CMOS Questions

1) The solution has to be done first by hand using only a calculator. 2) Then simulation by Ltspice is required to verify the answers. Problem#1: Calculate the gain of the following three circuits, assuming that the transistors are biased in saturation and both channel length modulation and body effect can be ignored (λ=0, γ=0) Figure 1 a) Draw the small-signal equivalent for each of these circuits. b) Calculate the small-signal voltage gains, !! !! , !! !! , !! !! in terms of RD, RS, and gm. c) Calculate the product of these three gains. Is the product equal to 1? Why? RS VDD RD vd vg vg RS VDD RD vd vs Vbias RS VDD RD vs e) Use KVL and KCL to write two independent equations in terms of vs, vg, and vd. f) Use these two equations to calculate !! !! , !! !! , !! !! , again: g) Recalculate the product, !! !! × !! !! × !! !! h) Can you explain why this happened? Please state your answer. Figure 2 RS VDD RD vd vs vg d) Draw the small-signal model for the following circuit (Figure2) without applying an explicit voltage source .