# Practical Electronics/π Network

## Intro

A network consist of three resistors connected like a π

## Analysis

$I_1 = \frac{V_i}{R_1}$
$I_3 = \frac{V_o}{R_3}$
$I_2 = \frac{V_i - V_o}{R_2}$
$I_1 = I_2 + I_3$
$\frac{V_i}{R_1} = \frac{V_o}{R_3} + \frac{V_i - V_o}{R_2}$
$\frac{V_o}{V_i} = \frac{R_3 - R_2}{R_1 - R_2}$

## Formula

$V_o = V_i \frac{R_3+R_2}{R_1+R_2}$

## Choosing Resistance's Value

• R2 = 0
The fomula above now becomes
$V_o = V_i \frac{R_3}{R_1}$
R3 > R1 , Vo > V1 . This network acts as Voltage Amplifier
R3 = R1 , Vo = V1 . This network acts as Voltage Follower
R3 < R1 , Vo < V1 . This network acts as Voltage Attenuator
• R3 = 0
The fomula above now becomes
$V_o = V_i \frac{R_2}{R_2+R_1}$
This network acts as Voltage Attenuator
• R1 = 0
The fomula above now becomes
$V_o = V_i \frac{R_3 + R_2}{R_2}$
This network acts as Voltage Amplifier 1 + $\frac{R_3}{R_2}$

## Summary

This network can be used as Voltage Amplifier, Voltage Follower, Voltage Attenuator by choosing the right value for the resistors