Lesson 4 Flashcards

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1. Why do radars pulse instead of transmitting continuously?

A pulse marks a transmit time, so the echo's round-trip delay gives range directly: \(R = c\,\Delta t / 2\). Continuous-wave radars struggle to time-stamp echoes.

2. Define PW, PRI, PRF, and duty cycle.

PW: pulse on-time. PRI: time between pulse starts. PRF: \(1/\text{PRI}\), pulses per second. Duty cycle: \(\text{PW}/\text{PRI}\).

3. What sets range resolution?

Pulse width: \(\Delta R = c\,\text{PW}/2\). A 1 µs pulse gives 150 m; 0.1 µs gives 15 m. Shorter pulses resolve finer but carry less energy.

4. Write the unambiguous range.

\(R_u = c/(2\,\text{PRF})\). The echo must return before the next pulse goes out; low PRF gives long \(R_u\).

5. Write the unambiguous velocity.

\(v_u = \lambda\,\text{PRF}/4\). The pulse train samples Doppler at the PRF, so velocity is unambiguous only to \(\pm\text{PRF}/2\); high PRF gives large \(v_u\).

6. State the range–Doppler ambiguity invariant.

\(R_u \cdot v_u = c\lambda/8\) — independent of PRF. You trade range coverage for velocity coverage, but their product is fixed by wavelength.

7. At X-band, PRF = 1 kHz, what are \(R_u\) and \(v_u\)?

\(R_u = 150\) km, \(v_u = 7.5\) m/s. At 200 kHz they become 0.75 km and 1500 m/s — the same product.

8. What is range folding?

A target beyond \(R_u\) has its echo arrive after the next pulse, so it appears at \(R_\text{apparent} = R_\text{true} \bmod R_u\).

9. A B-21 at 200 km, PRF = 800 Hz — where does it appear?

\(R_u = 187.5\) km, so \(R_\text{apparent} = 200 - 187.5 = 12.5\) km. A large, exploitable error.

10. Contrast low-, medium-, and high-PRF regimes.

Low PRF: unambiguous range, ambiguous velocity. High PRF: unambiguous velocity and good clutter rejection, ambiguous range. Medium PRF: balanced but ambiguous in both, resolved by using multiple PRFs.

11. How do real radars beat the single-PRF tradeoff?

They transmit at multiple PRFs and resolve the ambiguities across them, recovering true range and velocity that no single PRF could give unambiguously.