# Lesson 4 Flashcards

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<summary><strong>1. Why do radars pulse instead of transmitting continuously?</strong></summary>
<div class="card-answer"><p>A pulse marks a transmit time, so the echo's round-trip delay gives range directly: <span class="math notranslate nohighlight">\(R = c\,\Delta t / 2\)</span>. Continuous-wave radars struggle to time-stamp echoes.</p></div>
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<summary><strong>2. Define PW, PRI, PRF, and duty cycle.</strong></summary>
<div class="card-answer"><p>PW: pulse on-time. PRI: time between pulse starts. PRF: <span class="math notranslate nohighlight">\(1/\text{PRI}\)</span>, pulses per second. Duty cycle: <span class="math notranslate nohighlight">\(\text{PW}/\text{PRI}\)</span>.</p></div>
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<summary><strong>3. What sets range resolution?</strong></summary>
<div class="card-answer"><p>Pulse width: <span class="math notranslate nohighlight">\(\Delta R = c\,\text{PW}/2\)</span>. A 1 µs pulse gives 150 m; 0.1 µs gives 15 m. Shorter pulses resolve finer but carry less energy.</p></div>
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<summary><strong>4. Write the unambiguous range.</strong></summary>
<div class="card-answer"><p><span class="math notranslate nohighlight">\(R_u = c/(2\,\text{PRF})\)</span>. The echo must return before the next pulse goes out; low PRF gives long <span class="math notranslate nohighlight">\(R_u\)</span>.</p></div>
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<summary><strong>5. Write the unambiguous velocity.</strong></summary>
<div class="card-answer"><p><span class="math notranslate nohighlight">\(v_u = \lambda\,\text{PRF}/4\)</span>. The pulse train samples Doppler at the PRF, so velocity is unambiguous only to <span class="math notranslate nohighlight">\(\pm\text{PRF}/2\)</span>; high PRF gives large <span class="math notranslate nohighlight">\(v_u\)</span>.</p></div>
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<summary><strong>6. State the range–Doppler ambiguity invariant.</strong></summary>
<div class="card-answer"><p><span class="math notranslate nohighlight">\(R_u \cdot v_u = c\lambda/8\)</span> — independent of PRF. You trade range coverage for velocity coverage, but their product is fixed by wavelength.</p></div>
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<summary><strong>7. At X-band, PRF = 1 kHz, what are <span class="math notranslate nohighlight">\(R_u\)</span> and <span class="math notranslate nohighlight">\(v_u\)</span>?</strong></summary>
<div class="card-answer"><p><span class="math notranslate nohighlight">\(R_u = 150\)</span> km, <span class="math notranslate nohighlight">\(v_u = 7.5\)</span> m/s. At 200 kHz they become 0.75 km and 1500 m/s — the same product.</p></div>
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<summary><strong>8. What is range folding?</strong></summary>
<div class="card-answer"><p>A target beyond <span class="math notranslate nohighlight">\(R_u\)</span> has its echo arrive after the next pulse, so it appears at <span class="math notranslate nohighlight">\(R_\text{apparent} = R_\text{true} \bmod R_u\)</span>.</p></div>
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<summary><strong>9. A B-21 at 200 km, PRF = 800 Hz — where does it appear?</strong></summary>
<div class="card-answer"><p><span class="math notranslate nohighlight">\(R_u = 187.5\)</span> km, so <span class="math notranslate nohighlight">\(R_\text{apparent} = 200 - 187.5 = 12.5\)</span> km. A large, exploitable error.</p></div>
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<summary><strong>10. Contrast low-, medium-, and high-PRF regimes.</strong></summary>
<div class="card-answer"><p>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.</p></div>
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<summary><strong>11. How do real radars beat the single-PRF tradeoff?</strong></summary>
<div class="card-answer"><p>They transmit at multiple PRFs and resolve the ambiguities across them, recovering true range and velocity that no single PRF could give unambiguously.</p></div>
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