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GATE 2020 EC – Question 23

Electromagnetics · Transmission Lines · 1 mark · Multiple choice

The impedances $Z=jX$, for all $X$ in the range $(-\infty,\infty)$, map to the Smith chart as

  1. a circle of radius 1 with centre at $(0,0)$.
  2. a point at the centre of the chart.
  3. a line passing through the centre of the chart.
  4. a circle of radius 0.5 with centre at $(0.5,0)$.

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Show answer and explanation

Correct answer: (A) a circle of radius 1 with centre at $(0,0)$.

Explanation

A purely reactive impedance has zero resistance, so its reflection coefficient has magnitude $|\Gamma|=1$. This is the outer boundary of the Smith chart, a circle of radius 1 centred at the origin.