Question 8-5A5

To avoid range ambiguity in a RADAR system, the echo from a target at the maximum desired range must return to the receiver before the next pulse is transmitted. This ensures that each received echo can be unambiguously associated with its corresponding transmitted pulse. The maximum unambiguous range ($R_{max}$) is given by the formula: $R_{max} = \frac{c \times T}{2} = \frac{c}{2 \times PRF}$ where $c$ is the speed of light ($3 \times 10^8$ m/s), $T$ is the pulse repetition interval (PRI), and $PRF = 1/T$. Rearranging for PRF: $PRF_{max} = \frac{c}{2 \times R_{max}}$ Given $R_{max} = 30$ nautical miles: 1 nautical mile $\approx$ 1852 meters $30 \text{ NM} = 30 \times 1852 \text{ m} = 55,560 \text{ m}$ Now, calculate $PRF_{max}$: $PRF_{max} = \frac{3 \times 10^8 \text{ m/s}}{2 \times 55,560 \text{ m}} = \frac{3 \times 10^8}{111,120} \approx 2699.8 \text{ Hz}$ This means the Pulse Repetition Frequency must be 2699.8 Hz or less to prevent echoes from targets at 30 NM (or further) from being mistakenly identified as coming from closer targets. 2699.8 Hz is approximately 2.7 kHz. Therefore, a PRF of "2.7 kHz or less" (Option B) is correct. * **Option A (0.27 kHz or less):** This PRF would allow for a much greater unambiguous range (300 NM), which is not necessary and would result in a lower data refresh rate. * **Option C (27 kHz or more):** A PRF of 27 kHz is too high. It would cause ambiguity for targets beyond approximately 3 NM, as the radar would transmit new pulses before echoes from targets at 30 NM could return. * **Option D (2.7 Hz or more):** 2.7 Hz is far too low for typical radar PRFs, yielding an extremely long unambiguous range and a very slow update rate.