Demo — Pulse Timeline

Demo — Pulse Timeline#

The PRF Explorer gives you the numbers the tradeoff produces. This one shows you where those numbers come from. A radar has exactly one pulse train, and every limit in this lesson falls out of it: how long each pulse is sets \(\Delta R\), how long the radar waits between pulses sets \(R_u\), and how fast it revisits a target sets \(v_u\). Watch the pulses physically travel out, bounce, and come back — and watch the A-scope underneath report what the radar believes it saw.

Interactive demo#

Open in full screen

Walkthrough#

  1. Drag B toward A until the echoes merge. Each returning echo is a band of length \(c\tau\); two of them stay separable only while the targets are more than \(\Delta R = c\tau/2\) apart. At the default \(\tau = 10\) µs, \(\Delta R = 1.5\) km — so A at 12.0 km and B at 12.9 km already arrive as one lump, on the wire and on the A-scope. Drag B past 13.5 km and the lump splits in two. That threshold is range resolution: closer than \(\Delta R\), the radar reports one target where there are two.

  2. On the Medium preset, follow C’s drop-line. C sits at 18 km, past \(R_u = 15\) km, so its echo arrives after the next pulse has already left — the radar times it from the wrong launch and reports it at 3.0 km. The dashed drop-line elbows left by exactly \(R_u\) to show where the truth lands. The blip itself is indistinguishable from a real 3 km target. Switch to Low 1 kHz and the fold disappears: \(R_u\) jumps to 150 km, off the end of the wire, and every target drops straight down.

  3. Sweep target A’s speed. The dial steps once per echo, by \(\Delta\phi = 4\pi v T/\lambda\). At 50 m/s the step is 120° and the radar reads the speed true. At 100 m/s the step is 240°, which is indistinguishable from −120°, so the radar reports −50 m/s — an inbound fighter read as outbound. At 150 m/s the step is a full 360°: the needle freezes, the target looks stationary, and MTI throws it away with the clutter. That is the first blind speed, and it is L5’s opening move.

Key observations#

  • All three limits are one pulse train. \(\Delta R\) is the pulse’s length, \(R_u\) is the wait between pulses, \(v_u\) is the revisit rate. There is nothing else in the picture.

  • The radar cannot tell a fold from the truth. Only the drop-lines — which the radar does not have — reveal which blip is lying.

  • Velocity ambiguity is aliasing, literally. The dial is a wagon wheel filmed at the PRF: past \(v_u\) it turns backward, and at one full turn per pulse it stands still.

Contents