[SOLVED] deep triode region definition according to Razavi

[BartlebyScrivener]

I am working through Design of Analog CMOS integrated circuits by B, Razavi.

It derives the drain current of an NMOS to be

Id = u*Cox*(W/L)*[(Vgs - Vth)Vds - 1/2Vds^2]

Which I am happy with, and that it gives a parabolic shape with the max value at Vgs-Vth

It then goes on to claim if in the above equation, Vds << 2(Vgs - Vth), we have

Id approx = u*Cox*(W/L)*(Vgs-Vth)Vds

and that the drain current is a linear function of Vds. I sort of understand this as due to the Vds^2 term becomes incredibly small compared to the overdrive term and thus can be ignored but ...

I cannot understand the relevance of Vds << 2(Vgs - Vth) why not simply (Vgs - Vth) or surely from looking at the curve, even smaller than that? I have had a look around and can't seem to find a definitive answer.

Thanks.

 

[erikl]

If you put out the factor (1/2)*Vds from the expression in the square bracket in equ. (2.8), you stay with Id = u*Cox*(W/L)*(1/2)*Vds*[2(Vgs - Vth) - Vds]. If you now want to disappear the summand Vds in the square brackets by claiming Vds << 2(Vgs - Vth) , you arrive seamlessly at Razavi's equ. (2.10). So mathematically it's quite ok, I think.

Practically, the factor 2 doesn't mean a lot compared to the meaning of "<<", IMHO. Perhaps it looks better if you write it (1/2)*Vds << (Vgs - Vth) ;-)