To produce unambiguous range information the radar system must remain silent between pulses for sufficient time for the pulse to travel out to the furthest target and return to the antenna.
The distance traveled by the signal = c x travel time
The travel time = the time between the transmission of successive pulses, which is equal to 1/PRF.
So distance traveled by the signal = c x 1/PRF which = c / PRF
But the signal must travel out to the furthest target and back to the antenna, so maximum range to the furthest target is half of the distance that the signal travels.
So maximum range = c / ( 2 x PRF)
Rearranging this equation gives
PRF = c / ( 2 x max range)
C is the speed of light, which is approximately 300 000 KM/sec or 162 000 NM / second.
For a range of 30 Nm the above equation gives
PRF = 162 000 NM/sec / ( 2 x 30 NM) = 2700 pulses per second
So your initial calculation was correct, but 2700 pps is not an option in this question.
BUT EASA CQB 15 does contain the following similar question.
The maximum pulse repetition frequency (PRF) that can be used by a primary radar facility in order to detect targets unambiguously at a range of 50 NM is?
A 713 pps
B 610 pps
C 1620 pps
D 3240 pps
The correct answer to this question is option C 1620 pps
This can be calculated at follows
PRF = 162 000 NM/sec / ( 2 x 50 NM) = 1620 pulses per second
The 50 micro second pulse width quoted in your question does not affect the maximum range, but will determine the minimum range.
Last edited by keith williams; 26th Jan 2013 at 13:52.