GATE EC 2026 Set 1 — Question 52
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Electromagnetics → Transmission Lines → Input Impedance & Reflection
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Question
A complex load (in ) is represented as on the Smith chart. A co-axial cable with a characteristic impedance of is connected to the load. The new input impedance of the load now moves to a diametrically opposite point on the same circle on the Smith chart. Which option is the nearest input impedance of the cable connected load (in )?
Correct answer
(B) 17.7 - j11.8
Solution
Given the reflection coefficient at the load is and the characteristic impedance is .Moving to a diametrically opposite point on the Smith chart corresponds to a phase shift in the reflection coefficient. Thus, the input reflection coefficient is:Alternatively, a diametrically opposite point on the Smith chart represents the normalized admittance , or the reciprocal of the normalized impedance . Thus, the new normalized input impedance is:Calculating :The actual input impedance is:The nearest option is (B).
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