Estimate the maximum detection distance of a monostatic radar using the full radar equation. Includes advanced considerations: pulse integration, noise figure, and atmospheric limitations.
The standard monostatic radar equation relates maximum detection range to system parameters. The basic version used in the calculator is:
Rmax = ⁴√ (Pt G² λ² σ) / ( (4π)³ Smin L )
Where:
Pt = transmit power (W), G = antenna gain (linear), λ = wavelength (m), σ = radar cross section (m²),
Smin = minimum detectable signal (W), L = system loss factor (≥1).
If np pulses are coherently integrated, the SNR improves by a factor np (coherent) or √np (non-coherent). Our calculator applies coherent integration (best case) by dividing Smin by np. Enter np in advanced settings.
Smin can be expressed as k T0 B Fn (SNR)min. Here we assume (SNR)min=1 and use the entered Smin directly. Adjusting Fn or B recalculates Smin if desired (see advanced panel).
| Parameter | Symbol | Typical Range | Impact on Range | How to Obtain |
|---|---|---|---|---|
| Transmit Power | Pt | W (automotive) … MW (surveillance) | R ∝ ⁴√Pt | Spec sheet or measurement |
| Antenna Gain | G | 10…50 dBi | R ∝ √G (since G² under fourth root → √G) | From dimensions: G ≈ 4πAe/λ² |
| Frequency / λ | f, λ | VHF (100 MHz) … W band (100 GHz) | R ∝ √λ (lower frequency gives longer range for fixed gain) | Design choice |
| RCS | σ | 0.001 m² (insect) … 1000 m² (ship) | R ∝ ⁴√σ | Estimated from target type or EM simulation |
| Min. Detectable Signal | Smin | 10⁻¹⁰ … 10⁻¹⁵ W | R ∝ 1/⁴√Smin | From receiver noise figure & bandwidth |
| System Loss | L | 1…10 | R ∝ 1/⁴√L | Budgeted from component datasheets |
The AN/FPS-117 is a L-band (1215-1400 MHz) air surveillance radar. Typical parameters: Pt = 2.5 kW (average), G = 28 dBi, σ = 1 m² (fighter), Smin ≈ 5×10⁻¹⁴ W, L = 3. Using the calculator, the theoretical range is ~220 km. In practice, with pulse integration (about 20 pulses) the range extends beyond 250 km, matching its advertised range of 200-250 nm (370-460 km) – note that our simple equation does not include integration gain, elevation coverage, or ducting, which increase effective range.
For very long ranges (above ~300 km), Earth's curvature and atmospheric refraction become dominant. The calculator will display a note when range exceeds 300 km.
| Band | Frequency | Typical Use | Pros/Cons |
|---|---|---|---|
| HF | 3-30 MHz | Over-the-horizon radar | Very long range, low resolution |
| VHF/UHF | 30-1000 MHz | Early warning, wind profilers | Good range, large antennas |
| L-band | 1-2 GHz | Air traffic control, long range | Good all-weather, moderate resolution |
| S-band | 2-4 GHz | Surveillance, weather | Balance of range & resolution |
| C-band | 4-8 GHz | Weather, medium range tracking | Higher resolution, more attenuation |
| X-band | 8-12 GHz | Fire control, marine radar | Good resolution, shorter range |
| Ku/K/Ka | 12-40 GHz | Automotive, satellite | Very high resolution, heavy attenuation |