1. BEC/ECE/TSR Angle Modulation

2. BEC/ECE/TSR Contents  Properties of Angle (exponential) Modulation  Types –Phase Modulation –Frequency Modulation  Line Spectrum & Phase Diagram  Implementation  Power

3. 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

4. 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

5. 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)

6. 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

7. 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

8. BEC/ECE/TSR Waveforms

9. 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

10. 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:

11. 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 .

12. 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

13. BEC/ECE/TSR FM Spectrum J0()J0() cc 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. BEC/ECE/TSR FM Spectrum - cont’d. The number of side bands with significant amplitude depend on  see below cc  = 0.5 cc  = 1.0 cc  = 2.5 cc  = 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. 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 +  )