BEC/ECE/TSR Contents Properties of Angle (exponential) Modulation Types –Phase Modulation –Frequency Modulation Line Spectrum & Phase Diagram Implementation Power
BEC/ECE/TSR Properties Linear CW Modulation (AM): –Modulated spectrum is translated message spectrum –Bandwidth message bandwidth –SNR o at the output can be improved only by increasing the transmitted power Angle Modulation: A non-linear process:- –Modulated spectrum is not simply related to the message spectrum –Bandwidth >>message bandwidth. This results in improved SNR o without increasing the transmitted power
BEC/ECE/TSR Basic Concept First introduced in 1931 A sinusoidal carrier signal is defined as: For un-modulated carrier signal the total instantaneous angle is: Thus one can express c(t) as: Thus: Varying the frequency f c Frequency modulation Varying the phase c Phase modulation
BEC/ECE/TSR Basic Concept - Cont’d. In angle modulation: Amplitude is constant, but angle varies (increases linearly) with time t Amplitude Ec Initial phase c Unmodulated carrier Slope = c / t t = 0 t (ms) Unmodulated carrier 0 c (t) (red) - /2 11 /2 23 /2 35 /2 47 /2 1 2 3 4 Phase-modulated angle Frequency-modulated angle 2 0 m(t)m(t)
BEC/ECE/TSR Phase Modulation (PM) PM is defined If Thus Where K p is known as the phase modulation index EcEc c(t)c(t) c(t)c(t) c(t)c(t) i(t)i(t) Instantaneous frequency Rotating Phasor diagram Instantaneous phase
BEC/ECE/TSR Frequency Modulation (FM) The instantaneous frequency is; Where K f is known as the frequency deviation (or frequency modulation index). Note: K f 0. Note that Integrating Substituting c (t) in c(t) results in: Instantaneous phase
BEC/ECE/TSR Important Terms Carrier Frequency Deviation (peak) Frequency swing Rated System Deviation (i.e. maximum deviation allowed) F D = 75 kHz, FM Radio, (88-108 MHz band) 25 kHz, TV sound broadcast 5 kHz, 2-way mobile radio 2.5 kHz, 2-way mobile radio Percent Modulation Modulation Index
BEC/ECE/TSR FM Spectral Analysis Let modulating signal m(t) = E m cos m t Substituting it in c(t) FM expression and integrating it results in: Sinceand the terms cos ( sin m t) and sin ( sin m t) are defined in trigonometric series, which gives Bessel Function Coefficient as:
BEC/ECE/TSR Bessel Function Coefficients cos ( sin x) =J 0 ( ) + 2 [J 2 ( ) cos 2x + J 4 ( ) cos 4x +....] And sin ( sin x) = 2 [J 1 ( ) sin x + J 3 ( ) sin 3x +....] where J n ( ) are the coefficient of Bessel function of the 1st kind, of the order n and argument of .
BEC/ECE/TSR FM Spectral Analysis - Cont’d. Substituting the Bessel coefficient results in: Expanding it results in: Carrier signal Side-bands signal (infinite sets) SinceThen
BEC/ECE/TSR FM Spectrum J0()J0() cc J1()J1() c + m c + 2 m c + 3 m c + 4 m J2()J2() J3()J3() J4()J4() Side bands Bandwidth (?) c - 3 m J2()J2() J3()J3() J4()J4() c - 2 m c - 4 m
BEC/ECE/TSR FM Spectrum - cont’d. The number of side bands with significant amplitude depend on see below cc = 0.5 cc = 1.0 cc = 2.5 cc = 4 Bandwidth Generation and transmission of pure FM requires infinite bandwidth, whether or not the modulating signal is bandlimited. However practical FM systems do have a finite bandwidth with quite well pwerformance. Most practical FM systems have 2 < < 10
BEC/ECE/TSR FM Bandwidth B FM The commonly rule used to determine the bandwidth is: –Sideband amplitudes 0.01 For large values of , B FM =2nf m =2 f m =2 (f c / f m ).f m = 2 f c For small values of , B FM =2f m For limited cases General case: use Carson equation B FM 2(f c + f m ) B FM 2 f m (1 + )
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