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3 V 10 k2 30 k2 5.4 V 20 k2 +, 3.9 V Vo 30 k2 + Q+

3 V 10 k2 30 k2 5.4 V 20 k2 +, 3.9 V Vo 30 k2 + Q+

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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5.37  Determine the output of the summing amplifier in Fig. 5.74.

### Operational Amplifier Inverting Summing Amplifier Circuit This diagram illustrates an inverting summing amplifier using an operational amplifier (op-amp). Here's a detailed breakdown of the components and their connections: #### Components 1. **Voltage Sources**: - **3 V** source connected through a **10 kΩ** resistor. - **5.4 V** source connected through a **20 kΩ** resistor. - **3.9 V** source connected through a **30 kΩ** resistor. 2. **Resistors**: - Input resistors: 10 kΩ, 20 kΩ, and 30 kΩ connected to respective voltage sources. - Feedback resistor: **30 kΩ** connected from the output to the inverting input of the op-amp. 3. **Operational Amplifier**: - Inverts and sums the input voltages. - The inverting input is connected to all input resistors, and feedback is provided through the 30 kΩ resistor. - Non-inverting input is grounded. 4. **Output**: - The output voltage (\(V_o\)) is designated at the op-amp's output terminal, which is referenced to ground. #### Functionality The circuit sums the input voltages, each weighted by the inverse of their corresponding resistance, and inverts the result. The output voltage (\(V_o\)) is determined by the formula: \[ V_o = - \left( \frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3} \right) \times R_f \] Where: - \(V_1 = 3 \, \text{V}\), \(R_1 = 10 \, \text{kΩ}\) - \(V_2 = 5.4 \, \text{V}\), \(R_2 = 20 \, \text{kΩ}\) - \(V_3 = 3.9 \, \text{V}\), \(R_3 = 30 \, \text{kΩ}\) - \(R_f = 30 \, \text{kΩ}\) (feedback resistor) This configuration showcases a basic application of operational amplifiers in electronics, particularly useful in analog signal processing for combining signals.
Transcribed Image Text:### Operational Amplifier Inverting Summing Amplifier Circuit This diagram illustrates an inverting summing amplifier using an operational amplifier (op-amp). Here's a detailed breakdown of the components and their connections: #### Components 1. **Voltage Sources**: - **3 V** source connected through a **10 kΩ** resistor. - **5.4 V** source connected through a **20 kΩ** resistor. - **3.9 V** source connected through a **30 kΩ** resistor. 2. **Resistors**: - Input resistors: 10 kΩ, 20 kΩ, and 30 kΩ connected to respective voltage sources. - Feedback resistor: **30 kΩ** connected from the output to the inverting input of the op-amp. 3. **Operational Amplifier**: - Inverts and sums the input voltages. - The inverting input is connected to all input resistors, and feedback is provided through the 30 kΩ resistor. - Non-inverting input is grounded. 4. **Output**: - The output voltage (\(V_o\)) is designated at the op-amp's output terminal, which is referenced to ground. #### Functionality The circuit sums the input voltages, each weighted by the inverse of their corresponding resistance, and inverts the result. The output voltage (\(V_o\)) is determined by the formula: \[ V_o = - \left( \frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3} \right) \times R_f \] Where: - \(V_1 = 3 \, \text{V}\), \(R_1 = 10 \, \text{kΩ}\) - \(V_2 = 5.4 \, \text{V}\), \(R_2 = 20 \, \text{kΩ}\) - \(V_3 = 3.9 \, \text{V}\), \(R_3 = 30 \, \text{kΩ}\) - \(R_f = 30 \, \text{kΩ}\) (feedback resistor) This configuration showcases a basic application of operational amplifiers in electronics, particularly useful in analog signal processing for combining signals.
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