Gain Enhancement

Negative Conductance

Quit

eq1={I1==Gm3*V2,
I2==Gm3*V1}

sol1=Solve[eq1,{I1,I2}]

sol1[[1,1]]

I1=I1 /. sol1[[1,1]]

sol1[[1,2]]

I2=I2 /. sol1[[1,2]]

Iin=Simplify[I1-I2]

Iin=Iin /. {V1->Vin/2,V2->-Vin/2}

Gmeq=Iin/Vin

Small-signal Analysis

Quit

eq1={Gm1*VG1+Gm2*Vo1+Gm3*Vo2==0,
Gm1*VG2+Gm2*Vo2+Gm3*Vo1==0,
Gm1*VG1+Gm1*VG2==YS*VS,
VG1==Vi1-VS,
VG2==Vi2-VS}

sol1=Solve[eq1,{Vo1,Vo2,VS,VG1,VG2}]

sol1[[1,1]]

Vo1=Vo1 /. sol1[[1,1]]

sol1[[1,2]]

Vo2=Vo2 /. sol1[[1,2]]

Vod =Simplify[Vo1-Vo2]

Vod=Simplify[Vod /. {Vi1->Vic+Vid/2,Vi2->Vic-Vid/2}]

Ad=Simplify[Vod/Vid]

With load Capacitance

Small-signal Analysis

Quit

eq1={Gm1*VG1+Gm2*Vo1+Gm3*Vo2+s*CL*Vo1==0,
Gm1*VG2+Gm2*Vo2+Gm3*Vo1+s*CL*Vo2==0,
Gm1*VG1+Gm1*VG2==YS*VS,
VG1==Vi1-VS,
VG2==Vi2-VS}

sol1=Solve[eq1,{Vo1,Vo2,VS,VG1,VG2}]

sol1[[1,1]]

Vo1=Vo1 /. sol1[[1,1]]

sol1[[1,2]]

Vo2=Vo2 /. sol1[[1,2]]

Vod =Simplify[Vo1-Vo2]

Vod=Simplify[Vod /. {Vi1->Vic+Vid/2,Vi2->Vic-Vid/2}]

Ad=Simplify[Vod/Vid]

num=Numerator[Ad]
den=Denominator[Ad]

Adc=-Gm1/(Gm2-Gm3)

wc=(Gm2-Gm3)/CL

wu=Simplify[-Adc*wc]

Noise Analysis

Quit

eq1={Gm1*VG1+In1a+Gm2*Vo1+Gm3*Vo2+In2a+In3a==0,
Gm1*VG2+In1b+Gm2*Vo2+Gm3*Vo1+In2b+In3b==0,
Gm1*VG1+In1a+Gm1*VG2+In1b==YS*VS,
VG1==Vi1-VS,
VG2==Vi2-VS}

sol1=Solve[eq1,{Vo1,Vo2,VS,VG1,VG2}]

sol1[[1,1]]

Vo1=Vo1 /. sol1[[1,1]]

sol1[[1,2]]

Vo2=Vo2 /. sol1[[1,2]]

Vod =Simplify[Vo1-Vo2]

Von=Simplify[Vod /. {Vi1->0,Vi2->0}]

Rnout=2*(Gn1+Gn2+Gn3)/(Gm2-Gm3)^2

Ad=-(Gm1/(Gm2-Gm3))

Rnin=Simplify[Rnout/Ad^2]

eta=Simplify[Gm1^2/(2*Gn1)*Rnin-1]

Thermal noise

Rnt=Simplify[Rnin /. {Gn1->gamman1*Gm1,Gn2->gamman2*Gm2,Gn3->gamman3*Gm3}]

Rnt=Expand[Rnt]

etath=Simplify[Gm1/(2*gamman1)*Rnt-1]

etath=Expand[etath]

Rnt1=2*gamman1/Gm1*(1+etath)

Simplify[Rnt1-Rnt]

Flicker noise

Rnf=Simplify[Rnin /. {Gn1->Gm1^2*rhon/(f*W1*L1),Gn2->Gm2^2*rhop/(f*W2*L2),Gn3->Gm3^2*rhop/(f*W3*L3)}]

Rnfl=Expand[Rnf]

etafl=Expand[f*W1*L1/(2*rhon)*Rnf-1]

Rnf1=2*rhon/(f*W1*L1)*(1+etafl)

Simplify[Rnf1-Rnf]