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UWB Impulse Radar Range Calculator & Formula

By RF Wireless Expert Team

To calculate maximum operating range (Rmax) of an Ultra-Wideband (UWB) Impulse Radar system, we can use radar range equation. Unlike communication links, radar signals must travel to the target and back, effectively doubling the distance the signal must cover. The received power decreases with the fourth power of the distance (R^4) due to this round trip.

Inputs

Outputs

Example Calculation Values

Scenario Example: We will calculate the range for the Novelda x4 module to detect a sitting person with following parameters:

INPUTs:

  • Center Frequency (f) = 8.748 GHz
  • Allowable Path Loss (Lradar) = 76.8 dB
  • Target Radar Cross Section (σ) = 0.5 m²

OUTPUTs:

  • Wavelength (λ) = 0.0343 meters
  • R = Maximum Operating Range = 1.94 meters

Constants:

  • Speed of Light (c): Approximately 299,792,458 meters per second (m/s), Approximately equals 3 x 10^8 m/s.

UWB Radar Range Formula

Lradar (dB) = 10*log10(( (4 * π)^3 _ R^4 ) / ( λ^2 * σ ))

Where:

  • R = Maximum Operating Range (meters)
  • λ = Wavelength (meters) = c / f, where c is the speed of light (approximately 3 x 10^8 m/s)
  • σ = Radar Cross Section (square meters)
  • Lradar = Allowable Path Loss (dB)

Rearranging the formula to solve for R: R = 10^((Lradar - 10*log10((4 * π)^3) + 20*log10(λ) + 10*log10(σ)) / 40)

Conclusion

The calculation confirms that the high path loss inherent in radar systems (1/R^4 law) significantly limits the maximum operating range compared to typical UWB communication (1/R^2 ) , which can reach about 10-30 meters. This is crucial for applications like presence detection, where short range accuracy is more important than long distance communication.

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