Police microwave radars all use the Doppler Principle to measure speed. The radar transmits a continuous microwave signal and simultaneously measures the echo that is frequency shifted proportional to speed, the Doppler Shift. The frequency shift is measured in cycles per second and has unit dimensions of Hertz (Hz).
The horn from a moving train is a good example of the Doppler effect. As the train approaches a stationary listener the frequency pitch of the whistle sounds higher than when the train is even with the listener. As the train recedes from the listener the pitch decreases. Car horns exhibit the same phenomenon, as does all sound.
In the above example if a car horn is stationary and a listener is on the train the Doppler principle still applies. As the listener on the train approaches the stationary horn the pitch of the horn sounds higher, as the train recedes from the stationary horn the pitch sounds lower to anyone on the train.
Stationary Radar
Microwave signals travel at the speed of light but still obey the Doppler Principle. Microwave radars receive a Doppler frequency shifted reflection from a moving object. Frequency is shifted higher for approaching objects, and lower for receding objects. The frequency shift is proportional to speed.
| Echo Frequency Shift | ||
|---|---|---|
| Approaching Traffic | Receding Traffic | |
| ft = fo + fd | ft = fo - fd | |
ft = Traffic Echo (return) Frequency
fo = Transmit Frequency
fd = Radar Doppler Shift
Radar Doppler shift (fd) is a function of transmit frequency (fo), speed of wave (c = speed of light), and target vehicle speed (v). Speed is positive (+v) for approaching traffic and negative (-v) for receding traffic.
|
fd = Radar Doppler Shift fo = Transmit Frequency |
v = vehicle speed c = Speed of Light |
| |||||||||
A moving vehicle with a radar detector will receive a radar signal Doppler shifted proportional to speed. The radar will receive a reflection shifted again, proportional to speed. The echo the radar receives has twice the Doppler shift the target vehicle radar detector receives.
|
v = Traffic Speed (-v for receding traffic) fd = Radar Doppler Shift (-fd for receding traffic) fo = Transmit Frequency c = Speed of Light |
Radar Doppler Shift at Police Frequencies
The table below shows radar Doppler shift per speed unit (1 unit) for common police radar frequencies. Radar Doppler shift is unit shift multiplied by speed. For example an X band radar Doppler shift for a 100 mph vehicle is 31.39 Hz/mph multiplied by 100 mph and equals 3,139 Hertz.
| Radar Transmit Frequency |
Radar Doppler Shift |
|||
| Band | GHz | Hz/kph | Hz/mph | Hz/knot |
| S | 2.455 | 4.53 | 7.29 | 8.39 |
| X | 9.410 | 17.44 | 28.06 | 32.30 |
| X | 9.900 | 18.34 | 29.53 | 33.98 |
| X | 10.525 | 19.50 | 31.39 | 36.12 |
| Ku | 13.450 | 24.92 | 40.11 | 46.16 |
| K | 24.125 | 44.71 | 71.95 | 82.80 |
| K | 24.150 | 44.75 | 72.02 | 82.88 |
| Ka | 33.4 - 36.0 |
61.89 - 66.71 |
99.61 - 107.36 |
114.63 - 123.55 |
Frequency Spectrum
The transmit signal has some noise skirts that interfere with echoes from slow moving objects. Most radars have a minimum speed specification, typically 10 - 15 mph minimum target speed. A few radars have a 1 - 3 mph minimum speed.
Ground echo clutter is usually the strongest signal reflection, but because the ground is not moving it is does not have a Doppler shift. With moving-mode radar the ground echo is frequency shifted by the speed of the patrol vehicle, and so are all other reflections except those at the same speed as the radar.
kTBF is the average receiver noise level and is a function of temperature (T), radar receiver noise bandwidth (B), receiver noise factor (F), and Boltzmann's constant (k).