1. ANGLE MODULATION CHAPTER 3

2. ANGLE MODULATION Part 1 Introduction

3. Angle modulation is the process by which the angle (frequency or Phase) of the carrier signal is changed in accordance with the instantaneous amplitude of modulating or message signal. also known as “Exponential modulation"

4. Cont’d… classified into two types such as Frequency modulation (FM) Phase modulation (PM) Used for : Commercial radio broadcasting Television sound transmission Two way mobile radio Cellular radio Microwave and satellite communication system

5. Frequency Modulation (FM) Introduction FM is the process of varying the frequency of a carrier wave in proportion to a modulating signal. The amplitude of the carrier wave is kept constant while its frequency and a rate of change are varied by the modulating signal.

6. FM :Introduction (cont…) Fig 3.1 : Frequency Modulated signal

7. FM :Introduction (cont…) The important features about FM waveforms are : i. The frequency varies. ii. The rate of change of carrier frequency changes is the same as the frequency of the information signal. iii. The amount of carrier frequency changes is proportional to the amplitude of the information signal. iv. The amplitude is constant.

8. FM :Introduction (cont…) The FM modulator receives two signals,the information signal from an external source and the carrier signal from a built in oscillator. The modulator circuit combines the two signals producing a FM signal which passed on to the transmission medium. The demodulator receives the FM signal and separates it, passing the information signal on and eliminating the carrier signal. Federal Communication Coporation (FCC) allocation for a standard broadcast FM station is as shown in Fig.3.2

9. Figure 3.2: FM frequency allocation by FCC

10. Analysis of FM Mathematical analysis: Let message signal: (3.1) And carrier signal: (3.2) Where carrier frequency is very much higher than message frequency.

11. Analysis of FM (cont’d) In FM, frequency changes with the change of the amplitude of the information signal. So the instantenous frequency of the FM wave is; (3.3) K is constant of proportionality

12. Analysis of FM (cont’d) Thus, we get the FM wave as: 3.4 Where modulation index for FM is given by

13. Analysis of FM (cont’d) Frequency deviation: ∆f is the relative placement of carrier frequency (Hz) w.r.t its unmodulated value. Given as:

14. FM(cont’d) Therefore:

15. Example 3.1 FM broadcast station is allowed to have a frequency deviation of 75 kHz. If a 4 kHz (highest voice frequency) audio signal causes full deviation (i.e. at maximun amplitude of information signal), calculate the modulation index.

16. Example 3.2 Determine the peak frequency deviation,, and the modulation index, mf, for an FM modulator with a deviation Kf = 10 kHz/V. The modulating signal to be transmitted is Vm(t) = 5 cos (10kπt).

17. Equations for Phase- and Frequency-Modulated Carriers Tomasi Electronic Communications Systems, 5e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

18. FM&PM (Bessel function) Thus, for general equation:

19. Bessel function

20. B.F. (cont’d) It is seen that each pair of side band is preceded by J coefficients. The order of the coefficient is denoted by subscript m. The Bessel function can be written as N=number of the side frequency M=modulation index

21. Bessel Functions of the First Kind, J n (m) for some value of modulation index

22. B.F. (cont’d)

23. Representation of frequency spectrum