Find T-Network Equiv of ∏ (Pi) Network - AC Equiv Circuits

[agata78]

Homework Statement

Determine the T-network equivalent of the ∏ (Pi) network shown in the Figure?

Homework Equations

I started working on this question and don't know if I am heading in the right direction.

The impedances of the T network (Z1, Z2, Z3) can be found from the impedances of the equivalent pi network with the following equations:

Z1= ( Za x Zb ) / ( Za+ Zb + Zc )
Z2= ( Zb x Zc ) / ( Za+ Zb +Zc )
Z3 = ( Za x ZB ) / ( Za + Zb + Zc )

And then we can use our details:
C1 = Za
L1 = Zc
C2 = Zb

Z1 = (-j20 x j10 ) / (-j20+j10-j20)= -200j^2 / -30j = j6.67
Z2 = (-j20 x j10 ) / ( -j20+j10-j20) = -200j^2 / -30j = j6.67
Z3 = ((-j20 ) x (-20j )) / (-20j+ 10j -20j) = 400j^2 / -j30 = -j13.333

and now we come out with equivalent T -network. At least I hope!

The Attempt at a Solution

 

[agata78]

Yes i know, I had to edit my post and add my attempt!

 

[gneill]

Yes i know that and i have already edit my post and i added my attemps!

No worries. Next time perhaps, leave a message in the post indicating that it's "in progress". That'll help us to avoid jumping the gun.

The approach you've shown looks fine. It's a basic Δ-Y transformation and appears to be correct.