Chapter 3. Amplitude Modulation

1. Chapter 3. Amplitude Modulation Essentials of Communication Systems Engineering

2. Amplitude Modulation • Speech, music, images, and video are examples of analog signals • Speech and audio signals : • The signal has just one component, which measures air pressure • Speech: Bandwidth of up to 4 kHz • Music signal : Bandwidth of 20 kHz • Color video • The signal has four components, namely, the red, green, and blue color components, plus a fourth component for the intensity • Video signals have a much higher bandwidth, about 6 MHz • The general trend is the digital transmission of analog signals • We still have a significant amount of analog signal transmission, especially in audio and video broadcast • In this chapter, we study amplitude-modulation systems, where the message signals change the amplitude of the carrier

3. INTRODUCTION TO MODULATION • Assume that the analog signal m(t) is denoted as follows • A lowpass signal of bandwidth W, that is, M(f) = 0, for |f| > W • The power content of this signal is denoted by • The message signal m(t) is transmitted through the channel by impressing it on a carrier signal of the form • A, fc, c : Carrier amplitude, Carrier frequency, Carrier phase , respectively • cdepends on the choice of the time origin. we assume that the time origin is chosen such that c= 0 • Modulation converts m(t) from lowpass signal to bandpass signal, in the neighborhood of the carrier frequency fc

4. INTRODUCTION TO MODULATION • Modulation of the carrier c(t) by the message signal m(t) is performed to achieve the following objectives • Match the passband characteristics of the channel • To translate the lowpass signal to the passband of the channel so that the spectrum of the transmitted bandpass signal will match the passband characteristics of the channel • Simplify the structure of the transmitter • For instance, in the wireless communications, 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) • Frequency-division multiplexing (FDM) • To accommodate for the simultaneous transmission of signals from several message sources, by means of FDM (See Section 3.4.)

5. AMPLITUDE MODULATION (AM) • In amplitude modulation, the message signal m(t) is impressed on the amplitude of the carrier signal c(t) = Accos(2fct) • This results in a sinusoidal signal whose amplitude is a function of the message signal m(t) • There are several different ways of amplitude modulating the carrier signal by m(t) • Double sideband, suppressed-carrier AM (DSB-SC AM) • Conventional double-sideband AM • Single-sideband AM (SSB AM) • Vestigial-sideband AM (VSB AM) • Each results in different spectral characteristics for the transmitted signal

6. Double-Sideband Suppressed-Carrier AM • A double-sideband, suppressed-carrier (DSB-SC) AM signal is obtained by multiplying the message signal m(t) with the carrier c(t) • Amplitude-modulated signal • An example of the message signal m(t), the carrier c(t), and the modulated signal u (t) are shown in Figure 3.1 • This figure shows that a relatively slowly varying message signal m(t) is changed into a rapidly varying modulated signal u(t), and due to its rapid changes with time, it contains higher frequency components • At the same time, the modulated signal retains the main characteristics of the message signal, and it can be used to retrieve the message signal at the receiver

7. Double-Sideband Suppressed-Carrier AM • Figure 3.1 An example of message, carrier, and DSB-SC modulated signals

8. Spectrum of the DSB-SC AM Signal • Spectrum of the modulated signal can be obtained by taking the FT of u(t) • 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 • The channel bandwidth required to transmit the modulated signal u(t) is Bc= 2W Magnitude spectra of the message signal m(t) and the DSB-AM signal u(t)

9. Spectrum of the DSB-SC AM Signal • The frequency content of the modulated signal u(t) in the frequency band | f | > fcis called the upper sideband of U(f) • The frequency content in the frequency band | f | < fcis called the lower sideband of U(f) • Either one of the sidebands of U(f) contains all the frequencies that are in M(f) • Since U(f) contains both the upper and the lower sidebands, it is called a double-sideband (DSB) AM signal

10. Spectrum of the DSB-SC AM Signal • The other characteristic of the modulated signal u(t) is that it does not contain a carrier component • That is, all the transmitted power is contained in the modulating (message) signal m(t) • For this reason, u(t) is called a suppressed-carrier signal • Therefore, u(t) is a DSB-SC AM signal.

11. Power Content of DSB-SC Signals • The power content of the DSB-SC signal • Pmindicates the power in the message signal m(t) • Since the envelope of m2(t)cos(4fct) is slowly varying, the positive and the negative halves of each cycle have almost the same amplitude • Thus, the overall integral of m2(t)cos(4fct) is almost zero Plot of m2(t)cos(4fct)