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

IV.2 Dimensioning the Rauch Filter
IV.2.a Choice of the Components Values
IV.2.a.i Selectivity
From Figure 143, it may be noticed that a quality factor of 3 can be reached for a
10dB gain filter. It allows harmonic frequencies to be rejected by nearly 20dB (see Figure
144) and it enables to take advantage of some rejection of adjacent channels on both sides of
the filter central frequency, especially at the low-end of the VHF band. Indeed, a 15dB
rejection of the N+6 is obtained at 40MHz. However, such selectivity does not allow reaching
the UHF range since it requires larger Q for a same adjacent selectivity.
As explained, a more selective filter would lead to higher filter amplification. To take
advantage of the Friis formula, it has been chosen to limit filter gain to 10dB. Relaxing the
constraints on the filter amplification by increasing the gain on the RF filter would involve
more stringent constraints on the LNA noise versus gain trade-off.
Figure 144. Harmonics and adjacent channels rejections for Q=3
IV.2.a.ii Noise Optimization
To keep noise as low as possible, all impedances values have been decreased. Indeed,
since a Q-factor of 3 for a 10dB gain have been set, there is very little margin on the choice of
K. The combination R1=2R2 and R3=3R1, which is often used in the literature, is the best one.
A change in this combination results in an increase of the overall noise of the filter.
However, since the central frequency is proportional to1 / RC , the use of large
capacitances is required to reach the low-end of the VHF band located at 45MHz. The circuit
being fully-differential, it requires a large on-chip area to realize all capacitors. Values have
been summarized in Table 21.
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