Editing Continuous-wave radar (section)

===Unmodulated continuous-wave===
[[File:Doppler effect diagrammatic.png|thumb|400px|Change of wavelength caused by motion of the source]]
This kind of radar can cost less than $10 (2021). Return frequencies are shifted away from the transmitted frequency based on the [[Doppler effect]] when objects are moving. There is no way to evaluate distance. This type of radar is typically used with competition sports, like golf, tennis, baseball, [[NASCAR]] racing, and some smart-home appliances including light-bulbs and motion sensors.

The Doppler frequency change depends on the [[speed of light]] in the air (''c’ ≈ c/1.0003''<!--Standard sea level conditions--> is slightly slower than in vacuum) and ''v'' the speed of the target:<ref>{{Cite book |last=Ditchburn |first= R. W. |title=Light |orig-year=1961 |year=1991 |publisher=Dover publications Inc. |pages=331–333 |isbn=0-486-66667-0}}</ref>

:<math>f_r = f_t \left( \frac{1+v/c'}{1-v/c'} \right)</math>

The Doppler frequency is thus:<ref>{{Cite book|author = James M. Ridenour  |title= Radar System Engineering|series=MIT Radiation Lab series |volume= 1 |year= 1947|page=629|author-link= James M. Ridenour}}</ref>

:<math>f_d = f_r-f_t = 2v \frac {f_t}{c'-v}</math>

Since the usual variation of targets' speed of a radar is much smaller than <math>c', (v \ll c')</math>, it is possible to simplify with <math>c'-v \approx  c' </math> :

:<math>f_d \approx 2v \frac {f_t}{c'} </math>

Continuous-wave radar without frequency modulation (FM) only detects moving targets, as stationary targets (along the [[line of sight (telecommunications)|line of sight]]) will not cause a Doppler shift. Reflected signals from stationary and slow-moving objects are masked by the transmit signal, which overwhelms reflections from slow-moving objects during normal operation.