
simply tracks the input signal. It results in smaller insertion loss at the central frequency of the
filter. Indeed, -2dB gain is obtained for 20% duty cycle against -3.5dB for 25% duty cycle.
A duty cycle higher than 1/N results in undesired charge sharing since two switches
can be ON at the same time. The shape of the filter is totally destructed due to large insertion
loss (-13dB in Figure 191).
Figure 191. Impact of the duty cylce
V.2.c RF Performances
As explained in [V.5], most output noise power is due to thermal noise of the source
and switch resistances. Moreover, noise foldings from around the harmonics of fclk have to be
taken into account. Noise figure values below 5dB are reported, where noise is mainly caused
by the noise folding of noise coming from the source resistance [V.5].
As far as linearity is concerned, it is determined by the switch sizes and the
implemented capacitors. That is why very high linearity levels and 1dB compression points
are reported in the literature (see Table 31).
Reference [V.6] details the impact of diverse imperfection sources which may degrade
the performances of an N-path filter. These imperfections have four main sources:
- LO phase noise, which causes reciprocal down-conversion to on top of the desired
signal;
- Second order non-linearity of the switches in presence of mismatch, which can
fold an amplitude modulated blocker to on top of the desired signal;
- Quadrature inaccuracy of the duty cycle, which involves an image folding to on
top of the desired signal;
- Thermal noise of the switches, since harmonics down-conversion increases
thermal noise contribution.
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