Explanation Given data: Refer to Figure 16.109 in the textbook. The transfer function is, V o ( s ) V i ( s ) = − s + 1000 2 ( s + 4000 ) . (1) The value of capacitance ( C 1 ) is 10 μ F . Formula used: Write a general expression to calculate the impedance of a resistor in s -domain. Z R = R (2) Here, R is the value of resistor. Write a general expression to calculate the impedance of a capacitor in s -domain. Z C = 1 s C (3) Here, C is the value of capacitor. Write a general expression to calculate the output voltage of an inverting amplifier. V out = − R f R i V in (4) Here, R i is the input resistance, R f is the feedback resistance, and V in is the input voltage. Calculation: The given circuit is redrawn as shown in Figure 1. Convert the Figure 1 into s -domain using equation (2) and (3). Refer to Figure 2, the resistor R 1 and capacitor C 1 is connected in parallel. The resistor R 2 and capacitor C 2 is connected in parallel. The impedance value of Z 1 is calculated as follows: Z 1 = R 1 ∥ 1 s C 1 = R 1 × 1 s C 1 R 1 + 1 s C 1 = ( R 1 s C 1 ) ( s R 1 C 1 + 1 s C 1 ) = R 1 s R 1 C 1 + 1 Simplify the above equation to find Z 1 . Z 1 = R 1 R 1 C 1 ( s + 1 R 1 C 1 ) = 1 C 1 ( s + 1 R 1 C 1 ) The impedance value of Z 2 is calculated as follows: Z 2 = R 2 ∥ 1 s C 2 = R 2 × 1 s C 2 R 2 + 1 s C 2 = ( R 2 s C 2 ) ( s R 2 C 2 + 1 s C 2 ) = R 2 s R 2 C 2 + 1 Simplify the above equation to find Z 2 . Z 2 = R 2 R 2 C 2 ( s + 1 R 2 C 2 ) = 1 C 2 ( s + 1 R 2 C 2 ) Now, the Figure 2 is reduced as shown in Figure 3. Refer to Figure 3, it is an inverting amplifier with the feedback resistance of Z 2 and input resistance of Z 1 . Substitute V o ( s ) for V out , Z 2 for R f , Z 1 for R i , and V i ( s ) for V in in equation (4) to find V o ( s ) . V o ( s ) = − Z 2 Z 1 V i ( s ) Rearrange the above equation to find V o ( s ) V i ( s ) . V o ( s ) V i ( s ) = − Z 2 Z 1 Substitute 1 C 1 ( s + 1 R 1 C 1 ) for Z 1 , and 1 C 2 ( s + 1 R 2 C 2 ) for Z 2 in above equation to find V o ( s ) V i ( s )

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ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

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Chapter 16, Problem 100P

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Design an op-amp circuit using Figure 16.109 and find the values of resistors R1, R2 and the capacitor C2.

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Chapter 16, Problem 99P

Chapter 16, Problem 101P

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Design an op-amp circuit using Figure 16.109 and find the values of resistors R 1 , R 2 and the capacitor C 2 .

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Design an op-amp circuit using Figure 16.109 and find the values of resistors R1, R2 and the capacitor C2.

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Chapter 16 Solutions