T to Pi transformation
Z123 = t2pi(Zabc)
impedances of T network = [Za,Zb,Zc]
impedances of Pi network = [Z1,Z2,Z3]
t2pi(Zabc) performs T to Pi transformation. Z123 and Zabc are Lx3 matrices, for transforming several cases at once. the transformation equations are:
Z1 = V/Za, Z2 = V/Zb, Z3 = V/Zc, where V = Za*Zb + Zb*Zc + Zc*Za
Za = Z2*Z3/U, Zb = Z3*Z1/U, Zc = Z1*Z2/U, where U = Z1 + Z2 + Z3
---[Zc]----|----[Za]---..........---|----[Z2]----|---
...........|........................|............|
..........[Zb]............==>......[Z1]..........[Z3]
...........|........................|............|
-----------|-----------..........---|------------|---
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