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about Gate-source voltage stabilizer

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Take the small signal equations for Iin, which is the input branch current and the Iout, which is the output branch current

Iin = gm1* Vgs1 = gm1*Iout*R1 ---- (1)

But Iout = gm2*Vgs2 = gm2*[Vdd - (R2*Iin) - (Iout*R1)] ------- (2)

Replace (1) in the equation,

Therefore, Iout/Vdd = 1/R1(1+gm1*R2)

Please do the simple math from the above equations 1 and 2 to get the solution. I hope it helps
 

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