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Find the value of Rf necessary to produce an output that is 10  times the sum of the inputs in the Figure.

Find the value of Rf necessary to produce an output that is 10  times the sum of the inputs in the Figure.

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
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Find the value of Rf necessary to produce an output that is 10  times the sum of the inputs in the Figure.

### Understanding Operational Amplifier Circuit: Differential Amplifier Example #### Circuit Description The image illustrates a differential amplifier circuit using an operational amplifier (op-amp). #### Components and Their Values: - **Resistors**: - \( R_1 = 2 \, k\Omega \) - \( R_2 = 2 \, k\Omega \) - \( R_f \) (Feedback Resistor) - **Voltages**: - Input Voltage \( V_{\text{in1}} = +0.5 \, V \) - Input Voltage \( V_{\text{in2}} = +1 \, V \) #### Circuit Operation The op-amp has two input terminals: - The inverting input (labeled as -) is connected through \( R_1 \) to \( V_{\text{in1}} \), and also to ground through \( R_2 \). - The non-inverting input (labeled as +) is directly grounded. - The feedback resistor \( R_f \) is connected from the output \( V_{\text{out}} \) back to the inverting input. #### Working Principle In this configuration: - The voltage difference between the inverting input and the non-inverting input is amplified. - The resistors \( R_1 \) and \( R_2 \) form a voltage divider network. - The resistor \( R_f \) provides feedback from the output to the inverting input to stabilize the circuit and set the gain. The voltage at the inverting input \( V_{\text{in-}} \) can be found using the voltage divider formula: \[ V_{\text{in-}} = V_{\text{in1}} \cdot \frac{R_2}{R_1 + R_2} \] Given \( R_1 = R_2 = 2 \, k\Omega \), this simplifies to: \[ V_{\text{in-}} = +0.5 \, V \cdot \frac{2 \, k\Omega}{2 \, k\Omega + 2 \, k\Omega} = +0.25 \, V \] The output voltage \( V_{\text{out}} \) of the op-amp can be calculated using: \[ V_{\text{out}} = -Gain \cdot (V_{\text{in1}} - V_{\
Transcribed Image Text:### Understanding Operational Amplifier Circuit: Differential Amplifier Example #### Circuit Description The image illustrates a differential amplifier circuit using an operational amplifier (op-amp). #### Components and Their Values: - **Resistors**: - \( R_1 = 2 \, k\Omega \) - \( R_2 = 2 \, k\Omega \) - \( R_f \) (Feedback Resistor) - **Voltages**: - Input Voltage \( V_{\text{in1}} = +0.5 \, V \) - Input Voltage \( V_{\text{in2}} = +1 \, V \) #### Circuit Operation The op-amp has two input terminals: - The inverting input (labeled as -) is connected through \( R_1 \) to \( V_{\text{in1}} \), and also to ground through \( R_2 \). - The non-inverting input (labeled as +) is directly grounded. - The feedback resistor \( R_f \) is connected from the output \( V_{\text{out}} \) back to the inverting input. #### Working Principle In this configuration: - The voltage difference between the inverting input and the non-inverting input is amplified. - The resistors \( R_1 \) and \( R_2 \) form a voltage divider network. - The resistor \( R_f \) provides feedback from the output to the inverting input to stabilize the circuit and set the gain. The voltage at the inverting input \( V_{\text{in-}} \) can be found using the voltage divider formula: \[ V_{\text{in-}} = V_{\text{in1}} \cdot \frac{R_2}{R_1 + R_2} \] Given \( R_1 = R_2 = 2 \, k\Omega \), this simplifies to: \[ V_{\text{in-}} = +0.5 \, V \cdot \frac{2 \, k\Omega}{2 \, k\Omega + 2 \, k\Omega} = +0.25 \, V \] The output voltage \( V_{\text{out}} \) of the op-amp can be calculated using: \[ V_{\text{out}} = -Gain \cdot (V_{\text{in1}} - V_{\
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