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Solved Problems-2

Problems-2
Find the y-parameters for the 2-port networks shown.
  1. Description: Description: 2113.png
  2.  Description: Description: 2120.png
  3. Description: Description: 2127.png
Solution
  1. We consider two cases to find out the y-parameters.
Case (I) Making port- 2 shorted and applying a voltage of V1 at port- 1
Description: Description: 2134.png
 
By KVL,
 
17I1 + 20I2 = V1
 
and 12I1 + 20I2 = 0
 
I1 = Description: Description: 3690.png
 
Solving,
 
I2 = Description: Description: 3699.png
 
Case (II) Making port-1 shorted and applying a voltage of V2 at port- 2
 
Description: Description: 2150.png
 
By KVL,
 
17I1 + 20I2 = – 0.2V2
 
and 12I1 + 20I2 = V2
 
I1 = Description: Description: 3705.png
 
Solving,
I2 = Description: Description: 3711.png
 
Thus, [ y] = Description: Description: 3717.png
 
  1. We consider two cases.
Case (I) V1 = 0
 
Case (II) V2 = 0
 
Description: Description: 2172.png
 
By KCL,
Description: Description: 3730.png
  1. For V1 = 0, the circuit becomes as shown.
∴ Description: Description: 3736.png
Also, Description: Description: 3742.png
 
Description: Description: 2193.png
 
For V2 = 0, the circuit becomes as shown.
∴ Description: Description: 3748.png(i)
 
Description: Description: 3754.png(ii)
 
I1 = I3 + I4 (iii)
 
and V1 = Description: Description: 3760.png (iv)
 
 
From (i) to (iv),
 
Description: Description: 3766.png
 
From (i), y21 = – 3
 
Thus, the y-parameters are:
[y] = Description: Description: 3772.png
 
From the interrelationship, we get the z-parameters as:
[z] = Description: Description: 3779.png
 




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