![Frequency Modulation
The process of varying frequency of
accordance with the instantaneous values of
the carrier in
the
modulating signal.
Relation between angle and frequency :
Consider carrier signal c(t)= Ac Cos (wct+φ)
= Ac Cos (2πfct +φ)
Where, Wc= Carrier frequency
φ = Phase
C(t) = Ac Cos[ψ(t)], where, ψ(t)= wct+φ
i.e Frequency can be obtained by derivating angle and
angle can be obtained by integrating frequency.](https://image.slidesharecdn.com/ppt-3-230829145202-e4b1ff3b/85/Angle-modulation-pptx-3-320.jpg)
![Frequency Modulation
The angle of the carrier
written as,
after modulation can be
Frequency modulated signal can be written as,
AFM(t) = Ac Cos [ψi(t)] = Ac Cos [wct + kfʃm(t)dt]
Frequency Deviation in FM:
The instantaneous frequency, wi = wc + kf m(t)
= wc + Δw
Where, Δw = kf m(t) is called frequency deviation which
may be positive or negative depending on the sign of
m(t).](https://image.slidesharecdn.com/ppt-3-230829145202-e4b1ff3b/85/Angle-modulation-pptx-5-320.jpg)
![Phase Modulation
The process of varying the phase of carrier in accordance
with instantaneous values of the modulating signal.
Consider modulating signal x(t) and carrier signal c(t) =
Ac Coswct
Phase modulating signal,
APM(t) = Ac Cos[ ψi(t)]
Where, ψi(t) = wct + kpm(t)
Where, kp = Phase sensitivity factor in rad/volt
APM(t) = Ac Cos[wct + kpm(t)]](https://image.slidesharecdn.com/ppt-3-230829145202-e4b1ff3b/85/Angle-modulation-pptx-6-320.jpg)
![Frequency Spectrum of FM
Frequency spectrum is a graph of amplitude versus frequency.
The frequency spectrum of FM wave tells us about number of
sideband present in the FM wave and their amplitudes.
The expression for FM wave is not simple. It is complex because it
is sine of sine function.
Only solution is to use ‘Bessels Function’.
Equation (2.32) may be expanded as,
eFM = {A J0 (mf) sin ct
+ J1 (mf) [sin (c + m) t − sin (c − m) t]
+ J1 (mf) [sin (c + 2m) t + sin (c − 2m) t]
+ J3 (mf) [sin (c + 3m) t − sin (c − 3m) t]
+ J4 (mf) [sin (c + 4m) t + sin (c − 4m) t]
+ } (2.33)
From this equation it is seen that the FM wave consists of:
(i)Carrier (First term in equation).
(ii)Infinite number of sidebands (All terms except first term are
sidebands).
The amplitudes of carrier and sidebands depend on ‘J’ coefficient.
c = 2fc, m = 2fm
So in place of c and m, we can use fc and fm.](https://image.slidesharecdn.com/ppt-3-230829145202-e4b1ff3b/85/Angle-modulation-pptx-11-320.jpg)
![Types of Frequency Modulation
FM (Frequency Modulation)
Narrowband
FM (NBFM)
[Whenmodulation indexissmall]
WidebandFM
(WBFM)
[Whenmodulationindexislarge]](https://image.slidesharecdn.com/ppt-3-230829145202-e4b1ff3b/85/Angle-modulation-pptx-15-320.jpg)
Angle modulation .pptx
- 1. ANALOG COMMUNICATION SYSTEMS By Ms. Swati Shrrpal Halunde Assistant Professor DEPT. of E.C.E S.I.T.C.O.E. Yadrav- Ichalkaranji ANGLE MODULATION
- 2. ANGLE MODULATION Angle modulation is a process carrier in accordance with the modulating signal. of varying angle of the instantaneous values of Angle can be varied by varying frequency or phase. Angle modulation is of 2 types. • Frequency Modulation • Phase Modulation
- 3. Frequency Modulation The process of varying frequency of accordance with the instantaneous values of the carrier in the modulating signal. Relation between angle and frequency : Consider carrier signal c(t)= Ac Cos (wct+φ) = Ac Cos (2πfct +φ) Where, Wc= Carrier frequency φ = Phase C(t) = Ac Cos[ψ(t)], where, ψ(t)= wct+φ i.e Frequency can be obtained by derivating angle and angle can be obtained by integrating frequency.
- 4. Frequency Modulation Frequency modulator converts input voltage into frequency i.e the amplitude of modulating signal m(t) changes to frequency at the output. Consider carrier signal c(t) =Ac Coswct The frequency variation at the output is called instantaneous frequency and is expressed as, wi = wc + kf m(t) Where, kf = frequency sensitivity factor in Hz/volt
- 5. Frequency Modulation The angle of the carrier written as, after modulation can be Frequency modulated signal can be written as, AFM(t) = Ac Cos [ψi(t)] = Ac Cos [wct + kfʃm(t)dt] Frequency Deviation in FM: The instantaneous frequency, wi = wc + kf m(t) = wc + Δw Where, Δw = kf m(t) is called frequency deviation which may be positive or negative depending on the sign of m(t).
- 6. Phase Modulation The process of varying the phase of carrier in accordance with instantaneous values of the modulating signal. Consider modulating signal x(t) and carrier signal c(t) = Ac Coswct Phase modulating signal, APM(t) = Ac Cos[ ψi(t)] Where, ψi(t) = wct + kpm(t) Where, kp = Phase sensitivity factor in rad/volt APM(t) = Ac Cos[wct + kpm(t)]
- 7. Phase Modulation Frequency deviation in PM: Conversion between Frequency and Phase Modulation:
- 8. Modulation Index Definition: Modulation Index is defined as the ratio of frequency deviation () to the modulating frequency (fm). M.I.=Frequency Deviation Modulating Frequency mf =δ fm In FM M.I.>1 Modulation Index of FM decides − (i)Bandwidth of the FM wave. (ii)Number of sidebands in FM wave.
- 9. Deviation Ratio The modulation index corresponding to maximum deviation and maximum modulating frequency is called deviation ratio. Deviation Ratio= Maximum Deviation Maximum modulating Frequency = δmax fmax In FM broadcasting the maximum value of deviation is limited to 75 kHz. The maximum modulating frequency is also limited to 15 kHz.
- 10. Percentage M.I. of FM The percentage modulation is defined as the ratio of the actual frequency deviation produced by the modulating signal to the maximum allowable frequency deviation. % M.I = Actual deviation Maximum allowable deviation
- 11. Frequency Spectrum of FM Frequency spectrum is a graph of amplitude versus frequency. The frequency spectrum of FM wave tells us about number of sideband present in the FM wave and their amplitudes. The expression for FM wave is not simple. It is complex because it is sine of sine function. Only solution is to use ‘Bessels Function’. Equation (2.32) may be expanded as, eFM = {A J0 (mf) sin ct + J1 (mf) [sin (c + m) t − sin (c − m) t] + J1 (mf) [sin (c + 2m) t + sin (c − 2m) t] + J3 (mf) [sin (c + 3m) t − sin (c − 3m) t] + J4 (mf) [sin (c + 4m) t + sin (c − 4m) t] + } (2.33) From this equation it is seen that the FM wave consists of: (i)Carrier (First term in equation). (ii)Infinite number of sidebands (All terms except first term are sidebands). The amplitudes of carrier and sidebands depend on ‘J’ coefficient. c = 2fc, m = 2fm So in place of c and m, we can use fc and fm.
- 12. Fig. : Ideal Frequency Spectrum of FM
- 13. Bandwidth of FM From frequency spectrum of FM wave shown in Fig. 2.26, we can say that the bandwidth of FM wave is infinite. But practically, it is calculated based on how many sidebands have significant amplitudes. (i)The Simple Method to calculate the bandwidth is − BW=2fmx Number of significant sidebands --(1) With increase in modulation index, the number of significant sidebands increases. So that bandwidth also increases. (ii)The second method to calculate bandwidth is by Carson’s rule.
- 14. Carson’s rule states that, the bandwidth of FM wave is twice the sum of deviation and highest modulating frequency. BW=2( +fmmax) (2) Highest order side band = To be found from table 2.1 after the calculation of modulation Index m where, m = /fm e.g. If m= 20KHZ/5KHZ From table, for modulation index 4, highest order side band is 7th. Therefore, the bandwidth is B.W. = 2 fm Highest order side band =2 5 kHz 7 =70 kHz
- 15. Types of Frequency Modulation FM (Frequency Modulation) Narrowband FM (NBFM) [Whenmodulation indexissmall] WidebandFM (WBFM) [Whenmodulationindexislarge]
- 16. Comparison between Narrowband and Wideband FM Sr. No. Parameter NBFM WBFM 1. Modulation index Less than or slightly greater than 1 Greater than 1 2. Maximum deviation 5 kHz 75 kHz 3. Range of modulating frequency 20 Hz to 3 kHz 20 Hz to 15 kHz 4. Maximum modulation index Slightly greater than 1 5 to 2500 5. Bandwidth Small approximately same as that of AM BW = 2fm Large about 15 times greater than that of NBFM. BW = 2(+fmmax) 6. Applications FM mobile communication like police wireless, ambulance, short range ship to shore communication etc. Entertainment broadcasting (can be used for high quality music transmission)
- 17. Representation of FM FM can be represented by two ways: 1. Time domain. 2. Frequency domain. 1.FM in Time Domain Time domain representation means continuous variation of voltage with respect to time as shown in Fig. . Fig. 1 FM in Time Domain 2.FM in Frequency Domain • Frequency domain is also known as frequency spectrum. • FM in frequency domain means graph or plot of amplitude versus frequency as shown in Fig. 2.29. Fig. 2: FM in Frequency Domain