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4okΩ Aokn Vina Ž 20kn 20k2 Viz' 20k2 1okn Vo Vizo 10kn 30kn 4okn For the op amp circuit shown, find the output voltage Vo în terms of the input voltages Viss Vizz and Viz Hint: Superposition.

4okΩ Aokn Vina Ž 20kn 20k2 Viz' 20k2 1okn Vo Vizo 10kn 30kn 4okn For the op amp circuit shown, find the output voltage Vo în terms of the input voltages Viss Vizz and Viz Hint: Superposition.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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### Operational Amplifier Circuit Analysis #### Problem Statement For the op-amp circuit shown, find the output voltage \( V_o \) in terms of the input voltages \( V_{i1} \), \( V_{i2} \), and \( V_{i3} \). Hint: Superposition. #### Circuit Description The circuit diagram consists of three operational amplifiers (op-amps) with different input voltages \( V_{i1} \), \( V_{i2} \), and \( V_{i3} \). The resistances in the circuit are either 10kΩ, 20kΩ, or 30kΩ as detailed below: 1. **First Op-Amp Configuration**: - Non-inverting input is \( V_{i1} \) through a 10kΩ resistor. - Inverting input is connected to a 10kΩ resistor that goes to ground. - Feedback resistor of 10kΩ. 2. **Second Op-Amp Configuration**: - Non-inverting input is \( V_{i2} \) through a 10kΩ resistor. - Inverting input is through a 20kΩ resistor and connected to ground. - Feedback resistor of 10kΩ in parallel with a series connection to the next stage. 3. **Third Op-Amp Configuration**: - Non-inverting input receives the output from the previous op-amp stage and \( V_{i3} \) through a parallel configuration of resistors. - Inverting input receives the combined input through a 10kΩ resistor. - This sets the final output voltage \( V_o \). #### Detailed Diagram Analysis - **Node Analysis at Each Op-Amp**: - For the first op-amp, utilize voltage divider and feedback concepts to find the intermediate outputs. - For the second and third op-amps, the superposition principle will be essential in analyzing the contributions from each voltage source \( V_{i1} \), \( V_{i2} \), and \( V_{i3} \). By applying the principles of superposition and circuit analysis, compute \( V_o \) by considering the individual effect of \( V_{i1} \), \( V_{i2} \), and \( V_{i3} \) on the output, and then summing these effects. This problem encourages a comprehensive understanding of
Transcribed Image Text:### Operational Amplifier Circuit Analysis #### Problem Statement For the op-amp circuit shown, find the output voltage \( V_o \) in terms of the input voltages \( V_{i1} \), \( V_{i2} \), and \( V_{i3} \). Hint: Superposition. #### Circuit Description The circuit diagram consists of three operational amplifiers (op-amps) with different input voltages \( V_{i1} \), \( V_{i2} \), and \( V_{i3} \). The resistances in the circuit are either 10kΩ, 20kΩ, or 30kΩ as detailed below: 1. **First Op-Amp Configuration**: - Non-inverting input is \( V_{i1} \) through a 10kΩ resistor. - Inverting input is connected to a 10kΩ resistor that goes to ground. - Feedback resistor of 10kΩ. 2. **Second Op-Amp Configuration**: - Non-inverting input is \( V_{i2} \) through a 10kΩ resistor. - Inverting input is through a 20kΩ resistor and connected to ground. - Feedback resistor of 10kΩ in parallel with a series connection to the next stage. 3. **Third Op-Amp Configuration**: - Non-inverting input receives the output from the previous op-amp stage and \( V_{i3} \) through a parallel configuration of resistors. - Inverting input receives the combined input through a 10kΩ resistor. - This sets the final output voltage \( V_o \). #### Detailed Diagram Analysis - **Node Analysis at Each Op-Amp**: - For the first op-amp, utilize voltage divider and feedback concepts to find the intermediate outputs. - For the second and third op-amps, the superposition principle will be essential in analyzing the contributions from each voltage source \( V_{i1} \), \( V_{i2} \), and \( V_{i3} \). By applying the principles of superposition and circuit analysis, compute \( V_o \) by considering the individual effect of \( V_{i1} \), \( V_{i2} \), and \( V_{i3} \) on the output, and then summing these effects. This problem encourages a comprehensive understanding of
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