help me on the application of mos in subthreshold area

[sunjiao3]

It is well known that in subthreshold area, VGS=ξ. VT. ln(ID/I0), that is, VGS has a linear relationship with log(e)ID. VGS is an independent variant, while ID is a varident depending on VGS, something like X=C+K.log(e)(F(X)). However, to make use of this logarithmic area, we usually need F(X)=C+k.log(e)(X) with X plays as the dependent variant. We need ID to be the independent variant. How could I solve this problem to make use of the logarithmic characteristic of MOS in subthreshold area?
Thank you.

 

[alok_ky]

Mos in the weak inversion is used in the bandgap references which are total CMOS, ie where no BJTs are used.

 

[Humungus]

sunjiao3

I don't see what you wanna solve???!!!

All you have to know is that
Id=f(Vgs, Vds, Vbs, physical parameters)

For given, and only for given, Vds, Vbs and physical parameters you can get a single value of Vgs for a given Id.

That's all!!!

Why do you wanna express it as F(x)=...+log(X)????

Where do you wanna go to?

Start at the beginning: go to Tsividis book and see also EKV model. Mybe this can clarify your mind.

 

[sunjiao3]

Humungus, thank you very much for your help.
Well, I understand that Id=f(Vds, Vgs, Vth). Here, I need a function to get y=k.ln(x)+c, while in cmos, only those working in subthreshold area has the function like Id=I0.exp(Vgs/Vt/ζ), which means Vgs=ζ.Vt.ln(Id)+c. However, as you said, Vgs determines the Id, not Id determines Vgs. That go opposite to my application.
So, the problem is, is it possible and how to make use of the subthreshold characteristic to get y=k.ln(x)+c, with x plays as the independent variant?
(By the way, please don't recommand BJT, I cannot use it here)
Thank you very much !