In the basic radar range equation, how does increasing target range affect the received power?

• A. It has no effect.
• B. It increases the received power.
• C. It reduces received power proportional to the fourth power of range (R^4).
• D. It doubles the received power.

Answer: (C)

Two-way path loss is the key idea. The transmitted power spreads out as it travels to the target, so the power density at the target falls off like 1/R^2. The target then reflects energy back toward the radar, and this backscattered energy also spreads out as it travels the distance R back, adding another 1/R^2 factor. Multiply those effects and you get a received power that scales as 1/R^4. In the basic radar range equation, Pr is proportional to 1/R^4 (assuming fixed transmitted power, antenna gains, wavelength, and target radar cross-section). So increasing range dramatically reduces received power; for example, doubling the range reduces Pr by a factor of 16.