Radar Maximum Unambiguous Range
Farthest range at which a pulse echo returns before the next pulse is sent; beyond it, targets appear at false (aliased) ranges.
Formula
Variables
Example
PRF 1000 Hz: R = 3×10⁸ ÷ (2×1000) = 150 km
How it works
A radar pulse has to travel out to a target and back again before the next pulse is transmitted, otherwise the receiver can confuse one echo with the next. The maximum unambiguous range is therefore set by the round-trip travel time allowed between pulses: if the pulse repetition frequency is higher, the time between pulses is shorter and the farthest unambiguous range decreases. The factor of 2 appears because the signal covers the distance twice, once on the way out and once on the return path.
When to use it
Use this formula when designing or checking a pulsed radar system to see the greatest distance that can be measured without range ambiguity. It is also useful when choosing pulse repetition frequency for air traffic radar, weather radar, or airborne surveillance systems.
Worked example, step by step
Given PRF = 2000 Hz Step 1: Write the formula: R_max = c / (2 × PRF) Step 2: Substitute the values: R_max = 3.0 × 10^8 / (2 × 2000) Step 3: Calculate the denominator: 2 × 2000 = 4000 Step 4: Divide: R_max = 3.0 × 10^8 / 4000 = 7.5 × 10^4 m Step 5: Convert to kilometres: 7.5 × 10^4 m = 75 km Final answer: R_max = 75 km
Common mistakes to avoid
- Forgetting the factor of 2 for the round-trip travel time
- Using the frequency of the radar carrier instead of the pulse repetition frequency
- Mixing up maximum unambiguous range with radar detection range or maximum instrumented range
Did You Know?
There is a fundamental trade-off: raising the PRF measures fast targets better but shrinks the unambiguous range — the “range–Doppler dilemma” of pulsed radar.
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