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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.

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.

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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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.
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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