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Solved Problems-8

Problems-8
  1. Find the equivalent π-network for the T-network shown in the Fig. (a).
  2. Find the equivalent T -network for the π-network shown in the Fig. (b).
Description: Description: 2251.png
                                (a)                                                    (b)
 
Solution
  1. Let the equivalent π-network have YC as the series admittance and YA and YB as the shunt admittances at port-1 and port-2, respectively.
Description: Description: 1010.png
 
Now, the z-parameters are given as:
 
z11 = Description: Description: 5582.png
 
∴ Δz = Description: Description: 5588.png
 
∴ y11 = Description: Description: 5594.png
 
y12 = y21 = Description: Description: 5601.png
 
y22 = Description: Description: 5608.png
 
∴ YA = Description: Description: 5614.png
 
∴ YB = Description: Description: 5620.png
 
and YC = Description: Description: 5629.png
 
Thus, the impedances of the equivalent π-networks are:
 
Description: Description: 1016.png
Equivalent π-network
 
Description: Description: 5635.png
 
  1. Description: Description: 2304.png
     
    π-network                                     Equivalent T-network
The y-parameters,
 
y11 = Description: Description: 5641.png
 
∴ Δy = Description: Description: 5647.png
 
∴ z11 = Description: Description: 5653.png
 
∴ Description: Description: 5665.png
 




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