Download presentation

Presentation is loading. Please wait.

Published byGarett Exum Modified over 5 years ago

1
Z. Ghassemlooy Angle Modulation Professor Z Ghassemlooy Electronics & IT Division Scholl of Engineering Sheffield Hallam University U.K. www.shu.ac.uk/ocr Professor Z Ghassemlooy Electronics & IT Division Scholl of Engineering Sheffield Hallam University U.K. www.shu.ac.uk/ocr

2
Z. Ghassemlooy Contents Properties of Angle (exponential) Modulation Types –Phase Modulation –Frequency Modulation Line Spectrum & Phase Diagram Implementation Power

3
Z. Ghassemlooy 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

4
Z. Ghassemlooy 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

5
Z. Ghassemlooy 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)

6
Z. Ghassemlooy 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

7
Z. Ghassemlooy 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

8
Z. Ghassemlooy Waveforms

9
Z. Ghassemlooy 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

10
Z. Ghassemlooy 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:

11
Z. Ghassemlooy 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 .

12
Z. Ghassemlooy FM Spectral Analysis - Cont’d. Substituting the Bessel coefficient results in: Expanding it results in: Carrier signal Side-bands signal (infinite sets) SinceThen

13
Z. Ghassemlooy 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

14
Z. Ghassemlooy 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

15
Z. Ghassemlooy 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 + )

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google