Analysis of the Cascode stage

Small-signal analysis

Equivalent Transconductance

eq1={Gm1*Vin+Gds1*VS2+Gms2*VS2+Gds2*VS2==0,
Iout+Gms2*VS2+Gds2*VS2==0}

sol1=Solve[eq1,{Iout,VS2}]

Iout=Iout /. sol1[[1,1]]

Gmeq=Simplify[Iout/Vin]

Gmeqa=Simplify[Gmeq /. {Gds1->0,Gds2->0}]

Output conductance

Quit

eq1={Gds1*VS2+Gms2*VS2+Gds2*(VS2-Vout)==0,
Iout+Gms2*VS2+Gds2*(VS2-Vout)==0}

sol1=Solve[eq1,{Iout,VS2}]

Iout=Iout /. sol1[[1,1]]

Gout=Simplify[Iout/Vout]

Gouta=Simplify[Gout /. Gds1+Gds2->0]

Noise analysis

Quit

eq1={In1+Gds1*VS2+Gms2*VS2+Gds2*VS2-In2==0,
Iout+Gms2*VS2+Gds2*VS2-In2==0}

sol1=Solve[eq1,{Iout,VS2}]

Iout=Iout /. sol1[[1,1]]

Inout=Collect[Iout,{In1,In2},Factor]

Hn1=Simplify[(Inout /. In2->0)/In1]

Hn1a=Simplify[Hn1 /. {Gds1->0,Gds2->0}]

Hn2=Simplify[(Inout /. In1->0)/In2]

Hn2a=Simplify[Hn2 /. Gds1+Gds2->0]

Gnout=Hn1^2*Gn1+Hn2^2*Gn2

Gnouta=Hn1a^2*Gn1+Hn2a^2*Gn2

Gmeq=((Gm1 (Gds2+Gms2))/(Gds1+Gds2+Gms2))

Rnin=Simplify[Gnout/Gmeq^2]

Rnin=Collect[Rnin,{Gn1,Gn2},Factor]

Rnina=Simplify[Rnin /. Gds2->0]

Rnina=Collect[Rnina,{Gn1,Gn2},Factor]

Rnt=Rnina /. {Gn1->gamman1*Gm1, Gn2->deltan2*Gms2}

gammacas=Simplify[Gm1*Rnt]

Rnf=Rnina /. {Gn1->Gm1^2*rhon/(WL1*f), Gn2->(Gms/n2)^2*rhon/(WL2*f)}

Simplify[Rnf*f*WL1/rhon]

Effect of the parasitic capacitance at node 1

Output conductance

Quit

eq1={(Gds1+s*Cp1)*VS2+Gms2*VS2+Gds2*(VS2-Vout)==0,
Iout+Gms2*VS2+Gds2*(VS2-Vout)==0}

sol1=Solve[eq1,{Iout,VS2}]

Iout=Iout /. sol1[[1,1]]

Yout=Simplify[Iout/Vout]

Youta=Simplify[Yout /. Gds1+Gds2->0]

Noise

Quit

eq1={In1+(Gds1+s*Cp1)*VS2+Gms2*VS2+Gds2*VS2-In2==0,
Iout+Gms2*VS2+Gds2*VS2-In2==0}

sol1=Solve[eq1,{Iout,VS2}]

Iout=Iout /. sol1[[1,1]]

Inout=Collect[Iout,{In1,In2},Factor]

Hn1=Simplify[(Inout /. In2->0)/In1]

Hn1a=Simplify[Hn1 /. {Gds1->0,Gds2->0}]

Hn2=Simplify[(Inout /. In1->0)/In2]

Hn2a=Simplify[Hn2 /. Gds1+Gds2->0]