How does pulse width affect range resolution, and what is the formula?

How does pulse width affect range resolution, and what is the formula?

• A. δ_R = c τ; shorter pulses yield coarser range resolution.
• B. δ_R = c τ / 2; longer pulses yield finer range resolution.
• C. δ_R = c τ / 2; shorter pulses yield finer range resolution.
• D. δ_R = 2 c τ; shorter pulses yield coarser range resolution.

Answer: (C)

In radar, range resolution is about how precisely you can tell two targets apart along the line of sight. The pulse width τ sets this limit: the shorter the pulse, the better you can separate reflections that come from nearby ranges. The relationship is δR ≈ c τ / 2, where c is the speed of light. This comes from the fact the pulse must travel to the target and back, so the full round-trip distance corresponding to the pulse duration is c τ. The one-way separation in range between two targets is half of that, hence δR = c τ / 2. So shorter pulses reduce δR, giving finer range resolution. For context, if τ is 1 microsecond, δR is about 150 meters; if τ is 0.1 microseconds, δR is about 15 meters. The other options don’t fit because they miss the 1/2 factor or state the opposite effect of pulse width on resolution.

In radar, range resolution is about how precisely you can tell two targets apart along the line of sight. The pulse width τ sets this limit: the shorter the pulse, the better you can separate reflections that come from nearby ranges.

The relationship is δR ≈ c τ / 2, where c is the speed of light. This comes from the fact the pulse must travel to the target and back, so the full round-trip distance corresponding to the pulse duration is c τ. The one-way separation in range between two targets is half of that, hence δR = c τ / 2. So shorter pulses reduce δR, giving finer range resolution.

For context, if τ is 1 microsecond, δR is about 150 meters; if τ is 0.1 microseconds, δR is about 15 meters.

The other options don’t fit because they miss the 1/2 factor or state the opposite effect of pulse width on resolution.