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## Chapter 3 Analog Signal Transmission and Reception

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**CONTENTS**• Introduction to Modulations • Amplitude Modulation • Angle Modulation • Radio and Television Broadcasting • Mobile Radio Systems**3.1 INTRODUCTION TO MODULATION**• Denote m(t) as the analog signal to be transmitted. • The signal m(t) is assumed to be a lowpass signal of bandwidth W and is a power-type signal with • The message signal m(t) is transmitted through the communication channel by putting it on a carrier signal of the form carrier amplitude carrier amplitude carrier phase**The signal m(t) modulates the carrier signal c(t) in three**forms • Amplitude Modulation (AM) • Frequency Modulation (FM) • Phase Modulation (PM) • Objectives of modulation • Translate the low pass signal m(t) to bandpass signal to match the passband characteristics of the channel. • Accommodate for simultaneous transmission - frequency-division multiplexing (FDM). • Increase the noise immunity in transmission by expanding the bandwidth of the transmitted signal.**3.2 AMPLITUDE MODULATION (AM)**• The message signal m(t) is impressed on the amplitude of the carrier signal c(t). • Types of amplitude modulation • Double-sideband, suppressed carruer AM (DSB-SC AM) • Conventional double-sideband AM • Single-sideband AM (SSB AM) • Vestigial-sideband AM (VSB AM)**3.2.1 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 signal c(t). • Amplitude modulated signal • The spectrum of the modulated signal can be obtained by taking the Fourier transform of u(t).**upper sideband**upper sideband lower sideband**The magnitude of the spectrum of the message signal m(t) has**been translated or shifted in frequency by an amount • The phase of the message signal has been translated in frequency and offset by the carrier phase • The bandwidth of the AM signal is 2W, where W is the bandwidth of m(t). • The upper sideband of U(f) contains all the frequency contain of the message signal M(f). • u(t) does not contain carrier components - u(t) is called a suppressed-carrier signal (DSB-SC AM signal)**To compute power content of DSB-SC signal, we first evaluate**the time-average autocorrelation function of the signal u(t) • We may show that the following equation equals to zero. Parseval’s relation No frequency overlap**Finally, we have**• Taking Fourier transform of both sides • The power spectral density of the DSB-SC signal is the power spectral density of the message shifted upward and downward by and scaled by • The power of the modulated signal where is the power of the message signal**Demodulation of DSB-SC AM Signal**• In the absence of noise, and with the assumption of an ideal channel, the received signal can be expressed as • Demodulation of DSB-SC AM signal • Multiply r(t) by a locally generated sinusoid • Pass the product signal through an ideal lowpass filter having a bandwidth W. • Multiplication**The lowpass filter rejects the high frequency components and**pass only the low frequency component. Hence, the output of the filter is • Note that m(t) is multiplied by . Thus the desired signal is scaled by a factor that depends on the phase difference between the pahse of the carrier and the phase of the locally generated sinusoid. • If the amplitude of the desired signal is reduced by • If the desired signal component vanishes. • For perfect demodulation, (Phase coherent)**Pilot Tone for Carrier Recovery in DSB AM**• Addition a pilot tone to a DSB AM signal- additional power requirement • Carrier recovery by a narrow band filter**3.2.2 Conventional Amplitude Modulation**• A conventional AM signal consists of a large carrier component in addition to the double sideband AM modulated signal. The transmitted signal can be expressed as • Advantage: easy to demodulate**It is convenient to express m(t) as**where is normalized such that The above equation can be done by using • The scale factor a is called the modulation index. The modulated signal can be expressed as**The spectrum of the amplitude modulated signal u(t) is**• The spectrum of a conventional AM signal occupies bandwidth twice the bandwidth of the message signal.**Example: Suppose that the modulating signal is a**sinusoid of the form Determine the DSB AM signal, its upper and lower sidebands, and its spectrum, assuming a modulation index of a. Solution: The DSB AM signal**We have already proved in the DSB-SC case, the power in the**modulated signal is • For the conventional AM • Finally, we have contains no DC component Message power Carrier power**Advantage of conventional AM signal: easy to be demodulated**• Envelope detector**3.2.3 Single-Sideband AM**• DSB-SC AM signal requires a channel bandwidth of • The transmission of either sideband is sufficient to reconstruct the message signal m(t) at the receiver. • We may reduce the transmitted bandwidth to W Hz by transmitting only the upper sideband or the lower sideband. • A single sideband AM signal can be represented mathematically as :Hilbert transform of m(t).**Generation of a single-sideband AM signal by Hilbert**transform**Generation of a single-sideband AM signal by bandpass filter****Let m(t) be a signal with Fourier transform M(f).**• An upper sideband AM signal is obtained by eliminating the lower sideband of a DSB AM signal. • We may pass the DSB AM signal through a highpass filter whose transfer function is given by • Obviously H(f) can be written as**The spectrum of the USSB AM signal is given by**• Taking the inverse Fourier transform of both sides, we obtain**For lower sideband (LSSB) AM signal, notice**• We have • Finally, we have proved USSB AM LSSB AM**To recover the message signal from SSB AM signal, we require**a phase coherent or synchronous demodulator. • First multiply the received signal with the local generated carrier , we have • By passing the above signal through an ideal lowpass filter, we have the output • For perfect demodulation, we must have . desired signal interference**3.2.4 Vestigial-Sideband AM**• Relaxing the SSB AM by allowing a part called vestige to appear at the output of the modulator. The resulting signal is called vestigial-sideband (VSB) AM. • Generation of VSB AM • generate a DSB-SC AM signal • pass the DSB-SC AM signal through a sideband filter with frequency response H(f)**In the time-domain the VSB signal may be expressed as**: impulse response of the VSB filter • In frequency domain • Consider the demodulation of the VSB signal**We have the product signal**• The lowpass filter rejects the double-frequency terms and pass only the components in the frequency range • The signal spectrum at the output of the lowpass filter is • Undistirtion requirement**3.2.5 Implementation of AM Modulator and Demodulator**• Power-Law Modulation • Nonliear device • voltage-current characteristic of P-N diode • input is the sum of the message signal and the carrier • Let be the input signal. The output of the nonlinear device can be expressed as**Power-Law AM modulator**• Suppose that the nonlinear device is approximated by a second order polynomial.**Input to the nonlinear device**• Output of the nonlinear device • The band pass filter with bandwidth 2W centered at yields where by design**Assume that**• Let • The diode will turn on if and will turn off if • The output across the load resistor is • Since s(t) is a periodic rectangular function, the Fourier series is**Hence**• Passing through a bandpass filter, we have**Ring modulator for DSB-SC AM**• If c(t) > 0, 1, 4 on, and 2, 3 off, • If c(t) < 0, 1,4 off, and 2,3 on, 1 2 3 4 C(t)**Therefore, we have**• Since c(t) is a periodic function, the Fourier series can be expressed as • The desired DSB-SC AM signal is obtained by passing through a bandpass filter with center frequency and bandwidth 2W.