Amplitude Modulation (AM)
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The document discusses amplitude modulation (AM), explaining its purpose for signal transmission and various modulation techniques, including double sideband suppressed-carrier (DSB-SC) AM, conventional AM, and single-sideband (SSB) AM. It highlights the demodulation process, channel requirements, and mentions multiplexing methods like frequency-division multiplexing (FDM). The section also touches upon the superheterodyne receiver used in AM radio, emphasizing its advantages in sensitivity and economy.
Amplitude Modulation (AM)
- 1. Amplitude Modulation CLO 2, Chapter 3
- 2. Modulation
- 3. Why Modulate the Signal? • (1) To translate the frequency of the lowpass signal to the passband of the channel. • (2) To simplify the structure of the transmitter by employing higher frequencies. Smaller wavelength allows smaller antenna (𝜆 = 𝑐/𝑓). • (3) To simultaneously transmit signals from several message sources, by means of frequency-division multiplexing (FDM). (See Section 3.4.) • (4) To expand the bandwidth of the transmitted signal in order to increase its noise and interference immunity (Chapter 6).
- 4. Amplitude Modulation • The message signal 𝑚(𝑡) is impressed on the amplitude of the carrier signal 𝑐(𝑡) = 𝐴 𝑐 cos(2𝜋𝑓𝑐 𝑡). • This results in a sinusoidal signal whose amplitude is a function of the message signal 𝑚(𝑡). • Various flavors of AM: • (a) Double Sideband Suppressed-Carrier (DSB-SC) AM, • (b) Conventional Double-Sideband AM • (c) Single-Sideband (SSB) AM • (d) Vestigial-Sideband (VSB) AM
- 5. Double-Sideband Suppressed-Carrier AM • A DSB-SC AM signal is obtained by multiplying the message signal m(t) with the carrier signal • c t = 𝐴 𝑐 cos(2𝜋𝑓𝑐 𝑡). • The DSB-SC modulated signal is • 𝑢 𝑡 = 𝑚 𝑡 𝑐 𝑡 • 𝑢(𝑡) = 𝐴 𝑐 𝑚(𝑡) cos(2𝜋𝑓𝑐 𝑡)
- 6. DSB-SC Spectrum • The spectrum of the modulated signal using the result of Example 2.3.14. Thus, we obtain • 𝑈(𝑓) = 𝐴 𝑐 2 𝑀 𝑓 − 𝑓𝑐 + 𝑀 𝑓 + 𝑓𝑐 • The magnitude of the spectrum of the message signal 𝑚(𝑡) has been translated or shifted in frequency by an amount 𝑓𝑐 · • The bandwidth occupancy of the amplitude-modulated signal is 2𝑊, whereas the bandwidth of the message signal 𝑚(𝑡) is 𝑊. • Channel bandwidth required to transmit the modulated signal 𝑢(𝑡) is 𝐵𝑐 = 2𝑊.
- 7. DSB-SC Spectrom • If 𝑚 𝑡 𝐹𝑜𝑢𝑟𝑖𝑒𝑟 𝑇𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚 𝑀 𝑓 • By frequency shifting property of Fourier transform: • 𝑚 𝑡 𝑒 𝑗2𝜋𝑓𝑐 𝑡 𝐹𝑜𝑢𝑟𝑖𝑒𝑟 𝑇𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚 𝑀 𝑓 − 𝑓𝑐 • ∵ cos(𝜃) = 1 2 (𝑒 𝑗𝜃 + 𝑒−𝑗𝜃) • 𝑢(𝑡) = 𝐴 𝑐 𝑚(𝑡) cos(2𝜋𝑓𝑐 𝑡) • 𝐴 𝑐 2 𝑒 𝑗2𝜋𝑓𝑐 𝑡 + 𝑒−𝑗2𝜋𝑓𝑐 𝑡 𝑚 𝑡 𝐹 1 2 𝐴 𝑐 𝑀 𝑓 − 𝑓𝑐 + 𝑀 𝑓 + 𝑓𝑐 = 𝑈(𝑓)
- 10. Assignment • How can we demodulate this signal?
- 11. • Let the message signal be 𝑚 𝑡 = sinc(104 𝑡). Determine the DSB-SC- modulated signal and its bandwidth when the carrier is a sinusoid with a frequency of 1 MHz • Carrier: 𝑐 𝑡 = cos 2𝜋106 𝑡 • 𝑢 𝐷𝑆𝐵−𝑆𝐶 𝑡 = sinc 104 𝑡 cos 2𝜋106 𝑡 • 𝑀 𝑓 = 10−4 Π 10−4 𝑓 • The Fourier transform is constant from -5kHz to 5kHz, and zero at other frequencies. • Message bandwidth 𝑊 = 5𝑘𝐻𝑧 • Modulated bandwidth = 2𝑊 = 10𝑘𝐻𝑧
- 12. Power Content of DSB-SC Signals
- 13. • Determine the DSB-SC AM signal and its upper and lower sidebands. 𝑚 𝑡 = 𝑎 cos 2𝜋𝑓𝑚 𝑡 • Determine the power in the modulated signal and the power in each of the sidebands. • 𝑢 𝑡 = 𝑚 𝑡 𝑐 𝑡 = 𝐴 𝑐 𝑎 cos 2𝜋𝑓𝑚 𝑡 cos 2𝜋𝑓𝑐 𝑡 • 𝑃𝑚 = 𝑎2 2 • 𝑃𝑢 = 𝐴 𝑐 2 2 𝑃𝑚 = 𝐴 𝑐 2 𝑎 4 • 𝑃𝑢𝑠 = 𝑃𝑙𝑠 = 𝐴 𝑐 2 𝑎 8
- 14. Demodulation of DSB-SC AM Signals • Suppose that the DSB-SC AM signal 𝑢(𝑡) is transmitted through an ideal channel (with no channel distortion and no noise) • We demodulate by multiplying 𝑟(𝑡) by a locally generated sinusoid cos 2𝜋𝑓𝑐 𝑡 + 𝜙 • Since 𝑚(𝑡) is limited to W Hz, low pass filtering gives:
- 15. • Power of received signal depends upon phase of locally generated carrier, 𝜙. 𝑦𝑙 𝑡 = 1 2 𝐴 𝑐 𝑚 𝑡 cos 𝜙 • If 𝜙 = 45°, the amplitude of the desired signal is reduced by 2 and the signal power is reduced by a factor of 2 • If 𝜙 = 90°, the desired signal component vanishes • DSB-SC requires phase-coherent or synchronous demodulator • Solutions ?
- 16. • Solutions • 1) Add pilot tone • 2) Use Phase Locked Loop
- 17. 3.2.2 Conventional Amplitude Modulation • A conventional AM signal consists of a large carrier component, in addition to the DSB AM-modulated signal. 𝑚 𝑡 < 1
- 21. Power for the Conventional AM Signal
- 23. Demodulation of Conventional DSB·AM Signals • There is no need for a synchronous demodulator. Since the message signal m(t) satisfies the condition l m(t) I < 1, the envelope (amplitude) 1 + m(t) > 0. • Envelope Detection: • 1) Rectify the received signal • 2) Pass the signal through a low pass filter of bandwidth matched to message signal • d(t)= g1+g2 m ( t ) • 3) Eliminate g1 by passing d(t) through a transformer
- 25. Single-Sideband AM • 𝑢 𝑡 = 𝐴 𝑐 𝑚 𝑡 cos 2𝜋𝑓𝑐 𝑡 ± 𝐴 𝑐 𝑚 𝑡 sin2𝜋𝑓𝑐 𝑡 ,
- 28. SSB Demodulation
- 32. IMPLEMENTATION OF AMPLITUDE MODULATORS AND DEMODULATORS • Power-Law Modulation
- 36. Ring Modulator
- 40. Demodulation of DSB-SC AM Signals.
- 41. Frequency-Division Multiplexing • Multiplexing: Combining separate message signals into a composite signal for transmission over a common channel is called • Types of Multiplexing: • (1) Time-division multiplexing (TDM). Used for digital signals. • (2) Frequency-division multiplexing (FDM). Used for analog/digital
- 42. • K-message signals at the transmitter • Transmitter lowpass filters (LPFs) ensure message bandwidth is W-Hz
- 43. Quadrature-Carrier Multiplexing • Use single carrier to multiplex two signals. • 𝑢 𝑡 = 𝐴 𝑐 𝑚1 𝑡 cos 2𝜋𝑓𝑐 𝑡 + 𝐴 𝑐 𝑚2 𝑡 sin 2𝜋𝑓𝑐 𝑡 • Requires synchronous demodulator • Each message transmitted by DSB-SC AM • 𝑢 𝑡 cos 2𝜋𝑓𝑐 𝑡 = 𝐴 𝑐 𝑚1 𝑡 cos2 (2𝜋𝑓𝑐 𝑡) + 𝐴 𝑐 𝑚2(𝑡) cos 2𝜋𝑓𝑐 𝑡 sin 2𝜋𝑓𝑐 𝑡 • = 𝐴 𝑐 2 𝑚1 𝑡 + 𝐴 𝑐 2 𝑚1 𝑡 cos 4𝜋𝑓𝑐 𝑡 + 𝐴 𝑐 2 𝑚2 𝑡 sin 4𝜋𝑓𝑐 𝑡 • Which is the low pass component in above expression?
- 45. Superheterodyne Receiver • Prior to the superhet receiver, radio listeners had to constantly play with a set of knobs on a radio to keep locked on to radio programs of the day • The receiver used in AM radio broadcast is super heterodyne receiver • 540-1600 kHz with 10 kHz spacing, 𝑓𝐼𝑓 = 455 𝑘𝐻𝑧, • Economy: lower frequency components can be used, • many components can be designed for a fixed frequency • Components can even be shared between different receiver designs • Sensitivity: Filtering out unwanted signals at IF is a much easier job than filtering them out at RF
- 46. • 𝑓𝐿𝑂 = 𝑓𝑐 + 𝑓𝐼𝐹 • The tuning range of the local oscillator is 995-2055 kHz • image frequency 𝑓𝑐 ′ = 𝑓𝐿𝑂 + 𝑓_𝐼𝐹
Editor's Notes
- #4: so that the spectrum of the transmitted bandpass signal will match the passband characteristics of the channel. For instance, in transmission of speech over microwave links in telephony transmission, the transmission frequencies must be increased to the gigahertz range for transmission over the channel. This means that modulation, or a combination of various modulation techniques, must be used to translate the speech signal from the low-frequency range (up to 4 kHz) to the gigahertz range. For instance, in the transmission of information using electromagnetic waves, transmission of the signal at low frequencies requires huge antennas. Modulation helps translate the frequency band to higher frequencies, thus requiring smaller antennas. This simplifies the structure of the transmitter (and the receiver).