§ 1-5 Network reduction by Δ -Y transformation
de
de
ad RRRR
RRRRRR
???
????
23
23
1
))((
)///// / ( '2'1'3 RRRRRR daad ??
aR
bR
cR
eR
dR
a
bc
d
1R
eR dR
a
c
d
2R3R
b
aR
dR
a
b
d
'3R
'2R
'1R
)4(:)3()2()1( 321
cba
accbba
RRR
RRRRRRRRR
??
???????
'1 )1(:)2()4(
cba
ac RRR RRR ????
'2 )2(:)3()4(
cba
ba RRR RRR ????
'3 )3(:)1()4(
cba
cb RRR RRR ????
电阻之和
相邻电阻之积
?
??
YR
? ? ? ??? abYab RR )1()(21
cba
cba RRR RRRRR ?? ????
? ? ? ??? bcYbc RR )2()(32
cba
acb RRR RRRRR ?? ????
? ? ? ??? caYca RR )3()(13
cba
bac RRR RRRRR ?? ????
Y??
a
bc
aR
bR
cR
a
bc
1R
2R3R
Any given arm of the Y network is found by taking the product
of the two adjacent arms of the Δ network and dividing by the
sum of the Δ network arms.
电阻之和
相邻电阻之积
?
??
YR
If Ra=Rb=Rc=R (balanced load)
then R1=R2=R3=R/3.
:??Y,)1()3()3()2()2()1( '''''' ??
'
2133221 )4()()(
)(
cba
cba
cba
cbacba RRR RRRRRR RRRRRRRRRRRR ????? ?????
321213133221'' //)(:)3()4( RRRRRRRRRRRRR a ???????
132321133221'' //)(:)1()4( RRRRRRRRRRRRR b ???????
213132133221'' //)(:)2()4( RRRRRRRRRRRRR c ???????
'1 )1(
cba
ac
RRR RRR ???
'2 )2(
cba
ba
RRR RRR ???
'3 )3(
cba
cb
RRR RRR ???
a
bc
aR
bR
cR
a
bc
1R
2R3R
相对电阻
两电阻之积
Y
YR ??
?
If R1=R2=R3=R (balanced load),then Ra=Rb=Rc=3R.
Any resistance of Δ network is equal to the sum of
the products of all possible pairs of the Y resistance
divided by the opposite resistance of the Y network.
321213133221'' //)(:)3()4( RRRRRRRRRRRRR a ???????
132321133221'' //)(:)1()4( RRRRRRRRRRRRR b ???????
213132133221'' //)(:)2()4( RRRRRRRRRRRRR c ???????
a
bc
aR
bR
cR
a
bc
1R
2R3R