Chapter 5 AM, FM, and Digital Modulated Systems Phase Modulation (PM) Frequency Modulation (FM)

1. Chapter 5 • AM, FM, and Digital Modulated Systems • Phase Modulation (PM) • Frequency Modulation (FM) • Generation of PM and FM • Spectrum of PM and FM • Carson’s Rule • Narrowband FM Huseyin Bilgekul Eeng360 Communication Systems I Department of Electrical and Electronic Engineering Eastern Mediterranean University

2. AM and FM Modulation (a) Carrier wave. (b) Sinusoidal modulating signal. (c) Amplitude-modulated signal. (d) Frequency modulated signal.

3. Angle Modulation • We have seen that an AM signal can be represented as Note that in this type of modulation the amplitude of signal carries information. • Now we will see that information can also be carried in the angleof the signal as Here the amplitude Ac remains constant and the angle is modulated. This Modulation Technique is called the Angle Modulation Angle modulation: Vary either the Phase or the Frequency of the carrier signal • Phase Modulation and Frequency Modulation are special cases of Angle Modulation

4. The Complex Envelope for an Angle Modulation is given by Is a constant Real envelope, The Angle-modulated Signal in time domain is given by Angle Modulation Representation of PM and FM signals: θ(t) - linear function of the modulating signal m(t) g(t) - Nonlinearfunction of the modulation. Special Case 1: For PM the phase is directly proportional to the modulating signal. i.e.; Where Dpis the Phase sensitivity of the phase modulator, having units of radians/volt. Special Case 2: For FM, the phase is proportional to the integral of m(t) so that where the frequency deviation constant Dfhas units of radians/volt-sec.

5. Resulting PM wave: • Frequency Modulation occurs when the instantaneous frequency is varied linearly with the message signal. Dfis the frequency deviation constant Resulting FM wave: Angle Modulation • Instantaneous Frequency (fi) of a signal is defined by • Phase Modulationoccurs when the instantaneous phase varied in proportion to that of the message signal. Dp is the phase sensitivity of the modulator

6. Phase Modulation Frequency Modulation Phase and Frequency Modulations Comparing above two equations , we see that if we have a PM signal modulated by mp(t), there is also FM on the signal, corresponding to a different modulation wave shape that is given by: Similarly if we have a FM signal modulated by mf(t),the corresponding phase modulation on this signal is: Where f and pdenote frequency and phase respectively.

7. Generation of FM from PM and vice versa Generation of FM using a Phase Modulator: Integrator Phase Modulator (Carrier Frequency fc) FM Signal Generation of PM using a Frequency Modulator: Differentiator Frequency Modulator (Carrier Frequency fc) PM signal

8. FM with sinusoidal modulating signal If a bandpass signal is represented by: ∆F is related to the peak modulating voltage by Where • The Peak-to-peak Deviationis given by • The Instantaneous Frequency of the FM signal is given by: • The Frequency Deviationfrom the carrier frequency: • The Peak Frequency Deviation is given by:

9. FM with sinusoidal modulating signal Vp BW   But,  Average Power does not change with modulation

10. Angle Modulation • Advantages: • Constant amplitude means Efficient Non-linear Power Amplifiers can be used. • Superior signal-to-noise ratio can be achieved (compared to AM) if bandwidth is sufficiently high. • Disadvantages: • Usually require more bandwidth than AM • More complicated hardware

11. ∆θ is related to the peak modulating voltage by: Where Where ∆θis the peak phase deviation • The Phase Modulation Indexis given by: • The Frequency Modulation Indexis given by: ∆F Peak Frequency Deviation B Bandwidth of the modulating signal Modulation Index • The Peak Phase Deviationis given by:

12. Spectrum of Angle modulated signal Where Spectra of Angle modulated signals • Spectra for AM, DSB-SC, and SSB can be obtained with simple formulas relating S(f) to M(f). • But for angle modulation signaling, because g(t) is a nonlinear function of m(t). Thus, a general formula relating G(f) to M(f) cannot be obtained. • To evaluate the spectrum for angle-modulated signal, G(f) must be evaluated on a case-by-case basis for particular modulating waveshape of interest.

13. Then Where is the phase Modulation Index. which is periodic with period Spectrum of PM or FM Signal with Sinusoidal Modulating Signal • Assume that the modulation on the PMsignal is Same θ(t) could also be obtained if FM were used where and The peak frequency deviation would be The Complex Envelope is:

14. Spectrum of PM or FM Signal with Sinusoidal Modulating Signal Where Which reduces to Is a special property of Bessel Functions or Using discrete Fourier series that is valid over all time, g(t) can be written as Jn(β) – Bessel function of the first kind of the nth order Taking the fourier transform of the complex envelopeg(t), we get

15. Bessel Functions of the First Kind J0(β)=0 at β=2.4, 5.52 & so on

16. Bessel Functions of the First Kind

17. Frequency spectrum of FM • The FM modulated signal in time domain Observations: • From this equation it can be seen that the frequency spectrum of an FM waveform with a sinusoidal modulating signal is a discrete frequency spectrum made up of components spaced at frequencies of c± nm. • By analogy with AM modulation, these frequency components are called sidebands. • We can see that the expression for s(t) is an infinite series. Therefore the frequency spectrum of an FM signal has an infinite number of sidebands. • The amplitudes of the carrier and sidebands of an FM signal are given by the corresponding Bessel functions, which are themselves functions of the modulation index

18. Spectra of an FM Signal with Sinusoidal Modulation • The following spectra show the effect of modulation index, , on the bandwidth of an FM signal, and the relative amplitudes of the carrier and sidebands 1.0 f BT

19. Spectra of an FM Signal with Sinusoidal Modulation J0(1.0) 1.0 J1(1.0) J2(1.0) f BT

20. Spectra of an FM Signal with Sinusoidal Modulation 1.0 f BT

21. Carson’s rule • Although the sidebands of an FM signal extend to infinity, it has been found experimentally that signal distortion is negligible for a bandlimited FM signal if 98% of the signal power is transmitted. • Based on the Bessel Functions, 98% of the power will be transmitted when the number of sidebands transmitted is 1+ on each side. (1+b)fm

22. For sinusoidal modulation Note: When β =0 i.e. baseband signals Carson’s rule • Therefore the Bandwidth required is given by β – phase modulation index/ frequency modulation index B – bandwidth of the modulating signal • Carson’s rule :Bandwidth of an FM signal is given by

23. Narrowband Angle Modulation • Narrowband Angle Modulation is a special case of angle modulation where θ(t) is restricted to a small value. • The complex envelope can be approximated by a Taylor's series in which only first two terms are used. becomes • The Narrowband Angle Modulated Signal is • The Spectrum of Narrowband Angle Modulated Signal is PM where FM

24. Balanced Modulator Indirect method of generating WBFM

25. Wideband Frequency modulation

26. FM Stero System

27. FM Stero System