why the input and output DC voltage are equal?

[patriot]

as the fig. shows, can some guys explain it?
thx in advance!

 

[ytliang]

I(M1)+I(M2)=2IB
I am guessing M1=M2...
Then I(M1)=I(M2)=IB
Hence, Vin = VGS1 = VGS2 = VDS2 = Vout

 

[patriot]

I(M1)+I(M2)=2IB
I am guessing M1=M2...
Then I(M1)=I(M2)=IB
Hence, Vin = VGS1 = VGS2 = VDS2 = Vout

But I(m1) is not equal to I(m2），because if that, Av=1

 

[ytliang]

From the Equation gm1/gm2 = sqrt((w/l1)/(w/l2)). It means I(m1) = I(m2) so they are canceled out.

I think a better question would be why does I(m1) = I(m2)...

Are you sure Vout = Vin for different sizing of the transistors?

 

[zopeon]

Note that M1 current would be
I1= βn*W1/L1(Vgs-Vth)*(1+ΛVds)
but for M2 ΛVds would not have much effect as Vgs would be more dominating compared to Lambda ( Λ ) .
I2=βn*W2/L2(Vgs1-Vth)
Now if we assume Vds is more than Vgs then ΛVds would cause increase in current I1 also due to increased Vds i.e. Vgs1 ( for M2) would increase I2
I1 + I2 is constant so Vds would have to be at value closer to Vgs where ΛVds would not be significant.

 

[patriot]

From the Equation gm1/gm2 = sqrt((w/l1)/(w/l2)). It means I(m1) = I(m2) so they are canceled out.

I think a better question would be why does I(m1) = I(m2)...

Are you sure Vout = Vin for different sizing of the transistors?

yes,as you said, from the equation gm1/gm2 = sqrt((w/l1)/(w/l2)). It means I(m1) = I(m2).

Maybe the following picture can express my question well, why the (Vgs-Vt) of both NMOS are equal?