Radar Detectors are easily defeatable with the radar units made in the last 10 years. Almost all of them have a Stand By mode (Instant On) ans it's merely just a couple fo seconds for it to aquire the object being tracked.
For a doppler radar, it's really pretty simple. You're better off trying to questions the Officer's Operational training in radar rather than trying to beat the radar itself. I know that when I was running traffic, I would visually aquire my target, turn on the radar, distinguish (by sound) that it was being properly tracked, then track for 5 seconds before locking in the speed. All of this usually took about 7 seconds.
Other things to watch for, are large vehicles traveling in the same direction or directly away from you. The angle in which the Officer is pointing when he has the radar on your vehicle. Any bridges or large signs around?
When I was really bored (usually about 2 or 3 a.m.) I would sit over I-35 and turn the radar on, just for grins and giggles when a gaggle of fast moving cars came along. It was always interesting to see who had detectors and who didn't. Those that did would almost stand their car on it's nose trying to slow down, while those that didn't, would take a few seconds longer to figure out what was going on. I've locked in vehicles traveling at 105 mph on I-35 that early in the morning! Takes them a little longer to slow down.
Of course this doesn't take into account Laser systems. They are more precise, but I don't know of any yet that work in motion. The Officer has to literally pick his target before getting any kind of return. Some of the early Laser Units, the effective cone was about 6 to 10 feet at one mile. That's also why you see a lot of them have a rifle scope on them. Alsthough, I don't think they are used much over .25 mile anyway. Anything much further than that, it gets hard to judge the speed anyway.
If you do get hit with a ticket, take a look at a few things. Road conditions for one. Wet roads will reflect radar differently than dry roads. High Temps and the Mirage effect can also play a factor. Usually this will return a bogus reading to the radar and the tone will warble enough that the officer (if properly trained) won't be able to use it. Find out what the volume setting is on the unit itself. What was the traffic like at the time. If you were in a gaggle of other vehicles, how did the officer single you out. Is there something nearby that could reflect the radar energy back and create a bogus reading? Cosign Angle Error used to be a defense, though most often that error usually went in the Ticketee's defense. One of the things I had to what for was the dash heater fan. Part of the radar energy would get reflected down into the windshield vents and if the fan was going, I could easily pick out a car going a contsant 80 mph! That's why you had to listen to the tone. That would tell you more than anything else. Find out the last time the unit was actually calibrated, then compare that with the manufacturer's recommendations. Find out if the officer did an operation check of the unit with tuning forks or whatever method is normally used.
And finally... Don't waste your time on a radar detector. On extremely long distances, it may give you an edge, but in the shorter range, the officer already has you.