Also known as the Tee-to-pi or Y-Delta transform, the star-triangle transform allow to
transform a star shaped
tripolar electrical network to a triangle shaped network with he same
behavior and backwards. Suppose we start from the following star/T/Y (the two bottom
nodes are in fact only one same node, as they are supraconductively connected) :
------ ------
0----| A |---| B |----0
------ | ------
|
-
| |
|C|
| |
-
|
0-----------------------0
The triangle/Pi/Delta we want to transform to is the following :
------
0---------| c |--------0
| ------ |
| |
- -
| | | |
|b| |a|
| | | |
- -
| |
0-----------------------0
The transformation
formulas are the as follows :
a=(A.B+B.C+A.C)/A
b=(A.B+B.C+A.C)/B
c=(A.B+B.C+A.C)/C
And backwards :
A=(b.c)/(a+b+c)
B=(a.c)/(a+b+c)
C=(a.b)/(a+b+c)
This is esily
proved by calculating the
impedance between each node. This gives a set of three equations that can be added / substracted to isolate any of the variables.