Avionics
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Radar Range Equation

Received echo power for a monostatic radar, combining transmit power, antenna gain, target size and range.

Formula

Pr=PtG2λ2σ(4π)3R4P_r = \dfrac{P_t G^2 \lambda^2 \sigma}{(4\pi)^3 R^4}

Variables

P_rReceived power
P_tTransmit power
GAntenna gain
λWavelength
σRadar cross-section
RRange

Example

Doubling range cuts received power by 2⁴ = 16× (−12 dB)

Did You Know?

The brutal R⁴ dependence means detecting a target at twice the range needs sixteen times the power — and is exactly why stealth aircraft chase tiny radar cross-sections instead.

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