Practical Electronics/π Network

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Intro[edit]

A network consist of three resistors connected like a π

Analysis[edit]

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[edit]

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

Choosing Resistance's Value[edit]

  • 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[edit]

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