**π or pi Network in Network Analysis:**

Consider following two port ’π’ or pi Network type network with assumed voltages V_{1} and V_{2} and current I_{1} end I_{2} as shown in Fig. 6.11.

Let the y-parameters of the above network are represented as follows,

We know that, y-parameter for any network can be calculated by short circuiting input and output ports ie by making V_{1} = 0 and V_{2} = 0.

**With the port 2-2′ short circuited :**

We have V_{2} = 0

Hence, y_{2} will be directly shorted.

Total admittance looking into network from port 1-1′ is equal to (y_{1} + y_{3}).

Hence, current I_{1} in port 1-1′ can be calculated as follows,

The current I_{2} in port 2-2′ can be calculated as follows.

Note that current I_{2} will be negative

**With the port 1-1′ short circuited :**

We have V_{1} = 0. Hence, y_{1} will be directly shorted. Total admittance looking back into network from port 2-2′ is equal to (y_{2} + y_{3}).

Hence, current I_{2} in port 2-2′ can be calculated as follows

The current I_{1} in port 1-1′ can be calculated as follows.

Note that current I_{1 }will be negative.

Consider the expression

substituting y_{3} = -y_{12} in first two expressions, we have,

Hence, the circuit elements of the equivalent ’π’ of pi network are as follows,