GATE EC 2014 Set 1 — Question 34
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Electromagnetics → Transmission Lines → S-Parameters
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Question
A two-port network has scattering parameters given by . If the port-2 of the two-port is short circuited, the parameter for the resultant one-port network is
Correct answer
(B) s₁₁ + s₁₁s₂₂ - s₁₂s₂₁1 + s₂₂
Solution
The scattering matrix equations for a two-port network are:
Now substitute and the expression for into equation (1):
The input reflection coefficient of the resultant one-port network is:
This matches option (B).
1.
2.
When port 2 is short-circuited, the reflection coefficient at the load is . The relationship between the incident and reflected waves at port 2 is .Substituting into equation (2):Now substitute and the expression for into equation (1):
The input reflection coefficient of the resultant one-port network is:
This matches option (B).
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