FMCW Radar
A frequency-modulated continuous-wave radar measures range from the beat frequency between the transmitted chirp and its echo, and velocity from the phase change across a frame of chirps. This tool gives the range resolution set by the sweep bandwidth, the chirp slope and beat frequency for a target, and the maximum unambiguous velocity and velocity resolution set by the chirp timing — the core numbers for automotive and short-range radar.
Equations & Parameters ▸
\(S=\dfrac{B}{T_{chirp}} \qquad \Delta R=\dfrac{c}{2B} \qquad f_{beat}=\dfrac{2R\,S}{c}\)
\(v_{max}=\dfrac{\lambda}{4\,T_{chirp}} \qquad \Delta v=\dfrac{\lambda}{2\,N\,T_{chirp}} \qquad \lambda=\dfrac{c}{f_0}\)
\(v_{max}=\dfrac{\lambda}{4\,T_{chirp}} \qquad \Delta v=\dfrac{\lambda}{2\,N\,T_{chirp}} \qquad \lambda=\dfrac{c}{f_0}\)
| B | Chirp sweep bandwidth (GHz). Sets the range resolution. |
| Tchirp | Single-chirp duration (µs). |
| f0 | Carrier frequency (GHz), for the wavelength. |
| N | Number of chirps per frame. More chirps → finer velocity resolution. |
| R | Target range (m), optional — gives the beat frequency. |
Reference: M. A. Richards, Fundamentals of Radar Signal Processing, 2nd ed., 2014; Texas Instruments, "The fundamentals of millimetre-wave radar sensors," 2020.
Inputs
GHz
Range resolutionµs
Per chirpGHz
For λ & velocityVelocity resolution
m
For beat freqResults
Range
Range resolution ΔR—
Chirp slope S—
Beat frequency—
Velocity
Wavelength λ—
Max unambiguous v—
Velocity resolution Δv—
Diagram