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

Figure 110. gm value versus C values to reach the low end of the TV band
Hence, the choice of the transconductance value gm is particularly critical. The use of
low gm values means a high filter noise. On the contrary, the use of a too high gm would result
in the use of larger capacitors to reach 45MHz and in a poor linearity. To limit Cmax to less
than 50pF, gm specification is limited to 13mS. That is why we specify that the
transconductance value should be as high as possible, in the limit of 13mS, and fulfil the
20dBm linearity level previously discussed.
Furthermore, the voltage gain gm.r0 has to be high enough to reach the desired filter
quality factor. If r0 is too low, most of the output current flows through it and not through the
capacitance, degrading the functionality of the filter. Indeed, it has been shown previously
that for Gm-cells with r0 as output resistance and gm1=gm2=gm, the quality factor is given by
the formula:
r 1
= g . (III.29)
0 Q + 2
2 r0
Hence, this gives the required r0 value:
( 2Q)
m
2
2
m
−1
r0
= . (III.30)
g
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