# 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