pi Network in Network Analysis

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.

pi Network in Network Analysis

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,

pi Network in Network Analysis

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

Note that current I2 will be negative

pi Network in Network Analysis

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.

pi Network in Network Analysis

Consider the expression

pi Network in Network Analysis

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

pi Network in Network Analysis

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

Updated: November 6, 2019 — 5:54 am