Condition for Symmetry in Two Port Network

Condition for Symmetry in Two Port Network:

If the impedance measured at one port is equal to the impedance measured at the other port with remaining port open circuited, the network is said to be Condition for Symmetry.

The impedances at two ports can be measured as shown in Fig. 6.6 (a) and (b).

Condition for Symmetry in Two Port Network

Condition of Symmetry for z-Parameters:

The basic equations of z-parameters are as follows.

Condition for Symmetry in Two Port Network

Consider Fig. 6.6 (a).

Hence equation (i) will become,

Consider Fig. 6.6 (b).

Equation (ii) can be written as,

Condition for Symmetry in Two Port Network

For symmetrical networks, both the port impedances must be equal i.e.

Condition for Symmetry in Two Port Network

Condition of Symmetry for y-Parameters:

The basic equations of y-parameters are as follows

Condition for Symmetry in Two Port Network

Consider Fig. 6.6 (a).

Equation (i) can be written as,

Equation (ii) can be written as,

Condition for Symmetry in Two Port Network

Substituting value of V2 in equation (iii), we have

Condition for Symmetry in Two Port Network

Consider Fig. 6.6 (b).

Equation (i) can be written as,

Condition for Symmetry in Two Port Network

Equation (ii) can be written as,

Condition for Symmetry in Two Port Network

Substituting value of V1 in equation (viii) from equation (vii), we have

Condition for Symmetry in Two Port Network

For symmetrical networks, both the port impedances must be equal i.e.

Condition for Symmetry in Two Port Network

Conditions of Symmetry for h-Parameters:

The basic equations of h-parameters are as follows,

Condition for Symmetry in Two Port Network

Consider Fig. 6.6 (a),

Equation (i) can be written as,

Condition for Symmetry in Two Port Network

Equation (ii) can be written as

Condition for Symmetry in Two Port Network

Substituting value of V2 in equation (iii), we have

Condition for Symmetry in Two Port Network

Condition for Symmetry in Two Port Network

Consider Fig. 6.6 (b),

Equation (i) can be written as

Condition for Symmetry in Two Port Network

Equation (ii) can be written as

Condition for Symmetry in Two Port Network

For symmetrical networks, both the port impedances must be equal i.e.

Condition of Symmetry for Transmission Parameters:

The basic equations for the transmission parameters are as following

Consider Fig. 6.6 (a),

Equation (i) can be written as,

Condition for Symmetry in Two Port Network

Equation (ii) can be written as,

Consider Fig. 6.6 (b),

Condition for Symmetry in Two Port Network

Equation (i) can be written as,

Equation (ii) can be written as,

Condition for Symmetry in Two Port Network

Condition for Symmetry in Two Port Network

For the symmetrical network, both the port impedances must be equal.

Condition for Symmetry in Two Port Network

Updated: November 5, 2019 — 10:32 pm