Practical Electronics/π Network

Intro

A network consist of three resistors connected like a π

Analysis

$I_1 = \frac{V_i}{R_1}$

$I_3 = \frac{V_o}{R_3}$

$I_2 = \frac{V_i - V_o}{R_2}$

I₁ = I₂ + I₃

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

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

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 , V_o > V₁ . This network acts as Voltage Amplifier

R₃ = R₁ , V_o = V₁ . This network acts as Voltage Follower

R₃ < R₁ , V_o < 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