Larry_80 wrote on Oct 17th, 2011, 5:49pm:Adc = gm2/[ (gds2+gds4)*(gds5/Gm5)+(gds7)*(gds8/Gm8)]
where Gmn=gmn+gmbn
True
only under certain conditions. Your expression assumes gm5 >> gds2, gds4 and gds5, which is not necessarily true, especially when Id is high. A general expression for the folded cascode can be found if you consider the combo of M2, M4 and M5 as an equivalent transconductance amplifier with a corresponding output resistance, which will be loaded with M7 and M8.
If you run that analysis you will find that:
GMeq = gm2 * (gm5+gds5) / (gm5+gds2+gds4+gds5) and
Go eq = gds5 * (gds2 + gds4) / gm5
Thus Adc = GM eq / (Goeq + gds7*(gds8/Gm8))
As you can see if gm5 is not >> gds2,4,5, then Adc cannot be simplified to your expression.
Since gm5 is proportional to √Id while gds5 is to Id, as you increase Id gm5 and gds5,4,2 will get closer in value to each other and the general formula should be used.
Note: in GMeq and Goeq you can see the current splitting effect I was talking about.
Best
Tosei