Ok so I have this diagram of a transistor. I have know problemsolving it while I

Question

Ok so I have this diagram of a transistor. I have know problemsolving it while I take lamda to be 0. In other words I neglect thechannel length modulation. So the saturation current would beid=Kn/2(Vgs-Vt)^2(1+Vds *Lamda) where lamda is 0. So if I set up KVL, 12 = 100k * id +Vds now if I assume saturation current, id = Kn/2 * (Vgs-Vt)^2(1+Lamda *Vds) However, because Vds = Vd - Vs, and Vgs = Vg - Vs, where Vs is= to 0, we can say that Vgs = Vds. Now given that I now the valuesof Kn and Vt if I subsitute in the KVL equation and the Vgs = Vdsinto the saturation current equation then I get, 12-Vds/100k = Kn/2(Vds -Vt)^2(1+lamda * Vds), where lamda isnon zero, I get a cubic function when I simplify this equationdown. Also, I get outragous values for Vds when solving it. What amI doing wrong in solving this equation. If you do attempt to solveit please take Kn' = 100uA/V^2 and Vt = .75v, and W/L = 20/1 Thanks

Explanation / Answer

I am solving for =.02 (12-Vds)/100k = Kn/2((Vds -Vt)^2)(1+lamda * Vds) =>12-Vds=100(.02Vds3+.97Vds2- 1.49Vds+.56) =>(.02Vds3+.97Vds2- 1.48Vds +.44)=0 Solving Vds comes out to be: 1.08v,-50v,0.40v The first one is the required answer.

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