a) Determine v, in terms of V1, V2, V3, V4. b) Design R1, R2, R3, R4, R5 to obtain v, (V + V2 + V3 + V4). This is known as an = - averaging amplifier, where the output is equal to the (negative) average of the inputs (Hint: Fix R5 = 1kN and pick the remaining resistors). V1 R1 V2 R2 V3 R3 ww R5 V4 R4 오+ 10-.

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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### Transcription for Educational Website:

#### Problem Statement

a) Determine \( v_o \) in terms of \( V_1, V_2, V_3, V_4 \).

b) Design \( R_1, R_2, R_3, R_4, R_5 \) to obtain \( v_o = -\frac{1}{4}(V_1 + V_2 + V_3 + V_4) \). This is known as an averaging amplifier, where the output is equal to the (negative) average of the inputs. (Hint: Fix \( R_5 = 1k\Omega \) and pick the remaining resistors).

#### Circuit Diagram Explanation

The circuit diagram shows an operational amplifier in an inverting configuration. It consists of:

- Four input voltage sources \( V_1, V_2, V_3, V_4 \).
- Four resistors \( R_1, R_2, R_3, R_4 \) connected to each input voltage source, respectively, leading into the inverting input of the operational amplifier.
- A feedback resistor \( R_5 \) connected between the output and the inverting input of the operational amplifier.
- The non-inverting input of the operational amplifier is connected to the ground.
- The output voltage \( v_o \) is taken from the output of the operational amplifier.

The goal is to configure the resistors such that the output voltage \( v_o \) is the negative average of the input voltages.
Transcribed Image Text:### Transcription for Educational Website: #### Problem Statement a) Determine \( v_o \) in terms of \( V_1, V_2, V_3, V_4 \). b) Design \( R_1, R_2, R_3, R_4, R_5 \) to obtain \( v_o = -\frac{1}{4}(V_1 + V_2 + V_3 + V_4) \). This is known as an averaging amplifier, where the output is equal to the (negative) average of the inputs. (Hint: Fix \( R_5 = 1k\Omega \) and pick the remaining resistors). #### Circuit Diagram Explanation The circuit diagram shows an operational amplifier in an inverting configuration. It consists of: - Four input voltage sources \( V_1, V_2, V_3, V_4 \). - Four resistors \( R_1, R_2, R_3, R_4 \) connected to each input voltage source, respectively, leading into the inverting input of the operational amplifier. - A feedback resistor \( R_5 \) connected between the output and the inverting input of the operational amplifier. - The non-inverting input of the operational amplifier is connected to the ground. - The output voltage \( v_o \) is taken from the output of the operational amplifier. The goal is to configure the resistors such that the output voltage \( v_o \) is the negative average of the input voltages.
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