Problem • Given the op-amp configuration, determin the value of R, required to produce a close loop voltage gain of -100. V (~) Vin R₁ www 2.2 ΚΩ R₁ W
Problem • Given the op-amp configuration, determin the value of R, required to produce a close loop voltage gain of -100. V (~) Vin R₁ www 2.2 ΚΩ R₁ W
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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![### Problem
Given the op-amp configuration, determine the value of \( R_f \) required to produce a closed-loop voltage gain of -100.
#### Explanation of Diagram
The diagram depicts an operational amplifier (op-amp) in an inverting amplifier configuration. Here's a detailed description:
- The input voltage \( V_{in} \) is supplied to the inverting input of the op-amp via a resistor \( R_1 \) with a value of 22 kΩ.
- The non-inverting input of the op-amp is grounded.
- A feedback resistor \( R_f \) is connected from the output of the op-amp to the inverting input.
- The output voltage \( V_{out} \) is taken from the output terminal of the op-amp.
In an inverting amplifier, the voltage gain \( A_v \) is given by the formula:
\[ A_v = -\frac{R_f}{R_1} \]
To achieve a gain of -100, we set:
\[ -100 = -\frac{R_f}{22\text{ kΩ}} \]
Solving for \( R_f \):
\[ R_f = 100 \times 22\text{ kΩ} \]
\[ R_f = 2200\text{ kΩ} \] or 2.2 MΩ
So, the required value of \( R_f \) is 2.2 MΩ.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53cd4567-e9c0-49bc-8f29-7fe4db37c68a%2F96dd270f-ef71-49a8-af66-de33d6ea4b67%2Fm2eaiq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem
Given the op-amp configuration, determine the value of \( R_f \) required to produce a closed-loop voltage gain of -100.
#### Explanation of Diagram
The diagram depicts an operational amplifier (op-amp) in an inverting amplifier configuration. Here's a detailed description:
- The input voltage \( V_{in} \) is supplied to the inverting input of the op-amp via a resistor \( R_1 \) with a value of 22 kΩ.
- The non-inverting input of the op-amp is grounded.
- A feedback resistor \( R_f \) is connected from the output of the op-amp to the inverting input.
- The output voltage \( V_{out} \) is taken from the output terminal of the op-amp.
In an inverting amplifier, the voltage gain \( A_v \) is given by the formula:
\[ A_v = -\frac{R_f}{R_1} \]
To achieve a gain of -100, we set:
\[ -100 = -\frac{R_f}{22\text{ kΩ}} \]
Solving for \( R_f \):
\[ R_f = 100 \times 22\text{ kΩ} \]
\[ R_f = 2200\text{ kΩ} \] or 2.2 MΩ
So, the required value of \( R_f \) is 2.2 MΩ.
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