Clear[kv,tp0,gm1,gm2,gm4,gds1,gds2,gds3,gds4,gds5,cw,cl,c5,cd,v1,v2,v3,vs,ii,id,s];

v1=((-v3 kv )/(1+s tp0)) ;
i1=gds1 (v2-vs);
i2=gds2 (v3-vs);
i3=(gds3+s cl) v2;
i4=gds4 v3;
i5=-(gds5+s c5) vs;
if=s cf (v3-v1);
id=s cd v3;
(*current at N2*)
solv1=Solve[gm1 v1+i1+i3==0,v2]

(*current at S*)
solv2=Solve[-gm2 vs+i2+i5+gm1 (v1-vs) + i1==0,vs]

(*current at N3*)
solv3=Solve[ii-id+gm2 vs - i2 -if - gm4 v2 - i4 ==0,ii]

solv4=solv2/.solv1
vstemp=vs/.%
solvedvf=Solve[vs==vstemp,vs]

solv5=solv1/.solvedvf
v2temp=v2/.%;
solvedv2=Solve[v2==v2temp,v2]

solv7=solv3/.solvedvf
solv8=%/.solvedv2
iitemp=ii/.%
tt=FullSimplify[v1/iitemp,{kv>0&&tp0>0&&gm1>0&&gm2>0&&gm4>0&&gds1>0&&gds2>0&&gds3>0&&gds4>0&&gds5>0&&cw>0&&cl>0&&c5>0&&v1>0&&v2>0&&v3>0&&vs>0&&ii>0&&s>0}]

(*"zeros"*)
Factor[((gm1+gm2+c5 s) (gds3+cl s)+gds1 (gm1+gm2+(c5+cl) s))]
(*Solve[((gm2+c5 s) (gds3+cl s)+gds1 (gm2+(c5+cl) s))==0,s]*)
(*FullSimplify[s/.%,{kv>0&&tp0>0&&gm1>0&&gm2>0&&gm4>0&&gds1>0&&gds2>0&&gds3>0&&gds4>0&&gds5>0&&cw>0&&cl>0&&c5>0&&s>0}]*)
Clear[z1,z2,Z1,Z2]
Expand[(1+(s/Z1)) (1+(s/Z2))]
(*for z1<<z2         
1+(s/z1)+((s^2)/(z1 z2))
*)
Z1=FullSimplify[((gds1 gm1+gds3 gm1+gds1 gm2+gds3 gm2)/(cl gm1+cl gm2)),gm1>0&&gm2>0]
Z1Z2=((gds1 gm1+gds3 gm1+gds1 gm2+gds3 gm2)/(c5 cl));
Z2=FullSimplify[(((gds1 gm1+gds3 gm1+gds1 gm2+gds3 gm2)/(c5 cl)))/(((gds1 gm1+gds3 gm1+gds1 gm2+gds3 gm2)/(cl gm1+cl gm2))),cl>>0]

(*gds<<gm, c5<<cl*)

ZS1=(((gds1+gds3) )/(cl ))

ZS2=((gm1+gm2)/c5)

(*poles -> assuming gm>>gds && gm1=gm2=gm, gds1=gds2=gds, kv>>1*)

Factor[(gds3 gds4 gds5+gds3 gds4 gm1+gds3 gds4 gm2+gds3 gm1 gm2 kv+gds5 gm1 gm4 kv+(gm1^2) gm4 kv+gm1 gm2 gm4 kv+c5 gds3 gds4 s+cd gds3 gds5 s+cf gds3 gds5 s+cl gds4 gds5 s+cd gds3 gm1 s+cf gds3 gm1 s+cl gds4 gm1 s+cd gds3 gm2 s+cf gds3 gm2 s+cl gds4 gm2 s+cf gds3 gds5 kv s+cf gds3 gm1 kv s+cf gds3 gm2 kv s+cl gm1 gm2 kv s+c5 gm1 gm4 kv s+c5 cd gds3 (s^2)+c5 cf gds3 (s^2)+c5 cl gds4 (s^2)+cd cl gds5 (s^2)+cf cl gds5 (s^2)+cd cl gm1 (s^2)+cf cl gm1 (s^2)+cd cl gm2 (s^2)+cf cl gm2 (s^2)+c5 cf gds3 kv (s^2)+cf cl gds5 kv (s^2)+cf cl gm1 kv (s^2)+cf cl gm2 kv (s^2)+c5 cd cl (s^3)+c5 cf cl (s^3)+c5 cf cl kv (s^3)+s (gds5+gm1+gm2+c5 s) (gds4+(cd+cf) s) (gds3+cl s) tp0+gds2 (cl s (gds4+gds5+(c5+cd+cf+cf kv) s+s (gds4+gds5+(c5+cd+cf) s) tp0)+gds3 (gds4+gds5+gm1+gm1 kv+(c5+cd+cf+cf kv) s+s (gds4+gds5+gm1+(c5+cd+cf) s) tp0)+gm1 (gm4 kv+cl s (1+kv+s tp0)))+gds1 (gds2 (gds3+gds4+gds5+gm1+gm4+(c5+cd+cf+cl+cf kv) s+s (gds3+gds4+gds5+gm1+gm4+(c5+cd+cf+cl) s) tp0)+(gds3+gds5+gm1+gm2+(c5+cl) s) (gds4+gds4 s tp0+s (cd+cf+cf kv+(cd+cf) s tp0))))]

(*asuming gm>>gds, gm1=gm2, kv>>1*)

A=gds1 gds2 gds3+gds1 gds2 gds4+gds1 gds3 gds4+gds2 gds3 gds4+gds1 gds2 gds5+gds2 gds3 gds5+gds1 gds4 gds5+gds3 gds4 gds5+gds1 gds2 gm1+gds2 gds3 gm1+gds1 gds4 gm1+gds3 gds4 gm1+gds1 gds4 gm2+gds3 gds4 gm2+gds1 gds2 gm4+gds2 gds3 gm1 kv+gds3 gm1 gm2 kv+gds2 gm1 gm4 kv+gds5 gm1 gm4 kv+(gm1^2) gm4 kv+gm1 gm2 gm4 kv

B=c5 gds1 gds2 s+cd gds1 gds2 s+cf gds1 gds2 s+cl gds1 gds2 s+cd gds1 gds3 s+cf gds1 gds3 s+c5 gds2 gds3 s+cd gds2 gds3 s+cf gds2 gds3 s+c5 gds1 gds4 s+cl gds1 gds4 s+cl gds2 gds4 s+c5 gds3 gds4 s+cd gds1 gds5 s+cf gds1 gds5 s+cl gds2 gds5 s+cd gds3 gds5 s+cf gds3 gds5 s+cl gds4 gds5 s+cd gds1 gm1 s+cf gds1 gm1 s+cl gds2 gm1 s+cd gds3 gm1 s+cf gds3 gm1 s+cl gds4 gm1 s+cd gds1 gm2 s+cf gds1 gm2 s+cd gds3 gm2 s+cf gds3 gm2 s+cl gds4 gm2 s+cf gds1 gds2 kv s+cf gds1 gds3 kv s+cf gds2 gds3 kv s+cf gds1 gds5 kv s+cf gds3 gds5 kv s+cf gds1 gm1 kv s+cl gds2 gm1 kv s+cf gds3 gm1 kv s+cf gds1 gm2 kv s+cf gds3 gm2 kv s+cl gm1 gm2 kv s+c5 gm1 gm4 kv s+gds1 gds2 gds3 s tp0+gds1 gds2 gds4 s tp0+gds1 gds3 gds4 s tp0+gds2 gds3 gds4 s tp0+gds1 gds2 gds5 s tp0+gds2 gds3 gds5 s tp0+gds1 gds4 gds5 s tp0+gds3 gds4 gds5 s tp0+gds1 gds2 gm1 s tp0+gds2 gds3 gm1 s tp0+gds1 gds4 gm1 s tp0+gds3 gds4 gm1 s tp0+gds1 gds4 gm2 s tp0+gds3 gds4 gm2 s tp0+gds1 gds2 gm4 s tp0

C=c5 cd gds1 (s^2)+c5 cf gds1 (s^2)+cd cl gds1 (s^2)+cf cl gds1 (s^2)+c5 cl gds2 (s^2)+cd cl gds2 (s^2)+cf cl gds2 (s^2)+c5 cd gds3 (s^2)+c5 cf gds3 (s^2)+c5 cl gds4 (s^2)+cd cl gds5 (s^2)+cf cl gds5 (s^2)+cd cl gm1 (s^2)+cf cl gm1 (s^2)+cd cl gm2 (s^2)+cf cl gm2 (s^2)+c5 cf gds1 kv (s^2)+cf cl gds1 kv (s^2)+cf cl gds2 kv (s^2)+c5 cf gds3 kv (s^2)+cf cl gds5 kv (s^2)+cf cl gm1 kv (s^2)+cf cl gm2 kv (s^2)+c5 gds1 gds2 (s^2) tp0+cd gds1 gds2 (s^2) tp0+cf gds1 gds2 (s^2) tp0+cl gds1 gds2 (s^2) tp0+cd gds1 gds3 (s^2) tp0+cf gds1 gds3 (s^2) tp0+c5 gds2 gds3 (s^2) tp0+cd gds2 gds3 (s^2) tp0+cf gds2 gds3 (s^2) tp0+c5 gds1 gds4 (s^2) tp0+cl gds1 gds4 (s^2) tp0+cl gds2 gds4 (s^2) tp0+c5 gds3 gds4 (s^2) tp0+cd gds1 gds5 (s^2) tp0+cf gds1 gds5 (s^2) tp0+cl gds2 gds5 (s^2) tp0+cd gds3 gds5 (s^2) tp0+cf gds3 gds5 (s^2) tp0+cl gds4 gds5 (s^2) tp0+cd gds1 gm1 (s^2) tp0+cf gds1 gm1 (s^2) tp0+cl gds2 gm1 (s^2) tp0+cd gds3 gm1 (s^2) tp0+cf gds3 gm1 (s^2) tp0+cl gds4 gm1 (s^2) tp0+cd gds1 gm2 (s^2) tp0+cf gds1 gm2 (s^2) tp0+cd gds3 gm2 (s^2) tp0+cf gds3 gm2 (s^2) tp0+cl gds4 gm2 (s^2) tp0

D=c5 cd cl (s^3)+c5 cf cl (s^3)+c5 cf cl kv (s^3)+c5 cd gds1 (s^3) tp0+c5 cf gds1 (s^3) tp0+cd cl gds1 (s^3) tp0+cf cl gds1 (s^3) tp0+c5 cl gds2 (s^3) tp0+cd cl gds2 (s^3) tp0+cf cl gds2 (s^3) tp0+c5 cd gds3 (s^3) tp0+c5 cf gds3 (s^3) tp0+c5 cl gds4 (s^3) tp0+cd cl gds5 (s^3) tp0+cf cl gds5 (s^3) tp0+cd cl gm1 (s^3) tp0+cf cl gm1 (s^3) tp0+cd cl gm2 (s^3) tp0+cf cl gm2 (s^3) tp0

E=c5 cd cl (s^4) tp0+c5 cf cl (s^4) tp0

AS=(gm1^2) gm4 kv+gm1 gm2 gm4 kv
BS=cd gds1 gm1 s+cd gds3 gm1 s+cd gds1 gm2 s+cd gds3 gm2 s+cl gm1 gm2 kv s+c5 gm1 gm4 kv s
CS=cd cl gm1 (s^2)+cd cl gm2 (s^2)+cf cl gm1 kv (s^2)+cf cl gm2 kv (s^2)
DS=c5 cd cl (s^3)+c5 cf cl kv (s^3)
ES=c5 (cf+cd) cl (s^4) tp0

Clear[p1,p2,p3,p4]
Expand[(1+(s/p1)) (1+(s/p2)) (1+(s/p3)) (1+(s/p4))]

(*for P1<<P2<<P3<<P4 poles well separated*)
1+(s/p1)+((s^2)/(p1 p2))+((s^3)/(p1 p2 p3))+((s^4)/(p1 p2 p3 p4))

Clear[P1,P2,P3,P4];
Pol1=(((gm1^2) gm4 kv+gm1 gm2 gm4 kv)/(cd gds1 gm1+cd gds3 gm1+cd gds1 gm2+cd gds3 gm2+cl gm1 gm2 kv+c5 gm1 gm4 kv))
Pole1=(((gm1^2) gm4 kv+gm1 gm2 gm4 kv)/(cl gm1 gm2 kv))

P1P2=(((gm1^2) gm4 kv+gm1 gm2 gm4 kv)/(cd cl gm1+cd cl gm2+cf cl gm1 kv+cf cl gm2 kv))

P1P2P3=(((gm1^2) gm4 kv+gm1 gm2 gm4 kv)/(c5 cd cl+c5 cf cl kv))

P1P2P3P4=(((gm1^2) gm4 kv+gm1 gm2 gm4 kv)/(c5 (cd+cf) cl tp0))

Pole1=FullSimplify[(((gm1^2) gm4 kv+gm1 gm2 gm4 kv)/(cl gm1 gm2 kv)),kv>0&&gm1>0]
Pole2=FullSimplify[(((gm1^2) gm4 kv+gm1 gm2 gm4 kv)/(cd cl gm1+cd cl gm2+cf cl gm1 kv+cf cl gm2 kv))/(((gm1+gm2) gm4)/(cl gm2)),kv>0&&gm1>0]
Pole3=FullSimplify[(((gm1^2) gm4 kv+gm1 gm2 gm4 kv)/(c5 cd cl+c5 cf cl kv))/(((gm1^2) gm4 kv+gm1 gm2 gm4 kv)/(cd cl gm1+cd cl gm2+cf cl gm1 kv+cf cl gm2 kv))]
Pole4=FullSimplify[(((gm1^2) gm4 kv+gm1 gm2 gm4 kv)/(c5 (cd+cf) cl tp0))/(((gm1^2) gm4 kv+gm1 gm2 gm4 kv)/(c5 cd cl+c5 cf cl kv))]