10.9 CONDITION FOR SYMMETRY

A two-port network is said to be symmetrical if the ports of the two-port network can be interchanged without changing the port voltages and currents as shown in 10.18(a) and (b), and the condition of symmetry is

1. Condition of symmetry for Z-parameters.

   By the condition of Figure 10.18(a) V ₁ = V _s, I ₁ = I ₁, V ₂ = V ₂, I ₂ = 0,

   
   

   By the condition of Figure 10.18(b) V ₂ = V _s, I ₂ = I ₂, I ₁ = 0, V ₁ = V ₁,

   
   

   
   Figure 10.18

   From the definition of symmetry

   
   

2. Condition of symmetry for Y-parameters,

   
   

   By the condition of Figure 10.18(a) V ₁ = V _s, I ₁ = I ₁, I ₂ = 0, V ₂ = V ₂,

   
   

   By the condition of Figure 10.18(b) V ₂ = V _s, I ₂ = I ₂, I ₁ = 0, V ₁ = V ₁,

   
   
   
   

3. Condition of symmetry for T-parameters.

   The T-parameter equations are

   
   

   By the condition of Figure 10.18(a) V ₁ = V _s, I ₁ = I ₁, I ₂ = 0, V ₂ = V ₂, we get

   
   

   then

   
   

   By the condition of Figure 10.18(b) V ₂ = V _s, I ₂ = I ₂,...