5.37 Determine the output of the summing amplifier 2 V + 3 V +- 10 km2 ww 20 ks2 30 km2 ww 30 ks2 www. 1 + 9 + 210-411
5.37 Determine the output of the summing amplifier 2 V + 3 V +- 10 km2 ww 20 ks2 30 km2 ww 30 ks2 www. 1 + 9 + 210-411
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
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![### Summing Amplifier Circuit Analysis
**Figure 5.37: Summing Amplifier Configuration**
This image shows a summing amplifier circuit using three voltage inputs connected to an operational amplifier (op-amp). The op-amp is configured as an inverting summing amplifier.
#### Circuit Components:
1. **Input Voltages:**
- **1 V** connected through a **10 kΩ** resistor.
- **2 V** connected through a **20 kΩ** resistor.
- **3 V** connected through a **30 kΩ** resistor.
2. **Feedback Resistor:**
- **30 kΩ** resistor connected from the output to the inverting input of the op-amp.
3. **Op-Amp Configuration:**
- The op-amp is shown with the inverting input connected to summing junctions of the input resistors.
#### Operation:
The output voltage (\( V_o \)) of the summing amplifier can be calculated using the principle of superposition and the formula for an inverting summing amplifier:
\[
V_o = - \left( \frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3} \right) \times R_f
\]
Where:
- \( V_1, V_2, V_3 \) are the input voltages.
- \( R_1, R_2, R_3 \) are the resistors associated with each input voltage.
- \( R_f \) is the feedback resistor.
Substituting the given values:
- \( V_1 = 1 \, \text{V}, R_1 = 10 \, \text{k}\Omega \)
- \( V_2 = 2 \, \text{V}, R_2 = 20 \, \text{k}\Omega \)
- \( V_3 = 3 \, \text{V}, R_3 = 30 \, \text{k}\Omega \)
- \( R_f = 30 \, \text{k}\Omega \)
\[
V_o = - \left( \frac{1}{10} + \frac{2}{20} + \frac{3}{30} \right) \times 30
\]
\[
V_o = - (0.1 + 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe36fb7f7-6381-4add-b52b-9085dfd27844%2F49fdb965-ccdd-4d76-a99d-b53bf74c6a8f%2Fxhpteoj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Summing Amplifier Circuit Analysis
**Figure 5.37: Summing Amplifier Configuration**
This image shows a summing amplifier circuit using three voltage inputs connected to an operational amplifier (op-amp). The op-amp is configured as an inverting summing amplifier.
#### Circuit Components:
1. **Input Voltages:**
- **1 V** connected through a **10 kΩ** resistor.
- **2 V** connected through a **20 kΩ** resistor.
- **3 V** connected through a **30 kΩ** resistor.
2. **Feedback Resistor:**
- **30 kΩ** resistor connected from the output to the inverting input of the op-amp.
3. **Op-Amp Configuration:**
- The op-amp is shown with the inverting input connected to summing junctions of the input resistors.
#### Operation:
The output voltage (\( V_o \)) of the summing amplifier can be calculated using the principle of superposition and the formula for an inverting summing amplifier:
\[
V_o = - \left( \frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3} \right) \times R_f
\]
Where:
- \( V_1, V_2, V_3 \) are the input voltages.
- \( R_1, R_2, R_3 \) are the resistors associated with each input voltage.
- \( R_f \) is the feedback resistor.
Substituting the given values:
- \( V_1 = 1 \, \text{V}, R_1 = 10 \, \text{k}\Omega \)
- \( V_2 = 2 \, \text{V}, R_2 = 20 \, \text{k}\Omega \)
- \( V_3 = 3 \, \text{V}, R_3 = 30 \, \text{k}\Omega \)
- \( R_f = 30 \, \text{k}\Omega \)
\[
V_o = - \left( \frac{1}{10} + \frac{2}{20} + \frac{3}{30} \right) \times 30
\]
\[
V_o = - (0.1 + 0
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