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.For the circuit below, use node analysis to write the model equation for Vout in terms of V1 and V2 R1 10k V1 Ovdo R5 100k U1 Vout R3 OUT 10k OPAMP R2 v2 100k Ovdo-

.For the circuit below, use node analysis to write the model equation for Vout in terms of V1 and V2 R1 10k V1 Ovdo R5 100k U1 Vout R3 OUT 10k OPAMP R2 v2 100k Ovdo-

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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In the given circuit, a node analysis is required to derive the expression for \( V_{\text{out}} \) in terms of \( V_1 \) and \( V_2 \). The circuit diagram includes the following components: 1. **Voltage Sources:** - \( V_1 \) at \( 0V \) DC - \( V_2 \) at \( 0V \) DC 2. **Resistors:** - \( R_1 = 10k\Omega \) - \( R_3 = 10k\Omega \) - \( R_2 = 100k\Omega \) - \( R_5 = 100k\Omega \) 3. **Operational Amplifier (OPAMP):** - The OPAMP U1 is configured with an inverting input (-) connected through \( R_2 \) and a non-inverting input (+) connected through \( R_5 \). ### Circuit Description: - \( V_1 \) is connected to the input of \( R_1 \), leading to the junction of \( R_5 \) and the non-inverting input of the OPAMP. - \( V_2 \) is connected to \( R_3 \), which connects to the other side of \( R_5 \). - The inverting input of U1 goes through \( R_2 \) and ties back to the output \( V_{\text{out}} \). - The output \( V_{\text{out}} \) is from the OPAMP's output terminal. ### Objective: Use node analysis to derive an equation for the output voltage \( V_{\text{out}} \) as a function of \( V_1 \) and \( V_2 \). ### Approach: 1. **Identify Nodes:** - Analyze each node where resistors intersect and where the OPAMP connects to determine the voltage relationships using Kirchhoff’s laws. 2. **Write Equations:** - Take into account the virtual short circuit condition for ideal OPAMPs (i.e., voltage at inverting = voltage at non-inverting). - Calculate the gain and the voltage output by considering the resistances and the input voltages. 3. **Solve:** - Solve the system of equations derived from the node analysis to express \( V_{\text{out}} \) in terms of \( V_1
Transcribed Image Text:In the given circuit, a node analysis is required to derive the expression for \( V_{\text{out}} \) in terms of \( V_1 \) and \( V_2 \). The circuit diagram includes the following components: 1. **Voltage Sources:** - \( V_1 \) at \( 0V \) DC - \( V_2 \) at \( 0V \) DC 2. **Resistors:** - \( R_1 = 10k\Omega \) - \( R_3 = 10k\Omega \) - \( R_2 = 100k\Omega \) - \( R_5 = 100k\Omega \) 3. **Operational Amplifier (OPAMP):** - The OPAMP U1 is configured with an inverting input (-) connected through \( R_2 \) and a non-inverting input (+) connected through \( R_5 \). ### Circuit Description: - \( V_1 \) is connected to the input of \( R_1 \), leading to the junction of \( R_5 \) and the non-inverting input of the OPAMP. - \( V_2 \) is connected to \( R_3 \), which connects to the other side of \( R_5 \). - The inverting input of U1 goes through \( R_2 \) and ties back to the output \( V_{\text{out}} \). - The output \( V_{\text{out}} \) is from the OPAMP's output terminal. ### Objective: Use node analysis to derive an equation for the output voltage \( V_{\text{out}} \) as a function of \( V_1 \) and \( V_2 \). ### Approach: 1. **Identify Nodes:** - Analyze each node where resistors intersect and where the OPAMP connects to determine the voltage relationships using Kirchhoff’s laws. 2. **Write Equations:** - Take into account the virtual short circuit condition for ideal OPAMPs (i.e., voltage at inverting = voltage at non-inverting). - Calculate the gain and the voltage output by considering the resistances and the input voltages. 3. **Solve:** - Solve the system of equations derived from the node analysis to express \( V_{\text{out}} \) in terms of \( V_1
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