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 , R 2 = 10 k , and C = . 1 F. in ( t ) 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 / 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 / C = V out parenleftbigg 1 R 2 + j C parenrightbigg . Hence, V out = parenleftbigg R 2 R 1 parenrightbiggparenleftbigg 1 1 + j R 2 C parenrightbigg V in = parenleftbigg R 2 R 1 parenrightbigg 1 j R 2 C 1 + 2 R 2 2 C 2 V in . For V in = . 5 V, R 1 = 2 k , R 2 = 10 k , = 2000 rad/s, and C = . 1 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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Solution+HW15 - Problem 7.59 The input signal in the op-amp...

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