A method that simplifies a more complex r-network is replacing the
network by repeatedly applying star-delta and/or delta-star transformations.
Example:
simple verbs
s2d=: 3 :0
'ra rc rb'=. y
N=. (ra*rb) + (ra*rc) + rb*rc
'rac rab rbc',&< N % rb, ra, rc
)
d2s=: 3 :0
'rac rab rbc'=.y
D=. rac + rab + rbc
'ra rc rb' ,&< D %~(rac*rab),(rbc*rab), rac * rbc
)
The method
DELTA STAR
c c
/\ |
rac / \ rbc rc|
/ \ |
a/______\b a______/ \_______b
rab ra rb
delta --> ster
D=. rac + rab + rbc
rac * rab
ra = ------------
D
rbc * rab
rb = ------------
D
rac * rbc
rc = ------------
D
star --> delta
N=. ra*rb + ra*rc + rb*rc
N
rac = ----
rb
N
rbc = ----
ra
N
rab = ----
rc
Example network:
A C
+--[1]--+--[1]--+
| | |
[1] [1] [1]
| | |
+--[1]--+--[1]--+
D B
What is R_AB ?
star ACD -> delta
A C
+------[3]------+
| \ / |
[1] [3] [3] [1]
| \ / |
+--[1]--+--[1]--+
D B
s2d 1 1 1
┌───────────┬─────┐
│rac rab rbc│3 3 3│
└───────────┴─────┘
rp=: *%+
]R_AD =. 3 rp 2x
6r5
A C
+------[3]---+-----+
| | |
| [3] [1]
| | |
+----[6/5]---+-[1]-+
D B
delta CDA --> star CDA
d2s 3 3 6r5
┌────────┬───────────┐
│ra rc rb│5r4 1r2 1r2│
└────────┴───────────┘
C
+---[5/4]---+---[1]---+
| |
A --[1/2]---+ + B
| |
+---[1/2]---+---[1]---+
D
R_AB =
1r2+ (*%+)/ 9r4 3r2
7r5
Or
x: 2 3 resistornw 0 0,:1 2
7r5
--
Met vriendelijke groet,
@@i = Arie Groeneveld
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