Z. Ghassemlooy,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 SNRo 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 SNRo without 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,Basic Concept - Contd.,In angle modulation: Amplitude is constant, but angle varies (increases linearly) with time,Z. Ghassemlooy,Phase Modulation (PM),PM is defined If,Thus,Where Kp is known as the phase modulation index,Instantaneous frequency,Rotating Phasor diagram,Instantaneous phase,Z. Ghassemlooy,Frequency Modulation (FM),The instantaneous frequency is;,Where Kf is known as the frequency deviation (or frequency modulation index). Note: Kf 0.,Note that,Integrating,Substituting c(t) in c(t) results in:,Instantaneous phase,Z. Ghassemlooy,Waveforms,Z. Ghassemlooy,Important Terms,Carrier Frequency Deviation (peak),Frequency swing,Rated System Deviation (i.e. maximum deviation allowed),Percent Modulation,Modulation Index,Z. Ghassemlooy,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 - Contd.,Substituting the Bessel coefficient results in:,Expanding it results in:,Carrier signal,Side-bands signal (infinite sets),Since,Then,Z. Ghassemlooy,FM Spectrum,Bandwidth (?),Z. Ghassemlooy,FM Spectrum - contd.,The number of side bands with significant amplitude depend on see below,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,Z. Ghassemlooy,FM Bandwidth BFM,The commonly rule used to determine the bandwidth is: Sideband amplitudes 0.01,For large values of ,BFM = 2nfm= 2fm=2 (fc/ fm).fm = 2 fc,For small values of ,BFM = 2fm,For limited cases,General case: use Carson equation,BFM 2(fc + fm),BFM 2 fm (1 + ),