If vanbsp vbnbsp vcnbsp vi determine the relationship

Question

Consider the three-input CMOS NAND circuit in Figure. Assume  = 2 and V_TN = |V_TP| = 0.8 V. (a) If v_A = v_B= 5 V, determine v_C such that both N₃ and P₃ are biased in the saturation region when (W/L)_p = 2(W/L)_n . (State any assumptions you make.)

(b) If v_A = v_B = v_C = v_I, determine the relationship between (W/L)_p and (W/L)_n such that v_I = 2.5 V when all transistors are biased in the saturation region.

(c) Using the results of part (b) and assuming v_A = v_B = 5 V, determine v_C such that both N₃ and P₃ are biased in the saturation region. (State any assumptions you make.)