# Transistor sizing and voltage selection

#### Tesla96

Joined Mar 22, 2020
11
Hello,

I got the following circuit where Vdd=2V. I want all three mosfets to be in saturation with inversion coefficient , IC=10 (strong inversion) and current I=40 uA. Also i want to have VSD,M1=0.5V, VDS,M2=1V ,VDS,M3=0.5V . Could anyone show me the logic of solving this problem?

Thank you

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#### Tako

Joined Oct 21, 2014
65
What's the problem? Have you tried to size them and run the simulation?

#### Tesla96

Joined Mar 22, 2020
11
Here is the way I approach the problem:
1. I select all transistors to have IC=10, I=40 uA and minimum length L=0.18 um and from the equation $W=(ID*L)/(IC*2*n*Kp*UT^2)$ I find W.
2. Then ,I find $qs=sqrt(0.25 + IC) - 0.5$ in order to find pinch-off voltage VP , $Vp = Ut*( 2*qs+log(qs) ) + Vs$
and finally I find V
G from $VG = Vp*n + Vto$.

So, the sizing of nmos transistors is the same and different for the pmos.I start from nmos M3. If I use the above equations for Vs=0 V, I find VG.Then for the input transistor,M2, i replaceVs=0.5 ,because I assume M3 has VDS=0.5 V, and I find VG for M2. The problem is that I can't select VD for M2 in some way because M1 is diode connected an the only thing i can adjust is its dimensions which are selected from the first bullet equations.

I think this gives you a better picture.If you could help me I would appreciate that!
Thank you