# AC Equivalent Circuits

1. Oct 7, 2013

### agata78

1. The problem statement, all variables and given/known data

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

2. Relevant equations

I started working on this question and dont 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!!!

3. The attempt at a solution

#### Attached Files:

• ###### T-network equivalent of the pi network.png
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Last edited: Oct 7, 2013
2. Oct 7, 2013

### agata78

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

Last edited: Oct 7, 2013
3. Oct 7, 2013

### Staff: Mentor

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.