Circuit Realization And Equations

Circuit realization (neglect gds Cgd)

Matlab Code and solution to find Zin(s) syms s Cgs1 Cgs2 Cgs3 Cgs4 gm1 gm2 gm3 gm4 I Y1=[s*Cgs4 0 -s*Cgs4; 0 s*Cgs3+s*Cgs2 0; -s*Cgs4 0 s*Cgs4+s*Cgs1] I1=[0 gm3 0; 0 -gm3 -gm1;gm4 -gm2 -gm4]; Y=Y1-I1 V=Y\[0; 0; I]; Zin=V(3)/I

Y1 = [ s*Cgs4, 0, -s*Cgs4] [ 0, s*Cgs3+s*Cgs2, 0] [ -s*Cgs4, 0, s*Cgs4+s*Cgs1]

Y= [ s*Cgs4, -gm3, -s*Cgs4] [ 0, s*Cgs3+s*Cgs2+gm3, gm1] [ -s*Cgs4-gm4, gm2, s*Cgs4+s*Cgs1+gm4]

Zin = s*Cgs4*(s*Cgs3+s*Cgs2+gm3)/ (gm3*gm4*gm1+gm3*s^2*Cgs4*Cgs1+s^3*Cgs3*Cgs4*Cgs1+gm3*s*Cgs4*gm1+ s^3*Cgs2*Cgs4*Cgs1-gm2*s*Cgs4*gm1) Then Zin could be approximated as (s*Cgs3+s*Cgs2)/ [s^2*(Cgs3+Cgs2)+s*Cgs1+gm1*(gm3-gm2)] If M4 was labeled as M2 and M2 as M4, Zin will be the same as given in the paper, and w0^2 and Q in terms of gm and Cgs will be the same as well. For M1: gm1=2*I/(VC-VT); VC-VT=sqrt(I/K1)  gm1=2*sqrt(I*K1) For M3: gm3=2*I/(VD-VB-VT); VD-VB-VT=sqrt(I/K3)  gm3=2*sqrt(I*K3) For M4: gm4=2*K4(VB-VT)=2*K4*(VD-2VT-sqrt(I/K3))

Additional Calculation for w0 and Q w0^2=gm1(gm3-gm4)Cgs1(Cgs3+Cgs4)=2IK1Cgs1(Cgs3+Cgs4)*2IK3+2K4IK32K4(VD-2VT)=4K1(K3+K4)K3Cgs1(Cgs3+Cgs4)*I*I-K4K3VD-2VTK3+K4=A*I*I-B where A and B is the same as specified in the paper

Q=w0*(Cgs3+Cgs4)/gm3=gm1gm3gm4(Cgs3+Cgs4)Cgs1gm3=Cgs3+Cgs4Cgs1*K3gm1*2*K3+K4*I-Bgm3 gm1gm32=K12*I*K3 Q=Cgs3+Cgs4Cgs1*K32(I-B)2*IK3+K4k3k1=D*1-BI where D=Cgs3+Cgs4Cgs1*K3K3+K4k3k1