Define standing wave ratio (SWR) and show its relation to the magnitude of the reflection coefficient Γ.

• A. SWR = (1+|Γ|)/(1−|Γ|); at Γ=0, SWR=1; as |Γ|→1, SWR→∞.
• B. SWR = |Γ|.
• C. SWR = (1−|Γ|)/(1+|Γ|).
• D. SWR is independent of Γ.

Answer: (A)

The standing-wave ratio measures how uneven the voltage along a transmission line is due to reflections, and it links directly to how much of the incident wave is reflected, quantified by the magnitude of the reflection coefficient Γ.

If the line is driven with an incident wave of amplitude a and a reflected wave of amplitude Γa, the total voltage along the line is V(z) = a e^{-jkz} + Γa e^{jkz}. The maximum along the line occurs when the two waves add in phase, and the minimum when they subtract. The peak voltage is proportional to 1 + |Γ| and the trough to 1 − |Γ|, giving the standing-wave ratio as SWR = |V|max / |V|min = (1 + |Γ|) / (1 − |Γ|).

This also shows the limiting behavior: with no reflection (Γ = 0), SWR = 1, indicating a perfectly matched line. As the magnitude of the reflection approaches 1 (strong reflection, such as open or short), SWR grows without bound toward infinity.

So the relation is SWR = (1 + |Γ|)/(1 − |Γ|); the other expressions do not match this fundamental ratio and would either misrepresent the dependence on Γ or imply no dependence at all.