I'm looking at problem 7, chapter 9 of T. Lee "The Design of CMOS Radio-frequency integrated circuits" regarding the input impedance of a capacitively-loaded source follower. Cgd and rg are assumed zero. DC biasing of the source is a constant-current sink so doesn't feature in the AC analysis. There is only Cgs and load capacitance CL. It asks over what range of load capacitance the real part of the input impedance is negative? Is this a trick question? I think it is for all CL:
Vg = Vgs + Vs
Vg = Ig (Ig + gm.Vgs) ------ + ------------- jw.Cgs jw.CL
Vg = Ig 1 Ig ------ + ----- (Ig + gm.------) jw.Cgs jw.CL jw.Cgs
Vg jw.CL + jw.Cgs + gm
-- = ------------------- Ig jw.CL . jw.Cgs
Vg -gm - jw(Cgs+CL)
-- = ---------------- Ig w^2 . Cgs . CL
View in a fixed pitch font.