Network Analysis XI

T to π / π to T

Conversion

The two configurations in question

• T-network

• π-network

T to π formulas

• 𝑅𝐴 =𝑅1𝑅2:𝑅2𝑅3:𝑅3𝑅1

𝑅1

• 𝑅𝐵 =𝑅1𝑅2:𝑅2𝑅3:𝑅3𝑅1

𝑅2

• 𝑅𝐶 =𝑅1𝑅2:𝑅2𝑅3:𝑅3𝑅1

𝑅3

Conversion 1

• Convert the T network shown into an equivalent π network.

Formulas for calculations

• 𝑅𝐴 =𝑅1𝑅2:𝑅2𝑅3:𝑅3𝑅1

𝑅1=

8 9 : 8 5 : 5 9

9=

72:40:45

9=

157

9= 17.444Ω

• 𝑅𝐵 =𝑅1𝑅2:𝑅2𝑅3:𝑅3𝑅1

𝑅2=

8 9 : 8 5 : 5 9

8=

72:40:45

8=

157

8= 19.625Ω

• 𝑅𝐶 =𝑅1𝑅2:𝑅2𝑅3:𝑅3𝑅1

𝑅3=

8 9 : 8 5 : 5 9

5=

72:40:45

5=

157

5= 31.4Ω

End result

RA

RC RB

1 3

2 2

π to T formulas

• 𝑅1 =𝑅𝐵𝑅𝐶

𝑅𝐴:𝑅𝐵:𝑅𝐶

• 𝑅2 =𝑅𝐴𝑅𝐶

𝑅𝐴:𝑅𝐵:𝑅𝐶

• 𝑅3 =𝑅𝐴𝑅𝐵

𝑅𝐴:𝑅𝐵:𝑅𝐶

Conversion 2

• Convert the π network shown into an equivalent T network.

RA

18ΩRC32Ω

RB20Ω

1 3

2 2

Formulas for calculations

• 𝑅1 =𝑅𝐵𝑅𝐶

𝑅𝐴:𝑅𝐵:𝑅𝐶=

20 32

18:20:32=

640

70= 9.143Ω

• 𝑅2 =𝑅𝐴𝑅𝐶

𝑅𝐴:𝑅𝐵:𝑅𝐶=

18 32

18:20:32=

576

70= 8.229Ω

• 𝑅3 =𝑅𝐴𝑅𝐵

𝑅𝐴:𝑅𝐵:𝑅𝐶=

18 20

18:20:32=

360

70= 5.143Ω

End result

R1

R2 R3A B

C

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