How does the radar equation work?

From RF Design Wiki · By the RF Design Wiki editorial team · Published October 21, 2026 · Last reviewed October 21, 2026 · How we research

Radar detects targets by transmitting and receiving reflected signals. The monostatic radar range equation gives received power P_r = P_tG²λ²σ/((4π)³R⁴), where σ is the radar cross section; received power falls with the fourth power of range. Range resolution is ΔR = c/(2B) for signal bandwidth B.^[1]

How does FMCW radar work?

Frequency-modulated continuous-wave radar transmits a linear chirp of bandwidth B over time T. Mixing the echo with the transmitted chirp produces a beat frequency f_b = 2RB/(cT) proportional to range; Doppler appears across successive chirps. 4 GHz of chirp bandwidth gives 3.75 cm range resolution, which is why automotive radar uses the wide 76–81 GHz band.^[1]

What determines velocity resolution?

Doppler shift is f_D = 2v/λ. Velocity resolution is set by observation time: Δv = λ/(2T_obs).^[1]

What RF challenges are specific to radar?

Transmit-to-receive leakage in FMCW (phase noise of the leakage sets the near-range noise floor).
High peak power and duplexing (circulators, T/R switches) in pulsed radar.
Linearity of chirps and phase noise for range accuracy.
Antenna arrays for angle resolution (MIMO virtual arrays).

What letter bands do radars use?

IEEE Std 521 designations: L (1–2 GHz), S (2–4), C (4–8), X (8–12), Ku (12–18), K (18–27), Ka (27–40), V (40–75), W (75–110) GHz. See radar band letters.^[2]

Frequently asked questions

Why R⁴?

Spreading loss applies on both the outbound and return paths.

What is radar cross section?

The equivalent area intercepting and isotropically reradiating power, in m² or dBsm.

Why 77 GHz for cars?

Wide available bandwidth for resolution and small antennas.

References

Online sources accessed October 21, 2026; printed works cited by edition. See all sources.

“Introduction to Radar Systems, 3rd ed.”. M. I. Skolnik, McGraw-Hill. 2001.
“IEEE Standard Letter Designations for Radar-Frequency Bands (IEEE Std 521)”. IEEE. 2019 revision.

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