phi[u_]:= u + (1-u)(1/Pi ArcTan[# (u-1)]+1/2)- (u+1)(1/Pi ArcTan[-# (u+1)]+1/2)&

phi[u]/@{1,2,3,10}

saturationLisse = Show[Plot[#, {u,-3,3}]&/@ (phi[u]/@{1,2,3,10})]

Export["saturationLisse.eps",saturationLisse]

Sum[i,{i,1,20}]

Neq[NN_,A_]:= 1/A 2/NN Sum[phi[A Sin[(-Pi + 2 k Pi/NN)]][10]Sin[-Pi+ 2 k Pi/NN],{k,0,NN-1}]

(* gamma = 10 *)

gainEquiv = Show[Plot[Neq[#,A], {A,0,10}]& /@ {3,10,20,100}]

Export["gainEquiv.eps",gainEquiv]

Neq[NN_,A_]:= 1/A 2/NN Sum[phi[A Sin[(-Pi + 2 k Pi/NN)]][1]Sin[-Pi+ 2 k Pi/NN],{k,0,NN-1}]

gainEquiv2 = Show[Plot[Neq[#,A], {A,0,10}]& /@ {3,10,20,100}]

Export["gainEquiv2.eps",gainEquiv2]