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

In summary, the T-network equivalent of the ∏ (Pi) network is found using the Δ-Y transformation with the equations Z1= ( Za x Zb ) / ( Za+ Zb + Zc ), Z2= ( Zb x Zc ) / ( Za+ Zb +Zc ), and Z3 = ( Za x ZB ) / ( Za + Zb + Zc ). In this case, C1 = Za, L1 = Zc, and C2 = Zb. Using these values, the equivalent T-network is calculated with Z1 = j6.67, Z2 = j6.67, and Z3 = -j13.333.
  • #1
agata78
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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

 

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  • #2
Yes i know, I had to edit my post and add my attempt!
 
Last edited:
  • #3
agata78 said:
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.
 

1. What is a T-network and a Pi-network in AC equivalent circuits?

A T-network and a Pi-network are two types of passive electrical networks used to convert a series impedance to a parallel impedance or vice versa. They consist of resistors, capacitors, and inductors arranged in a specific configuration to achieve the desired impedance transformation.

2. How do I find the T-network equivalent of a Pi-network?

To find the T-network equivalent of a Pi-network, you need to use the following equations:

  • RT = R1 + R2 + R3
  • LT = L1 + L2 + L3 + K12 + K13 + K23
  • CT = C1 + C2 + C3 + K12 + K13 + K23

Where R1, R2, and R3 are the resistors in the Pi-network, L1, L2, and L3 are the inductors, C1, C2, and C3 are the capacitors, and K12, K13, and K23 are the mutual inductances and capacitances between the components.

3. What is the purpose of finding the T-network equivalent of a Pi-network?

The purpose of finding the T-network equivalent of a Pi-network is to simplify a complex circuit into a simpler one that is easier to analyze. It also helps to reduce the number of components and increase the overall efficiency of the circuit.

4. Can a Pi-network and a T-network be used interchangeably?

No, a Pi-network and a T-network cannot be used interchangeably. While they both serve the same purpose of impedance transformation, their component values and configurations are different. Therefore, they cannot be substituted for each other in a circuit.

5. How do I choose which network to use in a circuit?

The choice between using a Pi-network or a T-network in a circuit depends on the specific requirements and constraints of the circuit. For example, if the circuit needs to minimize the overall size and weight, a T-network may be a better choice as it has fewer components. However, if the circuit needs to maintain a high-quality factor, a Pi-network may be a better option as it has a lower insertion loss. It is important to analyze the circuit and consider all factors before deciding on which network to use.

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