π or pi Network in Network Analysis:

Consider following two port ’π’ or pi Network type network with assumed voltages V₁ and V₂ and current I₁ end I₂ 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 V₁ = 0 and V₂ = 0.

With the port 2-2′ short circuited :

We have V₂ = 0

Hence, y₂ will be directly shorted.

Total admittance looking into network from port 1-1′ is equal to (y₁ + y₃).

Hence, current I₁ in port 1-1′ can be calculated as follows,

The current I₂ in port 2-2′ can be calculated as follows.

Note that current I₂ will be negative

With the port 1-1′ short circuited :

We have V₁ = 0. Hence, y₁ will be directly shorted. Total admittance looking back into network from port 2-2′ is equal to (y₂ + y₃).

Hence, current I₂ in port 2-2′ can be calculated as follows

The current I₁ in port 1-1′ can be calculated as follows.

Note that current I₁ will be negative.

Consider the expression

substituting y₃ = -y₁₂ in first two expressions, we have,

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