Library / Sensors & detection / SEN-04
Sensors & detection
Radar range resolution
Smallest separation at which two targets are seen as two.
- Ref
- SEN-04
- Rev
- v1
- Field
- Sensors & detection
- Result
- ΔR [m]
B is the bandwidth of the transmitted signal in MHz. Two targets closer than ΔR merge into one echo, because the signal cannot tell them apart in time. The bandwidth is roughly the reciprocal of the effective pulse width after compression, 1/B, so ΔR = c(1/B)/2.
Smallest separation at which two targets are seen as two. A wider signal bandwidth gives finer resolution.
Calculator
- Effective pulse width after compression, 1/B0.1 µs
- Bandwidth needed for 1 m resolution149.9 MHz
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A 10 MHz signal separates targets 15 m apart; to resolve targets 1 m apart a radar needs 150 MHz.
- Resolution depends on bandwidth, not on peak power or on how long the pulse is, which is why long coded (chirp) pulses with wide bandwidth give both range and energy.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| B Signal bandwidth | 0.1 to 5,000 MHz | 0.02998 | 1,499 | 1,499 | +10% | −9.09 % |
Sweep of Signal bandwidth
| Signal bandwidth (MHz) | Range resolution (m) |
|---|---|
| 0.1 | 1,499 |
| 0.3867 | 387.6 |
| 1.495 | 100.2 |
| 5.782 | 25.92 |
| 22.36 | 6.704 |
| 86.47 | 1.734 |
| 334.4 | 0.4483 |
| 1,293 | 0.1159 |
| 5,000 | 0.02998 |
Sweep one variable
Variables and how each one contributes
Range resolution
What the equation gives you. Everything else feeds it.
Signal bandwidth
The bandwidth of the transmitted signal, in MHz. Inverse: doubling the bandwidth halves ΔR, giving twice the resolution. A 10 % rise in B improves ΔR by about 9 %.
Worked example with the values above
- Convert bandwidth: B = 10 MHz = 1×107 Hz.
- Denominator: 2B = 2×107 Hz.
- ΔR = 2.998×108 / 2×107 = 14.99 m.
Assumptions and limits
- The signal occupies its full bandwidth with uniform weighting and the receiver is matched.
- Resolution is taken as the separation at which the main lobes just merge.
Common mistakes
- Confusing range resolution with range accuracy, which can be much better than ΔR for strong echoes.
- Confusing it with angular resolution, which depends on the antenna size.
Statistics and uncertainty
ΔR ∝ 1/B, so a 5 % error in the stated bandwidth gives a 5 % error in the resolution. The practical resolution is also widened by the weighting applied to suppress sidelobes, by about 20 to 40 %, so quoting c/2B alone is the best case.
Where it is used
- Choosing pulse bandwidth to separate closely spaced targets.
- Checking whether a radar can resolve two aircraft in formation.
Maths you need
- Speed of light: c = 3 × 10⁸ m/s
- Bandwidth: width of the frequency range