In fmcw radar rather than sending a signal at constant freq. we are sending a chirp which goes e.g. from 6-GHz to 6.1-GHz in 5ms.
What i cannot fit in my mind is this:(Nmbers are just for example)
The rf signal is moving at speed of light so while we are changing the chrip freq. linearly e.g. we start from 6Ghz and waited like 500us then increased it to 6.01 (this goes up to 6.1 ghz with sometime between each freq. change) and we already received the 6ghz signal from receiver without completing 5ms chirp period. So up to this point we have nothing to do with other frequencies of chirp (6.02,6.03...6.1). How is this generating IF like 5-10kHz based on distance. If so then by applying the formula in the picture we can find the distance, why we are changing the tarnsmitted signals' frequency since we already had a IF for a constant 6ghz part of signal chirp signal.
Shortly should i just simultaneously change chirp from 6to 6.1 and 6.1 to 6.0 back and forth and at the same time a/d convert the upcoming signal and save it somewhere until it makes 5ms then plot the fft of the whole 5ms block.
I hope i am clear. Please show me what i am missing here:)
LATER UPDATE: Everyone was trying make me understand the theoretical background where i already know but thank you guys for your time.I had a moment of enlightment and now i understand :)
I am teling this with examples so people who have same problem in future can understand. While sending a chirp we start sending with a fix freq. as a start point like 6ghz. While it is traveling to the target and coming back a little bit of time passed and during this time our TX chirp signals freq. changed a little bit linearly like 6+X GHz so multiplexer difference is X Hz. Therefore this change depend on the distance of the target since let say target is so far far away we will maybe receive the first signal which was at 6GHz while our chirp is at its halfway of 6 to 6.1 GHz cycle. So the difference will be like 6.05-6=0.5GHz.
Another way of saying, for stationary object nothing happening on the transmitted signal(doppler effect says reflected data is radited with same structure if object is stationary) but until the transmitted signal come we changed the transmitted signal so the upcoming signal will be multiplexed with different freq. signal and based on this change we are telling this is object at this much distance. Thank you