ee577_sp07_midterm_solutions_afternoon

# ee577_sp07_midterm_solutions_afternoon - EE577a Midterm...

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1 EE577a Midterm Instructor: Prof. Pedram March 8, 2007 Afternoon Session Name: __________TA___________________ Student ID #: ________________________________ Problem 1: _____________ / 10 Problem 2: _____________ / 10 Problem 3: _____________ / 10 Problem 4: _____________ / 10 Problem 5: _____________ / 10 Problem 6: _____________ / 10 Problem 7: _____________ / 10 Problem 8: _____________ / 10 Problem 9: _____________ / 10 Problem 10: _____________ / 10 Total: _____________ / 100

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2 1) A PMOS resistive-load inverter is shown below. Find the values of V OL , V OH , and V TH . V DD = 2.5V V T0,p = -0.6 V λ = 0 k p ’ = 74 μ A/V 2 R = 20 k Ω L = 2 μ m W = 20 μ m V DD V in R V out Solution: When the input voltage is high, i.e., V in >V DD –|V T0,p | , PMOS transistor is cut-off. Since I D =I R =0. It follows that the output voltage of the inverter under these condition is: V OL = 0 (2 points) To calculate V OH , we assume that the input voltage is equal to V OL , i.e., V in =V OL =0. Since V in –V DD +|V T0,p |< V out –V DD in this case, the PMOS transistor operates in the linear region. Also note that the load current I R is I R =V out /R Using KCL for the output node: [] [] 2 2 , 0 ' ) 5 . 2 ( ) 5 . 2 ( 9 . 1 2 37 20 ) ( ) ( |) | ( 2 2 OH OH OH OH DD OH DD p T DD p OH V V K V V V V V V V k R V × × = = μ (3 points) After simplifying the equation, we get the following quadratic equation: 0 25 . 3 15 . 0 2 = + OH OH V V V OH =1.73 V, -1.88 V (1 point) The right answer is V OH =1.73 V since V OH cannot be negative. V TH =V in =V out In this case the transistor is in saturation region. 2 2 , 0 ' ) 6 . 0 5 . 2 ( 37 20 |) | ( 2 = = TH TH p T in DD p out V K V V V V k R V (1 point) V TH 2 -5.15 V TH +3.61=0 V TH =4.31 V, 0.81 V The right answer is V TH =0.81 V since V TH must be between 0 and V DD . (3 points)
3 2) How does energy-delay product scale with CMOS technology assuming generalized scaling rules where doping densities are unchanged, V DD and V T are scaled by U , all horizontal dimensions are scaled by X , and all vertical dimensions

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ee577_sp07_midterm_solutions_afternoon - EE577a Midterm...

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