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Angle Modulation. Professor Z Ghassemlooy Electronics & IT Division Scholl of Engineering Sheffield Hallam University U.K. www.shu.ac.uk/ocr. Contents. Properties of Angle (exponential) Modulation Types Phase Modulation Frequency Modulation Line Spectrum & Phase Diagram

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## Angle Modulation

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**Angle Modulation**Professor Z Ghassemlooy Electronics & IT Division Scholl of Engineering Sheffield Hallam University U.K. www.shu.ac.uk/ocr Z. Ghassemlooy**Contents**• Properties of Angle (exponential) Modulation • Types • Phase Modulation • Frequency Modulation • Line Spectrum & Phase Diagram • Implementation • Power Z. Ghassemlooy**Properties**• Linear CW Modulation (AM): • Modulated spectrum is translated message spectrum • Bandwidth message bandwidth • SNRoat 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 SNRowithout increasing the transmitted power 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 fc Frequency modulation • Varying the phase c Phase modulation Z. Ghassemlooy**c(t)**(red) Unmodulated carrier Frequency-modulated angle 47/2 Unmodulated carrier 35/2 Phase-modulated angle Amplitude Ec 23/2 11/2 -/2 Slope =c/t t (ms) Initial phasec 0 1 2 4 3 t t = 0 m(t) 2 0 -1 Basic Concept - Cont’d. • In angle modulation: Amplitude is constant, but angle varies (increases linearly) with time Z. Ghassemlooy**i(t)**Ec c(t) c(t) c(t) Phase Modulation (PM) PM is defined If Thus Where Kp is known as the phase modulation index Instantaneous phase Instantaneous frequency Rotating Phasor diagram Z. Ghassemlooy**Frequency Modulation (FM)**The instantaneous frequency is; Where Kf is known as the frequency deviation (or frequency modulation index). Note: Kf < fc to make sure that f(t) >0. Instantaneous phase Note that Integrating Substituting c(t) in c(t) results in: Z. Ghassemlooy**Waveforms**Z. Ghassemlooy**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 FD = Important Terms • Carrier Frequency Deviation (peak) • Frequency swing • Rated System Deviation (i.e. maximum deviation allowed) • Percent Modulation • Modulation Index Z. Ghassemlooy**Since**and FM Spectral Analysis Let modulating signal m(t) = Em cos mt Substituting it in c(t)FM expression and integrating it results in: the terms cos ( sin mt) and sin ( sin mt) are defined in trigonometric series, which gives Bessel Function Coefficient as: Z. Ghassemlooy**Bessel Function Coefficients**cos ( sin x) = J0 () + 2 [J2() cos 2x + J4() cos 4x + ....] And sin ( sin x) = 2 [J1() sin x + J3() sin 3x + ....] where Jn() are the coefficient of Bessel function of the 1st kind, of the order n and argument of . Z. Ghassemlooy**FM Spectral Analysis - Cont’d.**Substituting the Bessel coefficient results in: Expanding it results in: Carrier signal Side-bands signal (infinite sets) Since Then Z. Ghassemlooy**J0()**Side bands J1() J4() J2() J2() J3() J4() c- 3m c- 4m c- 2m c+ m c+ 3m J3() c c+ 2m c+ 4m Side bands FM Spectrum Bandwidth (?) Z. Ghassemlooy** = 2.5** = 0.5 = 1.0 = 4 c c c c Bandwidth FM Spectrum - cont’d. • The number of side bands with significant amplitude depend on • see below Most practical FM systems have 2 < < 10 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. Z. Ghassemlooy**FM Bandwidth BFM**• The commonly rule used to determine the bandwidth is: • Sideband amplitudes < 1% of the un-modulated carrier can be ignored.Thus Jn()> 0.01 BFM = 2nfm= 2fm=2 (fc/ fm).fm = 2 fc For large values of , For small values of , BFM = 2fm For limited cases General case: use Carson equation BFM 2(fc + fm) BFM 2 fm (1 + ) Z. Ghassemlooy

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