21.2 Range, Pulse Width & PRF

21.2 Range, Pulse Width & PRF

Quick Answer: Range from time: R = c t / 2 (≈ 12.346 µs/NM). Short pulse → better range resolution and minimum range; long pulse → more energy for distant targets. Low PRF → greater maximum unambiguous range; high PRF → more pulses per scan on short scales. Long range = wide PW + slow PRF; short range = narrow PW + fast PRF. Duty cycle = PW × PRF.

Key topic 092 is almost pure trade-off reasoning. If you only memorize one sentence for radar timing, make it: long range wants energy and waiting time; short range wants precision and rapid updates.

Range from round-trip time

Electromagnetic energy travels at c ≈ 3 × 10⁸ m/s. For a target at one-way distance R, the pulse travels 2R, so:

[ R = \frac{c , t}{2} ]

In nautical-mile units used on marine displays:

[ R_{\mathrm{NM}} \approx \frac{t_{\mu\mathrm{s}}}{12.346} ]

The same physics underlies aircraft DME slant-range timing (Topic 3-K)—radar simply uses a passive echo instead of a ground transponder reply.

Pulse width — minimum range and range resolution

Minimum range

While the transmitter is on, the receiver is effectively deaf (duplexer isolation, TR firing, recovery time). If a target’s echo returns before the pulse ends and the receiver recovers, that echo is lost or corrupted. Therefore minimum detectable range grows with pulse width (plus recovery). Short-range harbor work demands narrow pulses.

Range resolution

Range resolution is the minimum range separation at which two targets on the same bearing still paint as two echoes:

[ \Delta R = \frac{c , \tau}{2} ]

Two ships 20 m apart in range look like one blob if τ is 0.25 µs, but may split cleanly with a 0.05–0.1 µs pulse. That is why short-range scales auto-select narrow PW.

Energy vs resolution trade-off

Longer pulses deliver more energy (Pt × τ) to the target, improving detection of weak or distant echoes, rain-filled paths, or small RCS objects—at the cost of resolution and minimum range. Shorter pulses do the opposite.

PRF / PRR — maximum unambiguous range

PRF (pulse repetition frequency) or PRR (pulse repetition rate) is the number of pulses transmitted per second. PRI = 1 / PRF is the listening window after each pulse.

Unambiguous range

The radar must receive an echo from a target before it transmits the next pulse—or it cannot tell whether a late return belongs to the latest pulse or an earlier one (second-time-around / range ambiguity).

[ R_{\mathrm{unamb}} = \frac{c}{2 , \mathrm{PRF}} = \frac{c , \mathrm{PRI}}{2} ]

Lower PRF → greater maximum unambiguous range. That is the pool relationship in one line. Higher PRF is fine on short scales where all real targets return quickly and you want more hits per antenna scan (smoother paint, better detection probability).

Hits per scan (qualitative)

As the antenna beam sweeps past a target, the number of pulses that “illuminate” it is roughly beamwidth / 360° × PRF / RPM. Higher PRF or slower rotation increases hits per scan—another reason short-range modes run faster PRFs.

Duty cycle and average power

Duty cycle is the fraction of time the transmitter is actually emitting RF:

[ D = \tau \times \mathrm{PRF} = \frac{\tau}{\mathrm{PRI}} ]

Average power:

[ P_{\mathrm{avg}} = P_{\mathrm{peak}} \times D = P_{\mathrm{peak}} \times \tau \times \mathrm{PRF} ]

Worked example (classic numbers): peak power 25 kW, τ = 0.5 µs, PRF = 1,000 Hz:

[ D = 0.5 \times 10^{-6} \times 1000 = 5 \times 10^{-4} = 0.05% ] [ P_{\mathrm{avg}} = 25{,}000 \times 5 \times 10^{-4} = \mathbf{12.5\ W} ]

Marine radars are peak-hungry but average-power modest—important for power-supply sizing and for understanding why a “25 kW radar” does not draw 25 kW continuously from the ship’s bus.

Range-scale pairing table (memorize for 092)

Element 3 asks which pulse width and pulse repetition rate pair with common range scales. Pattern: far = wide + slow; near = narrow + fast.

Verbal rules (exact pool wording)

• Long ranges: use a wide pulse width and slow repetition rate.
• Short ranges: use a narrow pulse width and fast repetition rates.

Wrong combinations to reject on sight:

• Wide pulse + fast PRF on long range (wastes unambiguous margin, smears close targets if used short).
• Narrow pulse + slow PRF on short range (poor update/hits, not the pool’s “most appropriate”).
• Extremely long pulses (e.g., 2.5 µs) paired with high PRF—usually distractors.

Putting the three knobs together

When the operator (or automatic range logic) changes the range scale, the radar typically changes PW and PRF together:

1. Zoom in (harbor): narrow τ for resolution/min range; high PRF for dense paint; unambiguous range still covers the short scale.
2. Zoom out (open sea): wide τ for echo energy; low PRF so 48 NM targets return before the next pulse.
3. Duty cycle may stay in a similar order of magnitude even as τ and PRF move in opposite directions—designers balance average power and magnetron stress.

Qualitative radar equation reminder

Even with perfect PW/PRF choice, detection still needs enough Pr. Peak power, antenna gain, target RCS, and R⁴ loss dominate. A technician chasing “no long-range targets” checks magnetron power, waveguide SWR, antenna height/obstructions, and tune—not only the PRF number on the menu.

Exam-day checklist (3-O 092 + 090 timing)

1. R = c t / 2; NM ≈ t_µs / 12.346.
2. PW controls min range and range resolution (ΔR = cτ/2).
3. PRF controls max unambiguous range (lower PRF → farther unambiguous).
4. Long range: wide PW + slow PRF; short range: narrow PW + fast PRF.
5. Memorize table anchors: 1.5 mi → 0.05 µs / 2000 pps; 6 mi → 0.25 µs / 1000; 25–48 mi → 1.0 µs / 500.
6. Duty cycle = PW × PRF; Pavg = Ppeak × D.

Next section moves the pulse from the modulator to space: slotted arrays, waveguides, beamwidth, and SART painting on the PPI.