Can we get valid output resistance from characterization using gm/Id method ?

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melkord

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Can we get valid output resistance from characterization using gm/Id method ?

I characterizeed my NMOS and PMOS by sweeping VGS. VDS is kept constant at 0.9V (half the VDD), VBS=0.
I plot rout vs gm, rout vs gmid and found out their result are different.
The value of rout from real circuit simulation are also different with that of any of those plots, given the same gm or gmid.
I conclude that the gm/Id method cannot be used to characterise rout. is it correct?
 

gm/ID is used to give you a starting point in design instead of using the square law. Theoretically rout=1/gds= 1 /\[ rout= \frac{1}{gds}= \frac{1}{\lambda* ID } \]. This implies that plotting rout vs gm is expected to be different than gm/ID. Let us say that rout is not very sensitive to gm/ID. It is rather sensitive to L and VDS. The two main players in gm/ID are the L and gm/ID. In actual simulation your VDS would be different than VDD/2 so gds (rout) would be different.
To conclude, gm/ID methodology gives you a starting point. Designers usually plot intrinsic gain (gm/gds) vs gm/ID for different L rather than only gds.
If I am looking for rout requirements, I would be more interested in L rather than which bias point I have. A general rule gm/ID= 10 S/A is a sweet spot. gm/ID= 15 S/A is large but not very large. gm/ID= 8 S/A is low but not very low.
 

So, actually, we cannot evaluate any function which has term like gm*rout accurately ?
 

rout depends mainly on ID and L. If you have a constant biasing current, you are left with VGS and L as design parameter. You can change VGS and accordingly you have a new (W, gm, gm/ID). Larger L means smaller ID/W and consequently a large W to obtain the same biasing (gm/ID).
If you want to evaluate gm*rout accurately, you can try to estimate what would be your VDS, then extract draw gm*rout vs gm/ID at different L as shown in the picture.
If you have a constant current, you have two ways to increase gm*rout: First increase (gm/ID). this is actually increasing gm because ID is constant. And second way is to increase L.
If your current is not constant, the design variables available to you are more. You can decrease the current and have a large gm/ID but gm/ID range is limited.
 

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