Radar Range Equation

The Radar Range Equation relates the maximum detection range of a radar system to the characteristics of the transmitter, receiver, antenna, target, and the environment. The standard form for a monostatic radar (same antenna for transmit and receive) is:

R_max = [ (P_t * G² * λ² * σ) / ( (4π)³ * S_min ) ] ^ (1/4)

Where:

• R_max: Maximum Radar Range (meters)
• P_t: Transmitter Power (Watts)
• G: Antenna Gain (linear scale, dimensionless) - Assumed identical for transmit and receive.
• λ: Wavelength of the radar signal (meters)
• σ: Target Radar Cross Section (RCS) (square meters, m²) - Effective scattering area of the target.
• S_min: Minimum Detectable Signal Power (Watts) - Smallest signal power the receiver can reliably detect above noise.

The wavelength (λ) is related to the frequency (f) by:

λ = c / f

Where c is the speed of light (approximately 2.998 × 10⁸ m/s).

Key Assumptions and Notes:

• Assumes free space propagation (no atmospheric absorption, refraction, or multipath effects).
• Assumes the target is in the main beam of the antenna.
• Does not account for system losses (e.g., transmission line loss, processing loss).
• Represents the theoretical maximum range based purely on power budget; practical range can be limited by other factors (e.g., clutter, jamming, resolution).
• Antenna gain (G) is squared because the same antenna is used for transmitting and receiving, applying the gain twice (once for the outgoing wave, once for the incoming echo).
• The (4π)³ term arises from the spherical spreading of the wave (twice, for transmit and receive) and the antenna aperture formula.