III. Gm-C Filtering - Epublications - Université de Limoges
III. Gm-C Filtering - Epublications - Université de Limoges
III. Gm-C Filtering - Epublications - Université de Limoges
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and<br />
Loop gain LG and phase LP can be computed with the following formulas [IV.6]:<br />
( ) ⎟ ⎛ S 21 − S12<br />
⎞<br />
LG = 20 log<br />
⎜<br />
(IV.26)<br />
⎝1<br />
− S11.<br />
S 22 − S 21.<br />
S12<br />
− 2.<br />
S12<br />
⎠<br />
( ) ⎟ ⎛ S 21 − S12<br />
⎞<br />
LP = phase<br />
⎜<br />
. (IV.27)<br />
⎝1<br />
− S11.<br />
S 22 − S 21.<br />
S12<br />
− 2.<br />
S12<br />
⎠<br />
In the following, gain and phase margins (respectively GM and PM) are then <strong>de</strong>duced<br />
from these two expressions [IV.7] since:<br />
and<br />
GM (IV.28)<br />
= 0dB − LGLP<br />
= −180°<br />
PM −180<br />
+ LPLG<br />
= 0dB<br />
= . (IV.29)<br />
To ensure the stability of the system, an open-loop study has been carried out, taking<br />
into account parasitics effects. Large margins have been taken in nominal case, so that<br />
stability margins stay acceptable in worst cases (45MHz, -20°C, 3V supply and process<br />
dispersion). These margins, specified in Table 24, are crucial to ensure a robust<br />
industrialization.<br />
Table 24. Stability margins specifications<br />
Filter Specifications Nominal case Worst case Unit<br />
PM 50 40 <strong>de</strong>g<br />
GM 15 10 dB<br />
IV.2.b.iii Operational Amplifier Specifications<br />
Table 25 summarizes the specifications set on the OA <strong>de</strong>sign. As said, GBW has to be<br />
as high as possible to ensure that the transfer function second peaking takes place at very high<br />
frequency. A specification of 4GHz has been set.<br />
Furthermore, an OA voltage gain higher than 30dB is required so that gain K remains<br />
stable all over the frequency tuning range, as it has been observed previously.<br />
The output impedance Zout is very important as well since it <strong>de</strong>gra<strong>de</strong>s the filter quality<br />
factor when non zero. The specification on this parameter has been set to 2.5Ω.<br />
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