Network Analysis XI
T to ฯ / ฯ to T
Conversion
The two configurations in question
โข T-network
โข ฯ-network
T to ฯ formulas
โข ๐ ๐ด =๐ 1๐ 2:๐ 2๐ 3:๐ 3๐ 1
๐ 1
โข ๐ ๐ต =๐ 1๐ 2:๐ 2๐ 3:๐ 3๐ 1
๐ 2
โข ๐ ๐ถ =๐ 1๐ 2:๐ 2๐ 3:๐ 3๐ 1
๐ 3
Conversion 1
โข Convert the T network shown into an equivalent ฯ network.
Formulas for calculations
โข ๐ ๐ด =๐ 1๐ 2:๐ 2๐ 3:๐ 3๐ 1
๐ 1=
8 9 : 8 5 : 5 9
9=
72:40:45
9=
157
9= 17.444ฮฉ
โข ๐ ๐ต =๐ 1๐ 2:๐ 2๐ 3:๐ 3๐ 1
๐ 2=
8 9 : 8 5 : 5 9
8=
72:40:45
8=
157
8= 19.625ฮฉ
โข ๐ ๐ถ =๐ 1๐ 2:๐ 2๐ 3:๐ 3๐ 1
๐ 3=
8 9 : 8 5 : 5 9
5=
72:40:45
5=
157
5= 31.4ฮฉ
End result
RA
RC RB
1 3
2 2
ฯ to T formulas
โข ๐ 1 =๐ ๐ต๐ ๐ถ
๐ ๐ด:๐ ๐ต:๐ ๐ถ
โข ๐ 2 =๐ ๐ด๐ ๐ถ
๐ ๐ด:๐ ๐ต:๐ ๐ถ
โข ๐ 3 =๐ ๐ด๐ ๐ต
๐ ๐ด:๐ ๐ต:๐ ๐ถ
Conversion 2
โข Convert the ฯ network shown into an equivalent T network.
RA
18ฮฉRC32ฮฉ
RB20ฮฉ
1 3
2 2
Formulas for calculations
โข ๐ 1 =๐ ๐ต๐ ๐ถ
๐ ๐ด:๐ ๐ต:๐ ๐ถ=
20 32
18:20:32=
640
70= 9.143ฮฉ
โข ๐ 2 =๐ ๐ด๐ ๐ถ
๐ ๐ด:๐ ๐ต:๐ ๐ถ=
18 32
18:20:32=
576
70= 8.229ฮฉ
โข ๐ 3 =๐ ๐ด๐ ๐ต
๐ ๐ด:๐ ๐ต:๐ ๐ถ=
18 20
18:20:32=
360
70= 5.143ฮฉ
End result
R1
R2 R3A B
C
Any questions?
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โข Email:
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