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Solved Problems-7

Problems-7
Calculate the T-parameters for the block A and B separately and then using these results, calculate the T-parameters of the whole circuit shown in the figure. Prove any formula used.
  1. Description: Description: 2030.png
  2. Description: Description: 2037.png
Solution
  1. We consider the given network as a cascade connection of two networks as shown.
Description: Description: 880.png
 
For Block A:
 
Opening the port-2,
 
By KCL,
Description: Description: 5337.png
and Description: Description: 5343.png
 
Solving for V1 and V2,
 
V1 = Description: Description: 5349.png
 
Description: Description: 5355.png 
 
Short-circuiting port-2,
 
Description: Description: 886.png
 
∴ I1 = Description: Description: 5361.png
 
and V1 = Description: Description: 5367.png
 
and Da = Description: Description: 5373.png
 
For Block B:
 
Opening the port-2,
 
Description: Description: 911.png
 
By KCL,
 
Description: Description: 5381.png
 
and Description: Description: 5388.png
 
Solving for V1 and V2,
 
V1 = Description: Description: 5394.png
 
Description: Description: 5400.png 
 
Short-circuiting port-2,
 
 
Description: Description: 917.png
 
∴ I1 = Description: Description: 5406.png
 
and V1 = Description: Description: 5412.png
 
and Db = Description: Description: 5423.png
 
Since the two networks are connected in cascade, the overall transmission parameter matrix is obtained as,
[T] = Description: Description: 5429.png = Description: Description: 5435.png
  1. [Same as Prob. (a)]
Here, [Ta] = Description: Description: 5444.png
 
∴ [T] = Description: Description: 5450.png
 




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