# Lesson 28 Flashcards — Modulation and Amplitude Modulation

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<summary><strong>1. What is modulation?</strong></summary>
<div class="card-answer"><p>Varying a property of a high-frequency <strong>carrier</strong> according to a lower-frequency <strong>message</strong>.</p></div>
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<summary><strong>2. Give four reasons to modulate rather than transmit the message directly.</strong></summary>
<div class="card-answer"><p>Choose the transmission frequency; shrink the antenna; fit many channels in one band; and make long-distance transmission practical.</p></div>
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<summary><strong>3. How does modulation shrink the antenna?</strong></summary>
<div class="card-answer"><p>Antenna size scales with wavelength. A 3 kHz signal has <span class="math notranslate nohighlight">\(\lambda = 100\)</span> km, needing a 25 km quarter-wave antenna. On a 100 MHz carrier that becomes 75 cm.</p></div>
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<summary><strong>4. What three properties of a carrier can be modulated?</strong></summary>
<div class="card-answer"><p><strong>Amplitude</strong> (AM), <strong>frequency</strong> (FM), and <strong>phase</strong> (PM). A sinusoid has exactly three properties to vary.</p></div>
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<summary><strong>5. Compare AM, FM, and PM.</strong></summary>
<div class="card-answer"><p>AM is cheap and uses less bandwidth but is vulnerable to noise, since noise is also amplitude. FM and PM are noise-resistant and higher quality at the cost of bandwidth. PM underlies most digital modulation.</p></div>
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<summary><strong>6. Which signal is the modulating one, and which is modulated?</strong></summary>
<div class="card-answer"><p>The <strong>message</strong> does the modulat<em>ing</em>; the <strong>carrier</strong> is modulat<em>ed</em>. The carrier is always a sinusoid and always much higher in frequency.</p></div>
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<summary><strong>7. Write the output of a function multiplier with a biased message.</strong></summary>
<div class="card-answer"><p><span class="math notranslate nohighlight">\(v_\text{out}(t) = [\,B + v_m(t)\,]\cdot A_c\cos(2\pi f_c t)\)</span>, where <span class="math notranslate nohighlight">\(B\)</span> is a DC bias.</p></div>
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<summary><strong>8. Expand the AM product for a biased single-tone message.</strong></summary>
<div class="card-answer"><p>Three terms: <span class="math notranslate nohighlight">\(\tfrac{A_cA_m}{2}\cos[2\pi(f_c{-}f_m)t] + A_cB\cos(2\pi f_c t) + \tfrac{A_cA_m}{2}\cos[2\pi(f_c{+}f_m)t]\)</span> — the lower <strong>sideband</strong>, the <strong>carrier</strong>, and the upper sideband.</p></div>
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<summary><strong>9. With no bias, is there a carrier term in the output?</strong></summary>
<div class="card-answer"><p><strong>No.</strong> The product of two sinusoids gives only sum and difference terms. Adding the bias <span class="math notranslate nohighlight">\(B\)</span> puts the carrier back, with amplitude <span class="math notranslate nohighlight">\(A_cB\)</span> at <span class="math notranslate nohighlight">\(f_c\)</span>.</p></div>
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<summary><strong>10. Define the modulation index.</strong></summary>
<div class="card-answer"><p><span class="math notranslate nohighlight">\(\alpha = \max(\text{message})/B\)</span>. The carrier amplitude <span class="math notranslate nohighlight">\(A_c\)</span> multiplies both the envelope swing and the bias, so it <strong>cancels</strong> — <span class="math notranslate nohighlight">\(\alpha\)</span> does not depend on it.</p></div>
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<summary><strong>11. How do you read the modulation index off a single-tone AM spectrum?</strong></summary>
<div class="card-answer"><p>Twice a sideband's height over the carrier's height: <span class="math notranslate nohighlight">\(\alpha = 2\cdot\tfrac{A_cA_m}{2}\big/(A_cB) = A_m/B\)</span>. The equation sheet writes it <span class="math notranslate nohighlight">\(2\cdot Amp_{SB}/Amp_{Carrier}\)</span>.</p></div>
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<summary><strong>12. From Lesson 28 on, what does <span class="math notranslate nohighlight">\(f_c\)</span> mean, and how is a filter cutoff written?</strong></summary>
<div class="card-answer"><p><span class="math notranslate nohighlight">\(f_c\)</span> is the <strong>carrier</strong> frequency. A filter cutoff is written <span class="math notranslate nohighlight">\(f_\text{cutoff}\)</span>, as on the equation sheet.</p></div>
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<summary><strong>13. For intuition (not assessed): How should you draw an AM waveform?</strong></summary>
<div class="card-answer"><p><strong>Envelope first</strong> — the biased message scaled by the carrier amplitude, <span class="math notranslate nohighlight">\(A_c[B + v_m(t)]\)</span> — then mirror it below the axis, then fill in the carrier between. Label the envelope's maximum and minimum and the message period.</p></div>
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