Network Analysis VII - Electronics for calculations •𝑅 = 𝑅1𝑅2:𝑅2𝑅3:𝑅3𝑅1 𝑅1...
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Network Analysis XI T to π / π to T Conversion
Transcript of Network Analysis VII - Electronics for calculations •𝑅 = 𝑅1𝑅2:𝑅2𝑅3:𝑅3𝑅1 𝑅1...
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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