Autonomous Sensing, 77 GHz Automotive FMCW Radar & Signal Processing
FMCW Radar Chirp Bandwidth, Beat Frequency & Range Formula
Calculate 77 GHz Frequency-Modulated Continuous-Wave (FMCW) Chirp Radar Range Resolution ΔR = c/(2*B), Chirp Slope S (MHz/µs), Target IF Beat Frequency f_b (MHz), and ADC-Limited Maximum Unaliased Detection Range (m).
See the core FMCW radar trade-off: wider chirp bandwidth sharpens ΔR while shrinking ADC R_max!
In 77–81 GHz automotive ADAS Frequency-Modulated Continuous-Wave (FMCW) radar, a synthesizer sweeps bandwidth B (GHz) over ramp duration T_c (µs) at chirp slope S = (B * 1000) / T_c (MHz/µs)! Mixing the reflected echo (delayed by τ = 2*R / c, where c = 300 m/µs = 3 × 10^8 m/s) with the local TX chirp produces a constant Intermediate-Frequency (IF) Beat Tone f_b (MHz) = S * (2 * R / 300)! Crucially, Two-Target Range Resolution ΔR = c / (2 * B) = 0.15 / B_GHz (m) depends ONLY on sweep bandwidth B, whereas for a fixed baseband ADC anti-aliased IF bandwidth f_IF_max (MHz), steepening S shrinks Maximum Unaliased Range R_max = (f_IF_max * 300) / (2 * S)!
Verify on a Highway Adaptive-Cruise Chirp—Sweep_Bandwidth_B = 1.50 GHz (B2 -> Range Resolution ΔR = 0.15 / 1.50 = 0.1000 m or 10.0 cm in E2), Chirp_Ramp_Time_Tc = 50.0 µs (B3 -> Chirp Slope S = 1,500 / 50 = 30.00 MHz/µs in E3), Lead_Vehicle_Range = 60.0 m (B4 -> IF Beat Frequency = 30 * (120 / 300) = 12.00 MHz in E4), and Max_IF_Filter_Cutoff = 15.0 MHz (B5): Maximum Unaliased Detection Range reaches (15 * 300) / (2 * 30) = 75.00 m (E5)!
| 77 GHz FMCW Chirp Metric (B = 1.5 GHz, T_c = 50 µs, R = 60 m, f_IF_max = 15 MHz) | Formula | Verified Output |
|---|---|---|
| Range Resolution ΔR (m) | 0.15 / Sweep_Bandwidth_GHz | 0.1000 m (0.0500 m @ 3.0 GHz) |
| Chirp Slope S (MHz/µs) | (Sweep_Bandwidth_GHz * 1000) / T_c_us | 30.00 MHz/µs (60.00 @ 3.0 GHz) |
| Target IF Beat Freq f_b (MHz) | Chirp_Slope_S * (2 * Range_m / 300) | 12.00 MHz |
| Max Unaliased Range R_max (m) | (Max_IF_MHz * 300) / (2 * Chirp_Slope_S) | 75.00 m (37.50 m @ 3.0 GHz) |
FMCW Radar ADC-Limited Maximum Range Formula
Validate Bandwidth_GHz in (0, 10], Ramp_Time_us > 0, Target_Range > 0, and Max_IF_MHz > 0!
=LET(bw_g, B2, tc_u, B3, rg_m, B4, fm_x, B5, IF(OR(bw_g <= 0, bw_g > 10, tc_u <= 0, rg_m <= 0, fm_x <= 0), "Invalid FMCW Chirp Input", LET(sl_p, (bw_g * 1000) / tc_u, ROUND((fm_x * 300) / (2 * sl_p), 2))))3.0 GHz Ultra-Fine Parking-Mode Chirp Check
Double Sweep_Bandwidth_B B2 from 1.50 GHz to 3.00 GHz at the same 50 µs ramp and 15 MHz IF ADC: Range Resolution E2 sharpens in half to 0.0500 m (5.0 cm curb resolution!), Slope E3 doubles to 60.00 MHz/µs, and Max Unaliased Range E5 trades off cleanly from 75.00 m to 37.50 m!
=IF(ISTEXT(E5), E5, ROUND(0.15 / B2, 4))Try the example
Use the original values or change them to test your understanding.