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)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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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:
\[ V_{\text{out}} = -Gain \cdot (V_{\text{in1}} - V_{\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0bcab434-a2e9-4b06-adcc-8080d0b69f83%2F3f92badd-566e-485e-b4d2-b77e7afdd513%2Fdu6i75k_processed.jpeg&w=3840&q=75)
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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