Pulse Radar Ambiguity Limit from Maximum Range A pulse radar has a maximum unambiguous range of 120 km. What is the maximum allowable pulse repetition frequency (PRF) to maintain unambiguous reception?

Introduction / Context:
In pulse radar, echoes from a given pulse must return before the next pulse is transmitted to avoid range ambiguity. The pulse repetition frequency (PRF) and the maximum unambiguous range are therefore inversely related.

Given Data / Assumptions:

• Maximum unambiguous range R_max = 120 km = 120,000 m.
• Propagation speed c ≈ 3 * 10^8 m/s.
• Two-way travel time governs the timing between pulses.

Concept / Approach:

The maximum unambiguous range is R_max = c / (2 * PRF). Rearranging gives PRF_max = c / (2 * R_max). This ensures the echo from the farthest target returns before the next pulse is transmitted.

Step-by-Step Solution:

Verification / Alternative check:

Checking units: meters per second divided by meters gives s^-1, i.e., Hz; the magnitude 1250 Hz corresponds to a pulse repetition interval of 0.8 ms, which matches a round-trip time to 120 km.

Why Other Options Are Wrong:

330 and 625 are too low (overly conservative), while 2500 and 8330 exceed the allowable limit and would cause range ambiguities.

Common Pitfalls:

Forgetting the factor of 2 for the round trip; mixing Hz with kHz; using one-way time instead of two-way.

Final Answer:

1250