Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Find an expression for the output voltage Vout in the attached circuit. The op-amp is ideal (infinite gain, zero offset, infinite input impedance, zero phase shift at any frequency, zero output impedance) and the input voltages are V1 and V2.

### Operational Amplifier Summing Amplifier Circuit

In the diagram above, we observe a common configuration for an operational amplifier (op-amp) known as a summing amplifier. This specific setup allows multiple input voltages to be summed together into a single output voltage. Below is a detailed explanation of the various components and connections in this circuit:

#### Components:
1. **Operational Amplifier (Op-Amp):**
   - The op-amp is depicted as a triangle with inverting (-) and non-inverting (+) inputs. In this example, the output is fed back to the inverting input through resistor R2.
   
2. **Resistors:**
   - **R1:** Connected between input voltage source V1 and the inverting input (-) of the op-amp.
   - **R3:** Connected between input voltage source V2 and the inverting input (-) of the op-amp.
   - **R2:** Feedback resistor connected between the output (Vout) and the inverting input (-) of the op-amp.

    The non-inverting input (+) is typically connected to the ground in practical implementations, though it is not explicitly shown in this simple diagram.

#### Connections and Operation:
- **V1 and V2** are input voltage sources.
- The resistors R1 and R3 provide paths for V1 and V2 to connect with the inverting input (-) of the op-amp.
- The configuration ensures that the op-amp operates in closed-loop mode with its gain and stability determined by the external components R1, R2, and R3.

The governing equation for the summing amplifier output voltage (\( V_{\text{out}} \)) is:

\[ V_{\text{out}} = - \left( \frac{R2}{R1} V1 + \frac{R2}{R3} V2 \right) \]

#### Additional Notes:
- The negative sign signifies that the output voltage is inverted relative to the sum of the input voltages.
- This circuit design can be expanded to more input voltages by adding additional resistors in series with each input voltage and connecting them to the inverting input of the op-amp.

The summing amplifier is widely used in analog computing, audio mixing, and other fields where the combination of multiple signals into a single output is required.
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Transcribed Image Text:### Operational Amplifier Summing Amplifier Circuit In the diagram above, we observe a common configuration for an operational amplifier (op-amp) known as a summing amplifier. This specific setup allows multiple input voltages to be summed together into a single output voltage. Below is a detailed explanation of the various components and connections in this circuit: #### Components: 1. **Operational Amplifier (Op-Amp):** - The op-amp is depicted as a triangle with inverting (-) and non-inverting (+) inputs. In this example, the output is fed back to the inverting input through resistor R2. 2. **Resistors:** - **R1:** Connected between input voltage source V1 and the inverting input (-) of the op-amp. - **R3:** Connected between input voltage source V2 and the inverting input (-) of the op-amp. - **R2:** Feedback resistor connected between the output (Vout) and the inverting input (-) of the op-amp. The non-inverting input (+) is typically connected to the ground in practical implementations, though it is not explicitly shown in this simple diagram. #### Connections and Operation: - **V1 and V2** are input voltage sources. - The resistors R1 and R3 provide paths for V1 and V2 to connect with the inverting input (-) of the op-amp. - The configuration ensures that the op-amp operates in closed-loop mode with its gain and stability determined by the external components R1, R2, and R3. The governing equation for the summing amplifier output voltage (\( V_{\text{out}} \)) is: \[ V_{\text{out}} = - \left( \frac{R2}{R1} V1 + \frac{R2}{R3} V2 \right) \] #### Additional Notes: - The negative sign signifies that the output voltage is inverted relative to the sum of the input voltages. - This circuit design can be expanded to more input voltages by adding additional resistors in series with each input voltage and connecting them to the inverting input of the op-amp. The summing amplifier is widely used in analog computing, audio mixing, and other fields where the combination of multiple signals into a single output is required.
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