Solution+HW15

# Solution+HW15 - Problem 7.59 The input signal in the op-amp...

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Unformatted text preview: Problem 7.59 The input signal in the op-amp circuit of Fig. P7.59 is given by v in ( t ) = . 5cos2000 t V . Obtain an expression for v out ( t ) and then evaluate it for R 1 = 2 k Ω , R 2 = 10 k Ω , and C = . 1 μ F. υ in ( t ) υ out R 1 R 2 C _ + _ + _ Figure P7.59: Op-amp circuit for Problem 7.59. Solution: I 1 V in V out _ + + _ I 1 I 2 I C- j / ω C I n = 0 V n = V p = 0 R 2 R 1 V in = . 5 ∠ ◦ V. Since V n = 0, I 1 = V in R 1 . Also, I 1 = I 2 + I C = V n − V out R 2 + V n − V out − j / ϖ C = − V out parenleftbigg 1 R 2 + j ϖ C parenrightbigg . Hence, V out = − parenleftbigg R 2 R 1 parenrightbiggparenleftbigg 1 1 + j ϖ R 2 C parenrightbigg V in = − parenleftbigg R 2 R 1 parenrightbigg 1 − j ϖ R 2 C 1 + ϖ 2 R 2 2 C 2 V in . For V in = . 5 V, R 1 = 2 k Ω , R 2 = 10 k Ω , ϖ = 2000 rad/s, and C = . 1 μ F, V out = − . 5 ( 1 − j 2 ) = . 5 √ 5 e j 180 ◦ · e − j 63 . 4 ◦ = 1 . 12 e j 116 . 6 ◦ V ....
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## This note was uploaded on 02/21/2011 for the course MSE 231 taught by Professor Bedford during the Spring '10 term at University of Michigan.

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Solution+HW15 - Problem 7.59 The input signal in the op-amp...

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