frequency modulation

. Types of Modulation(Analog)
Phase-Frequency Relationships
FM and PM basics
Frequency deviation
MODULATION INDEX
Classification of FM
Narrow Band FM (NBFM)
generating a narrowband FM signal.
Wide Band FM (WBFM).
Carson’s Rule
Generation of WBFM
Average Power
FM BANDWIDTH
Comparing Frequency Modulation to Phase Modulation

1. Frequency modulation . Types of Modulation(Analog) Phase-Frequency Relationships FM and PM basics Frequency deviation MODULATION INDEX Classification of FM Narrow Band FM (NBFM) generating a narrowband FM signal. Wide Band FM (WBFM). Carson’s Rule Generation of WBFM Average Power FM BANDWIDTH Comparing Frequency Modulation to Phase Modulation

2. Types of Modulation(Analog) 1. Angle Modulation: In the angle modulation, again there are two different types of modulations. Frequency modulation Phase modulation . 2. Amplitude Modulation:

3.  t im e t i i C dt t  t Slope:  ( t )  d  ( t )   Phase-Frequency Relationship When Frequency is Constant  ( t )  A cos(  ( t ))  ( t ) is generalized angle  ( t )  A cos(  C t   )  ( t )  C t   3

4. Concept of Instantaneous Frequency  ( t ) is generalized angle  ( t )  A cos(  ( t ))   ( t )  A cos(  C t   )  ( t )  C t    ( t ) d  ( t ) dt t  t i Slope:  i ( t )    C time t t i 4

5. Frequency Modulation (FM) But in frequency modulation the instantaneous angular frequency  i varies linearly with the modulating signal m ( t ),  i   C  k f m ( t ) t  ) d          FM ( t )  A cos  C t  k f  m ( 5 k f m (  )) d    C t  k f t  ( t )   (  C t  m (  ) d    k f is frequency-deviation (sensitivity) constant. U nits: radians/volt-sec. Then FM and PM are very much related to each other. In PM the angle is directly proportional to m ( t ). In FM the angle is directly proportional to the integral of m ( t ), i.e. ,  m ( t ) dt

6. Frequency Modulation Frequency deviation Δ f

7. MODULATION INDEX   Directly proportional to the amplitude of the modulating signal and inversely proportional to the frequency of the modulating signal Ratio of the frequency deviation and the modulating frequency   as modulation index :   f m k A f m  

8. Classification of FM On the basis of modulation index, FM is classified in two parts : 1) If  < 1, then FM is said to be Narrow Band FM (NBFM). 2) If  >1, then FM is said to be Wide Band FM (WBFM).

9. Narrow Band Angle Modulation Definition Equation Comparison with AM Only phase difference of Pi/2 Frequency: similar Time: AM: frequency constant FM: amplitude constant Conclusion: NBFM signal is similar to AM signal NBFM has also bandwidth 2W. (twice message signal bandwidth)

10. Block diagram of a method for generating a narrowband FM signal.

11. Wide Band FM Wideband FM signal Fourier series representation

12. Bessel Function of First Kind

13. Spectrum of WBFM (Chapter 5.2) Spectrum when m(t) is single-tone Example 2.2

14. Bandwidth of FM Facts FM has side frequencies extending to infinite frequency  theoretically infinite bandwidth But side frequencies become negligibly small beyond a point  practically finite bandwidth FM signal bandwidth equals the required transmission (channel) bandwidth Bandwidth of FM signal is approximately by Carson’s Rule (which gives lower-bound)

15. Carson’s Rule Nearly all power lies within a bandwidth of For single-tone message signal with frequency f m For general message signal m(t) with bandwidth (or highest frequency) W

16. NBFM and WBFM In NBFM the maximum modulating frequency is 3KHz and maximum frequency deviation is 75KHz. In WBFM the maximum modulating frequency is 30Hz to 15KHz and maximum frequency deviation is 75KHz. Bandwidth of WBFM is 15 times of that of NBFM.

17. Pre-emphasis and De-emphasis If freq. ↑ then amplitude ↓. Due to this signal decreases hence decreasing the signal to noise ratio(SNR). Therefore, the high frequency component which have low SNR are boosted or emphasized prior to the transmission of the signal. This is done by using a pre-emphasis circuit and is used at the transmitting end just before the modulation takes place.

18. Pre-emphasis and De-emphasis Now, since the relative SNR for various frequency components has been disturbed then those frequency components which were initially boosted or emphasized are now brought down to the same level to keep the same quality of the signal. This is done by using a de-emphasis circuit and is used at the receiving end.

19. Generation of NBFM  NBFM Modulator :

20. Generation of WBFM There are two basic methods for generating FM signals known as direct and indirect methods. The direct method makes use of a device called voltage controlled oscillator (VCO) whose oscillation frequency depends linearly on the modulation voltage.

21. Generation of WBFM  I n di r ec t M e thod (Arm s t r on g ’ s M e thod ):

22. Average Power of a FM or PM Wave The amplitude A is constant in a phase modulated or a frequency modulated signal. RF power does not depend upon the frequency or the phase of the waveform.  F M o r P M ( t )  A c o s   C t  f ( k , m ( t ) )  Average Power  A 2 (always) 2 This is a result of FM and PM signals being constant amplitude . 22

23. Indirect Generation of an FM Signal Using Multiplication In this method, a narrowband frequency-modulated signal is first generated and then a frequency multiplier is used to increase the modulation index. The concept is shown below: FM  NB ( t ) FM  WB ( t ) NBFM F r eque nc y Multiplier m ( t ) 23 A frequency multiplier is used to increase both the carrier frequency and the modulation index by integer N .

24. Generation of Narrowband Frequency Modulation (NBFM) t     FM ( t )  A cos   C t  k f    m (  ) d   NBFM requires  << 1 radian DSB-SC modulator Lathi & Ding; Figure 5.10 Page 276 -  /2 NBFM  m ( t ) k f  24 A  cos(  c t ) A  sin(  c t ) Car r i er

25. Generation of Narrowband Phase Modulation (NBPM)  PM ( t )  A cos(  C t  k p m ( t )) -  /2 NBPM  A  cos(  c t ) m ( t ) k p A  sin(  c t ) 25

26. FREQUENCY MODULATION (FM) Variation of d  /dt produces Frequency Modulation Frequency modulation implies that d  /dt is proportional to the modulating signal. This yields c c c c f m c c f m m f m m c o s  ( t )  v FM ( t )  V c sin   c t   ( t )     V s in  t   '( t ) dt      V s in  t  k v ( t ) d t      V s in  t  k V sin  ( t ) d t   k V   V sin  t  c   c m      

27. Specifications for transmission of FM signal Table 1 display the transmission band that use FM and the legal frequency deviation limit for each category

28. FM BANDWIDTH  The total BW of an FM signal can be determined by knowing the modulation index and Bessel function. N = number of significant sidebands f m = modulating signal frequency (Hz) Another way to determine the BW is use Carson’s rule   This rule recognizes only the power in the most significant sidebands with amplitude greater than 2% of the carrier. BW  2 f m N

29. CARSON’S RULE f d (max) f m (max) = max. frequency deviation = max. modulating frequency   Carson’s rule always give a lower BW calculated with the formula BW = 2f m N. Consider only the power in the most significant sidebands whose amplitudes are greater than 1% of the carrier.  Rule for the transmission bandwidth of an FM signal generated by a single of frequency f m as follows: BW  2[ f d (max)  f m (max) ] o r T m  B  BW  2  f  2 f  2  f (1  1 ) = 2 f m  1   

30. DE V I A T I O N R A T IO ( DR )  Minimum bandwidth is greatest when maximum freq deviation is obtained with the maximum modulating signal frequency   Worst case modulation index and is equal to the maximum peak frequency deviation divided by the maximum modulating signal frequency Worst case modulation index produces the widest  output frequency spectrum Mathematically, max mod signal freq f m (max) DR  max peak freq deviation   f max

31.  P = V C /2R W 2  Thus the power contained in the FM signal is independent of the message signal. This is an important difference between FM and AM.  The time-average power of an FM signal m ay also be obtained from v FM ( t )  V c cos(2  f c t   ( t )) POWER IN ANGLE- MODULATED SIGNAL The power in an angle-modulated signal is easily computed

32. FM SIGNAL GENERATION They are two basic methods of generating frequency-Modulated signals: Direct Method Indirect Method

33. 13 A C cos(  C t )  C  2  f C A m cos(  m t ) A single tone frequency  m  2  f m (radians/sec) k f Carrier signal Carrier frequency Modulating wave m ( t ) Modulating frequency Deviation sensitivity Frequency deviation f m     max min 2  2  f   m  m  f  k A  k    f f m f i  f C  k f A m cos(  m t )  f C   f cos(  m t )                t  FM ( t )  A C  cos   C t  k f   m (  ) d     , generally Modulation Index Instantaneous frequency Remember Modulated wave F M C     ( t )  A C  cos   t          f m m m  k A sin(  t ) f  F M ( t )  A C   c os   C t   s i n (  m t )    Handout o r Equations for FM Wave with Single Tone Modulation