James Yates

Radar Tool

PRF & ambiguity explorer

Calculate unambiguous range, blind speeds, minimum range, range resolution and duty cycle from pulse repetition frequency and pulse width.

Pulse timing and ambiguity

After each pulse, the radar listens. It must assume any echo it hears belongs to the most recent pulse. So if an echo from a very distant target arrives after the next pulse has already gone out, the radar mistakes it for a close echo of the new pulse — a range ambiguity, or "second-time-around" echo. The listening time between pulses sets a ceiling:

Runamb  =  c2 · PRF

Pulse repetition also creates blind speeds. The radar measures target motion by comparing the echo's phase from pulse to pulse. If a target moves exactly half a wavelength (or any whole multiple of it) between pulses, its echo phase looks identical each time — to the radar, it appears stationary and gets filtered out along with the ground clutter:

vblind  =  n · λ · PRF2n = 1, 2, 3…

In this uncompressed-pulse model, the receiver is blanked during transmission. Pulse width τ sets the minimum range Rmin = c·τ/2 and the nominal range resolution.

High PRF supports a wider unambiguous Doppler interval but reduces unambiguous range. Low PRF increases unambiguous range. Multiple PRFs can be used to resolve ambiguities.

Inputs

Surveillance radars: hundreds of Hz. Airborne pulse-Doppler: up to hundreds of kHz.
Needed for blind speeds (sets the wavelength).
Max unambiguous range
Pulse repetition interval
Minimum range
Range resolution
Duty cycle
First blind speed

Two transmit pulses (cyan) with the listening window between them. Drag the slider to move a target: its echo (amber) slides through the window. Push it beyond the unambiguous range and the echo lands after the second pulse — the radar would wrongly read it as a short-range echo.

Blind speeds at this PRF and frequency

nm/skm/hknots

Real systems complicate this picture with pulse compression (long coded pulses that behave like short ones), staggered PRFs and multiple PRF sets — but they all start from the timing shown above.