Radar Equation
Understanding the Radar Equation
The radar equation is to radar what the Friis equation is to communications. It calculates the signal power returned from a target and determines whether the radar can detect the target at a given range.
Radar Equation Forms
Pr = (Pt G^2 lambda^2 sigma) / ((4pi)^3 R^4)
In dB:
Pr = Pt + 2G + 20log(lambda) + 10log(sigma)
- 30log(4pi) - 40log(R)
Detection range (solving for R):
R = [Pt G^2 lambda^2 sigma / ((4pi)^3 Smin)]^(1/4)
Key insight: Range goes as the 4th root of power.
Doubling range requires 16x power increase!
Improving Radar Range
- Increase power: 16x power = 2x range.
- Increase antenna gain: 4x gain (each way) = 2x range. (G appears squared.)
- Longer wavelength: Lower frequency = larger antenna for same gain.
- Longer integration: Coherent integration of N pulses = sqrt(N) range improvement.
Frequently Asked Questions
What is the radar equation?
The radar equation calculates received power from a target: Pr = Pt G^2 lambda^2 sigma / (4pi)^3 R^4. It determines the maximum detection range based on transmitter power, antenna gain, wavelength, target RCS, and receiver sensitivity.
Why does radar power vary as R^4?
Signal travels to the target (R^2 spreading loss), reflects from the target (RCS determines how much), and returns to the radar (R^2 spreading loss again). Total: R^2 x R^2 = R^4. This is why radar requires much more power than communication at the same range.
How do you double radar range?
Doubling range requires 16x power (R^4 law). Alternatively: 4x antenna gain (G appears squared), 4x integration time, or a target with 16x larger RCS. Radar range improvement is very expensive in power and antenna size.