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M216A_1_final_exam04_soln

M216A_1_final_exam04_soln - 1(20 Logical Effort(a(5...

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Electrical Engineering M216A Final Exam December 15, 2004 _______Solutions_____ Name (Last, First) _________________________ Student ID # (closed book/2 8.5x11 pages are permitted) You will need a calculator Please write answers in the box provided. Answers elsewhere will not be graded. GOOD LUCK! 1.(____/20) 2.(____/12) 3.(____/10) 4.(____/8) 5.(____/15) 6.(____/20) ______/85 1. (20) Logical Effort (a) (5) Determine the logical effort of this AOI gate, for all inputs. Assume that β=µ=µ N P = 3 (b) (4) Determine the parasitic effort of input a . Assume that C diff = 0.5C gate and no sharing of diffusions. (c) (3) Determine the parasitic effort of input c with the same assumptions as in (b). Include the internal nodes of the gate in your calculations. Answer: g a = 18/16 = 1.125 12 6 18 36 12 12 a a b b c c out g b = 30/16 = 1.875 g c = 48/16 = 3 key points: correct methodology reference inverter calculation Answer: p a_up = 36/32=1.125 p a_dn = 36/32 key points: correct methodology adjustment for Cdiff not equalling Cgate accounting for diffusions no internal nodes (because of a input) Answer: p c_up = 1.71 p c_dn = 1.437 5 6/(3*16*2)+36/(16*2) = pup 30/(3*16*2) + 36/(16*2) = pdown key points: correct methodology proper accounting for internal nodes
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(d) (4) Determine the logical effort of the a input if the β= 1.7 for the reference inverter. (e) (4) Determine the logical effort of the b input if we account for velocity saturation. The reference inverter has β= 2 and R Pno_stack =1.2R P_stacked , R Nno_stack =1.33R N_stacked . Assume that the values given already accounts for the effect of unequal stack sizes. 2. (12) Adder Design (a) (5) The PG network of a 16-bit Han-Carlson adder is shown below. Write the expressions for the logic performed by the two types of boxes. You can assume that the inputs from the top for each bit position (n) is P n and G n . Answer: g a_up = 0.94 g a_dn = 1.67 g a_up = (12+6)/(12(1+1/1.7) g a_dn = (12+6)/(4(1+1.7)) key points: correct methodology proper reference inverter separate calculation for up and dn. Answer: g b_up = 1.39 g b_dn = 1.88 g b_up = 30/(12*1.2*(1 + 1/ β )) g b_dn = 30/(4*1.33*(1+ β )) key points: proper reference inverter calculation adjustment for velocity saturation Answer: functions (dark box) −−> G MN = G MK P KN + G KN ; P MN = P MK P KN
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