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