A passive radar detector has a horn antenna that receives a...

A passive radar detector has a horn antenna that receives a range of frequencies that are around the known radar frequency. Unfortunately, this signal also contains far too many false signals (such as some burglar alarms, microwave radio links etc etc), and will be prone to many false alarms. To reduce these false alarms, the detector has its own oscillator inside, and it uses this internally generated signal as a reference to compare against the received signals. If it gets a match, then it will set the alarm off. The way that the police can detect these units is because the detector's oscillator actually radiates a weak signal itself. So the police can detect this by using a very sensitive receiver. The better made the detector (such as the Valentine) has an extremely well made aluminium case that is sealed against leakage.
Radar jammers are actually transmitters that broadcast a radar signal that is stronger than the reflected signal from your car. Since the speed guns use the Doppler shift method to measure your speed, if you broadcast the right frequency, at a strong enough level, back to the gun, it will display the speed you "selected" That is, you can dial up whatever speed you want the speed gun to display.