Practical Electronics/π Network

Intro

A network consist of three resistors connected like a π

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}}

V_{o} = V_{i} \frac{R_{3} + R_{2}}{R_{1} + R_{2}}

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

The fomula above now becomes

V_{o} = V_{i} \frac{R_{2}}{R_{2} + R_{1}}

This network acts as Voltage Attenuator

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}}

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