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2009-midtermII-solutions

# 2009-midtermII-solutions - Q1 Name Student No SOLUTIONS ELE...

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Name: Student No: ELE 311 ELECTRONICS II SOLUTIONS MIDTERM EXAM II (25%) Q1 Q2 Q3 TOTAL 32 33 35 100 December 30 𝑡ℎ , 2009 Answer all three questions. Explain your assumptions. Good Luck! Q1. Consider circuit shown below a) Express the output voltage 𝑣 𝑜 in terms of the input voltages 𝑣 1 , 𝑣 2 and 𝑣 3 . b) Find the value of 𝑣 3 if 𝑣 𝑜 = 9 V, 𝑣 1 = 5 V and 𝑣 2 = 13 V. Assume the opamp is ideal. SOLUTION: a) 𝑅 𝑥 = 𝑅 4 ∣∣ 𝑅 5 = 10 𝑘 ∣∣ 15 𝑘 = 6 kΩ Note that opamp is ideal, so 𝑖 + = 𝑖 6 = 0. Then we can write 𝑖 𝑥 = 𝑖 2 + 𝑖 3 where 𝑖 𝑥 = 𝑣 𝑥 𝑅 𝑥 , 𝑖 2 = 𝑣 2 𝑣 𝑥 𝑅 2 and 𝑖 3 = 𝑣 3 𝑣 𝑥 𝑅 3 Thus 𝑣 𝑥 = ( 𝑅 2 ∣∣ 𝑅 3 ∣∣ 𝑅 𝑥 ) ( 𝑣 2 𝑅 2 + 𝑣 3 𝑅 3 ) (1) As opamp is ideal 𝑣 𝑜 = 𝑅 7 𝑅 1 𝑣 1 + ( 1 + 𝑅 7 𝑅 1 ) 𝑣 𝑥 (2) Consequently 𝑣 𝑜 = 𝑅 7 𝑅 1 𝑣 1 + ( 1 + 𝑅 7 𝑅 1 ) ( 𝑅 2 ∣∣ 𝑅 3 ∣∣ 𝑅 𝑥 ) ( 𝑣 2 𝑅 2 + 𝑣 3 𝑅 3 ) (3) Let us insert the resistor values into the above equation 𝑣 𝑜 = 3 𝑣 1 + 24 13 𝑣 2 + 8 13 𝑣 3 (4)

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b) Using (2) with 𝑣 𝑜 = 9 V, 𝑣 1 = 5 V and 𝑣 2 = 13 V 𝑣 𝑥 = 6 V (5) Thus 𝑖 𝑥 = 1 mA, 𝑖 2 = 1 . 4 mA and 𝑖 3 = 0 . 4 mA So 𝑣 3 = 0 V . (6)
Q2. For the current source shown below,

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2009-midtermII-solutions - Q1 Name Student No SOLUTIONS ELE...

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