relationship between gm and Ids

[hung_wai_ming@hotmail.com]

gm 2ids

Relationship between gm and Ids can be drawn in the following:

(1) gm = uCox(W/L)(Vgs-Vt)
(2) gm = 2Ids/(Vgs-Vt)
(3) gm= sqrt(2uCox(W/L)Ids)

From 2, 3, we see gm is proportional to Ids and sqrt(Ids), so how should we interpret these two cases?

 

[safwatonline]

2- is for constant Veff >> gm prop. to Ids
3- is for constant size >> gm prop. to sqrt(Ids)

 

[hung_wai_ming@hotmail.com]

What if I have now a NMOS transistor biased at Vgs, with fixed W/L, and source to VSS, then I flow in different Ids from drain side, what is the relationship between Ids and gm?

 

[LvW]

I suppose you misinterpret the meaning of Ids.
Ids is NOT the actual current between drain and source, but instead the maximum possible drain current Id.

 

[fredflinstone]

your transistor needs to be in saturation. Ids in (1) (2) and (3) is the drain source current when the device is in saturation.

 

[ricklin]

In 2), for a given device, (Vgs-Vt) is prop. to sqrt(Ids), so 2) and 3) are actually equivalent.