Mumbai University > Computer Engineering > Sem 3 > Electronic Circuits and Communication Fundamentals

Marks: 10 Marks

Year: May 2016

1.If we take three equal resistors and connect one end of each to a common point, then apply three input voltages (one to each of the resistors’ free ends), the voltage seen at the common point will be the mathematical average of the three.

2.This circuit is really nothing more than a practical application of Millman’s Theorem:

3.This circuit is commonly known as a passive averager, because it generates an average voltage with non-amplifying components.

4.Passive simply means that it is an unamplified circuit. The large equation to the right of the average circuit comes from Millman’s Theorem, which describes the voltage produced by multiple voltage sources connected together through individual resistances.

5.Since the three resistors in the average circuit are equal to each other, we can simplify Millman’s formula by writing R1, R2, and R3 simply as R (one, equal resistance instead of three individual resistances):

$$V_{out}=\dfrac{\dfrac{V_1}{R}+\dfrac{V_2}{R}\dfrac{V_3}{R}}{\dfrac{1}{R}+\dfrac{1}{R}+\dfrac{1}{R}} \\ V_{out}=\dfrac{\dfrac{V_1+V_2+V_3}{R}}{\dfrac{3}{R}} \\ V_{out}=\dfrac{V_1+V_2+V_3}{3}$$

6.If we take a passive average and use it to connect three input voltages into an op-amp amplifier circuit with a gain of 3, we can turn this averaging function into an addition function.