1. CHAPTER 3 ANGLE MODULATION
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2. Introduction
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.
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3. Cont’d… classified into two types such as Used for :
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
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4. Cont’d… Advantages over AM:
Freedom from interference: all natural and external noise consist of amplitude variations, thus receiver usually cannot distinguish between amplitude of noise or desired signal. AM is noisy than FM.
Operate in very high frequency band (VHF): 88MHz-108MHz
Can transmit musical programs with higher degree of fidelity.
fidelity
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5. Principles of FM
A sine wave carrier can be modified for the purpose of transmitting information from one place to another by varying its frequency. This is known as frequency modulation (FM).
In FM, the carrier amplitude remains constant and the carrier frequency is changed by the modulating signal
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6. Principles of FM
As the amplitude of the information signal varies, the carrier frequency shifts proportionately.
As the modulating signal amplitude increases, the carrier frequency increases.
With no modulation the carrier is at its normal center or resting frequency
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7. Principles of FM
Frequency deviation (fd) is the amount of change in carrier frequency produced by the modulating signal.
The frequency deviation rate is how many times per second the carrier frequency deviates above or below its center frequency.
The frequency of the modulating signal determines the frequency deviation rate.
A type of modulation called frequency-shift keying (FSK) is used in transmission of binary data in digital cell phones and low- speed computer modems.

8. Principles of FM Carrier Modulating Signal FM signal
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9. Principles of Phase Modulation
When the amount of phase shift of a constant-frequency carrier is varied in accordance with a modulating signal, the resulting output is a phase-modulation (PM) signal.
Phase modulators produce a phase shift which is a time separation between two sine waves of the same frequency.
The greater the amplitude of the modulating signal, the greater the phase shift.

10. Principles of Phase Modulation
The maximum frequency deviation produced by a phase modulator occurs during the time that the modulating signal is changing at its most rapid rate.

11. Principles of Phase Modulation
Figure : A frequency shift occurs in PM only when the modulating signal amplitude varies. (a) Modulating signal. (b) FM signal. (c) PM signal.

12. Principles of Phase Modulation
Converting PM into FM
In order to make PM compatible with FM, the deviation produced by frequency variations in the modulating signal must be compensated for.
This compensation can be accomplished by passing the intelligence signal through a low-pass RC network.
This RC low-pass filter is called a frequency- correcting network, predistorter, or 1/f filter and causes the higher modulating frequencies to be attenuated.
The FM produced by a phase modulator is called indirect FM.

13. Principles of Phase Modulation
Phase-Shift Keying
The process of phase modulating a carrier with binary data is called phase-shift keying (PSK) or binary phase-shift keying (BPSK).
The PSK signal has a constant frequency, but the phase of the signal from some reference changes as the binary modulating signal occurs.

14. Principles of Phase Modulation
Figure: Phase modulation of a carrier by binary data produces PSK.

15. Mathematical analysis of FM
Let message signal:
And carrier signal:
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16. Mathematical analysis of FM
During the process of frequency modulations the frequency of carrier signal is changed in accordance with the instantaneous amplitude of message signal. Therefore the frequency of carrier after modulation is written as
To find the instantaneous phase angle of modulated signal, integrate equation above w.r.t. t
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17. Mathematical analysis of FM
Thus, we get the FM wave as:
Where modulation index for FM is given by
K1 = rad/s/V
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18. Mathematical analysis of FM
Therefore:
K1 – deviation sensitivities Hz/V
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19. Example 1 (FM)
Determine the peak frequency deviation (∆f) and modulation index (m) for an FM modulator with a deviation sensitivity K1 = 5 kHz/V and a modulating signal,
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20. Mathematical analysis of PM
The process by which changing the phase of carrier signal in accordance with the instantaneous of message signal. The amplitude remains constant after the modulation process.
Mathematical analysis:
Let message signal:
And carrier signal:
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21. PM (cont’d)
Where = phase angle of carrier signal. It is changed in accordance with the amplitude of the message signal;
i.e.
After phase modulation the instantaneous voltage will be or
Where mp = Modulation index of phase modulation
K is a constant and called deviation sensitivities of the phase
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22. Example 2 (PM)
Determine the peak phase deviation (m) for a PM modulator with a deviation sensitivity K = 2.5 rad/V and a modulating signal,
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23. Summary of Mathematical Equation for FM and PM
Tomasi Electronic Communications Systems, 5e
Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey All rights reserved.
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24. Modulation Index and Sidebands
Any modulation process produces sidebands.
When a constant-frequency sine wave modulates a carrier, two side frequencies are produced.
Side frequencies are the sum and difference of the carrier and modulating frequency.
The bandwidth of an FM signal is usually much wider than that of an AM signal with the same modulating signal.

25. Modulation Index and Sidebands
The ratio of the frequency deviation to the modulating frequency is known as the modulation index (mf).
In most communication systems using FM, maximum limits are put on both the frequency deviation and the modulating frequency.
In standard FM broadcasting, the maximum permitted frequency deviation is 75 kHz and the maximum permitted modulating frequency is 15 kHz.
The modulation index for standard FM broadcasting is therefore 5.

26. Modulation Index and Sidebands
Bessel Functions
The equation that expresses the phase angle in terms of the sine wave modulating signal is solved with a complex mathematical process known as Bessel functions.
Bessel coefficients are widely available and it is not necessary to memorize or calculate them.

27. FM&PM (Bessel function)
Thus, for general equation:
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28. Bessel function
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29. 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
Mf = modulation index
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30. Modulation Index and Sidebands
Bessel Functions
The symbol ! means factorial. This tells you to multiply all integers from 1 through the number to which the symbol is attached. (e.g. 5! Means 1 × 2 × 3 × 4 × 5 = 120)
Narrowband FM (NBFM) is any FM system in which the modulation index is less than π/2 = 1.57, or
mf < π /2.
NBFM is widely used in communication. It conserves spectrum space at the expense of the signal-to-noise ratio.

31. B.F. (cont’d)
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32. Bessel Functions of the First Kind, Jn(m) for some value of modulation index
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33. Representation of frequency spectrum
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34. Example 3
For an FM modulator with a modulation index m = 1, a modulating signal vm(t) = Vm sin(2π1000t), and an unmodulated carrier vc(t) = 10 sin(2π500kt). Determine the number of sets of significant side frequencies and their amplitudes. Then, draw the frequency spectrum showing their relative amplitudes.
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35. Comparison NBFM&WBFM WBFM NBFM Modulation index greater than 10
less than 1
Freq deviation
75 kHz
5 kHz
Modulation frequency
30 Hz- 15 kHZ
3 kHz
Spectrum
Infinite no of sidebands and carrier
Two sidebands and carrier
Bandwidth
15 x NBFM
2(δ*fm (max))
2 fm
Noise
More suppressed
Less suppressed
Application
Entertainment & Broadcasting
Mobile communication
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36. FM Bandwidth
Theoretically, the generation and transmission of FM requires infinite bandwidth. Practically, FM system have finite bandwidth and they perform well.
The value of modulation index determine the number of sidebands that have the significant relative amplitudes
If n is the number of sideband pairs, and line of frequency spectrum are spaced by fm, thus, the bandwidth is:
For n≥1
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37. FM Bandwidth (cont’d) Estimation of transmission b/w;
Assume mf is large and n is approximate mf + 2; thus
Bfm=2(mf + 2)fm =
(1) is called Carson’s rule
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38. Example 4
For an FM modulator with a peak frequency deviation, Δf = 10 kHz, a modulating-signal frequency fm = 10 kHz,
Vc = 10 V and a 500 kHz carrier, determine
Actual minimum bandwidth from the Bessel function table.
Approximate minimum bandwidth using Carson’s rule.
Plot the output frequency spectrum for the Bessel approximation.
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39. Deviation Ratio (DR)
The worse case modulation index which produces the widest output frequency spectrum.
Where
∆f(max) = max. peak frequency deviation
fm(max) = max. modulating signal frequency
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40. Example 5
Determine the deviation ratio and bandwidth for the worst-case (widest-bandwidth) modulation index for an FM broadcast-band transmitter with a maximum frequency deviation of 75 kHz and a maximum modulating-signal frequency of 15 kHz.
Determine the deviation ratio and maximum bandwidth for an equal modulation index with only half the peak frequency deviation and modulating-signal frequency.
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41. Angle Modulation Part 2 Power distribution of FM
Generation & Demodulation of FM
Noise in FM
FM Threshold Effect
Nonlinear Effect
Application of FM
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42. FM Power Distribution
As seen in Bessel function table, it shows that as the sideband relative amplitude increases, the carrier amplitude,J0 decreases.
This is because, in FM, the total transmitted power is always constant and the total average power is equal to the unmodulated carrier power, that is the amplitude of the FM remains constant whether or not it is modulated.
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43. FM Power Distribution (cont’d)
In effect, in FM, the total power that is originally in the carrier is redistributed between all components of the spectrum, in an amount determined by the modulation index, mf, and the corresponding Bessel functions.
At certain value of modulation index, the carrier component goes to zero, where in this condition, the power is carried by the sidebands only.
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44. Average Power The average power in unmodulated carrier
The total instantaneous power in the angle modulated carrier.
The total modulated power
Po = (Jo*Vc)^2/2R, Pn = 2(Jn*Vn)^2/2R
AVERAGE POWER = ~ UNMODULATED CARRIER POWER
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45. Example 6
For an FM modulator with a modulation index m = 1, a modulating signal
vm(t) = Vmsin(2π1000t)
and an unmodulated carrier
vc(t) = 10sin(2π500kt)
Determine the unmodulated carrier power for the FM modulator given with a load resistance, RL = 50Ω. Determine also the total power in the angle-modulated wave.
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46. Quiz For an FM modulator with modulation index,
m = 2, modulating signal,
vm(t) = Vmcos(2π2000t)
and an unmodulated carrier,
vc(t) = 10 cos(2π800kt)
Assume, RL=50Ω
Determine the number of sets of significant sidebands.
Determine their amplitudes.
Draw the frequency spectrum showing the relative amplitudes of the side frequencies.
Determine the bandwidth.
Determine the total power of the modulated wave.
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47. Generation of FM Two major FM generation: Direct method:
straight forward, requires a VCO whose oscillation frequency has linear dependence on applied voltage.
Advantage: large frequency deviation
Disadvantage: the carrier frequency tends to drift and must be stabilized.
Common methods:
FM Reactance modulators
Varactor diode modulators
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48. Generation of FM (cont’d)
1) Reactance modulator
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49. Generation of FM (cont’d)
2) Varactor diode modulator
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50. Generation of FM (cont’d)
ii) Indirect method:
Frequency-up conversion.
Two ways:
Heterodyne method
Multiplication method
One most popular indirect method is the Armstrong modulator
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51. Wideband Armstrong Modulator
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52. Armstrong Modulator
A complete Armstrong modulator is supposed to provide a 75kHz frequency deviation. It uses a balanced modulator and 90o phase shifter to phase-
modulate a crystal oscillator. Required deviation is obtained by combination of multipliers and mixing, raise the signal from
suitable for broadcasting.
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53. Generation of FM and PM
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54. FM Detection/Demodulation
FM demodulation
is a process of getting back or regenerate the original modulating signal from the modulated FM signal.
It can be achieved by converting the frequency deviation of FM signal to the variation of equivalent voltage.
The demodulator will produce an output where its instantaneous amplitude is proportional to the instantaneous frequency of the input FM signal.
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55. FM detection (cont’d)
To detect an FM signal, it is necessary to have a circuit whose output voltage varies linearly with the frequency of the input signal.
The most commonly used demodulator is the PLL demodulator. Can be use to detect either NBFM or WBFM.
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56. PLL Demodulator fvco V0(t) FM input Low pass Amplifier fi Phase filter
detector
fvco
VCO
Vc(t)
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57. PLL Demodulator
The phase detector produces an average output voltage that is linear function of the phase difference between the two input signals. Then low frequency component is pass through the LPF to get a small dc average voltage to the amplifier.
After amplification, part of the signal is fed back through VCO where it results in frequency modulation of the VCO frequency. When the loop is in lock, the VCO frequency follows or tracks the incoming frequency.
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58. PLL Demodulator Let instantaneous freq of FM Input, fi(t)=fc +k1vm(t),
and the VCO output frequency,
f VCO(t)=f0 + k2Vc(t);
f0 is the free running frequency.
For the VCO frequency to track the instantaneous incoming frequency,
fvco = fi; or ???
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59. PLL Demodulator f0 + k2Vc(t)= fc +k1vm(t), so,
If VCO can be tuned so that fc=f0, then
Where Vc(t) is also taken as the output voltage, which therefore is the demodulated output
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60. Noise in FM
Noise is interference generated by lightning, motors, automotive ignition systems, and power line switching that produces transient signals.
Noise is typically narrow spikes of voltage with high frequencies.
Noise (voltage spikes) add to a signal and interfere with it.
Some noise completely obliterates signal information.
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61. Noise in FM
In AM systems, noise easily distorts the transmitted signal however, in FM systems any added noise must create a frequency deviation in order to be perceptible. θ
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62. Noise in FM(Cont’d) δ = θfm
The maximum frequency deviation due to random noise occurs when the noise is at right angles to the resultant signal. In the worst case the signal frequency has been deviated by:
δ = θfm
This shows that the deviation due to noise increases as the modulation frequency increases. Since noise power is the square of the noise voltage, the signal to noise ratio can significantly degrade.
Noise occurs predominantly at the highest frequencies within the baseband
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63. Noise-Suppression Effects of FM
FM signals have a constant modulated carrier amplitude.
FM receivers contain limiter circuits that deliberately restrict the amplitude of the received signal.
Any amplitude variations occurring on the FM signal are effectively clipped by limiter circuits.
This amplitude clipping does not affect the information content of the FM signal, since it is contained solely within the frequency variations of the carrier.
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64. Noise-Suppression Effects of FM
Figure 5-11: An FM signal with noise.
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65. Noise-Suppression Effects of FM
Preemphasis
Noise can interfere with an FM signal and particularly with the high-frequency components of the modulating signal.
Noise is primarily sharp spikes of energy and contains a lot of harmonics and other high-frequency components.
To overcome high-frequency noise, a technique known as preemphasis is used.
A simple high-pass filter can serve as a transmitter’s pre-emphasis circuit.
Pre-emphasis provides more amplification of only high-frequency components.
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66. Noise-Suppression Effects of FM
Preemphasis circuit.
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67. Noise-Suppression Effects of FM
Preemphasis
A simple low-pass filter can operate as a deemphasis circuit in a receiver.
A deemphasis circuit returns the frequency response to its normal flat level.
The combined effect of preemphasis and deemphasis is to increase the signal-to-noise ratio for the high-frequency components during transmission so that they will be stronger and not masked by noise.
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68. Noise-Suppression Effects of FM
Deemphasis circuit.
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69. FM threshold effect
In FM systems where the signal level is well above noise received carrier-to-noise ratio and demodulated signal-to-noise ratio are related by:
= signal-to-noise ratio at output of FM demodulator
= modulation index
= carrier-to-noise ratio at input of FM demodulator
Does not apply when the carrier-to-noise ratio decreases below a certain point. Below this critical point the signal-to-noise ratio decreases significantly.
Known as the FM threshold effect
(FM threshold is usually defined as the carrier-to-noise ratio at which the demodulated signal-to-noise ratio fall 1 dB below the linear relationship given in equation. It generally is considered to occur at about 10 dB).
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70. Below the FM threshold point the noise signal (whose amplitude and phase are randomly varying), may instantaneously have an amplitude greater than that of the wanted signal.
When this happens the noise will produce a sudden change in the phase of the FM demodulator output.
In an audio system this sudden phase change makes a "click". In video, the term "click noise" is used to describe short horizontal black and white lines that appear randomly over a picture.
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71. Nonlinear Effect in FM
Strong nonlinearity; intentionally introduced in a controlled manner. It is introduced for particular application e.g. square law modulators, hard-limiters and frequency multipliers.
Weak nonlinearity; introduced because of imperfections in the communication channel. Such linearities reduce the useful signal levels.
In next slide, we will examine the effects of weak nonlinearities on FM signal
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72. Transfer characteristic of communication channel is given by Where We know that
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73. After filtering through bandpass filter, the fm signal output
Effect of nonlinearities: nonlinear nature of channel changes the amplitudes of the FM signal
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74. Application of FM
FM is commonly used at VHF radio frequencies for high-fidelity broadcasts of music and speech (FM broadcasting). Normal (analog) TV sound is also broadcast using FM. The type of FM used in broadcast is generally called wide-FM, or W-FM
A narrowband form is used for voice communications in commercial and amateur radio settings. In two-way radio, narrowband narrow-fm (N-FM) is used to conserve bandwidth. In addition, it is used to send signals into space.
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75. Frequency Modulation Versus Amplitude Modulation
Major applications of AM and FM

76. Advantages
Wideband FM gives significant improvement in the SNR at the output of the RX which proportional to the square of modulation index.
Angle modulation is resistant to propagation-induced selective fading since amplitude variations are unimportant and are removed at the receiver using a limiting circuit.
Angle modulation is very effective in rejecting interference. (minimizes the effect of noise).
Angle modulation allows the use of more efficient transmitter power in information.
Angle modulation is capable of handing a greater dynamic range of modulating signal without distortion than AM.
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77. Disadvantages
Angle modulation requires a transmission bandwidth much larger than the message signal bandwidth.
Angle modulation requires more complex and expensive circuits than AM.
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78. Summary of angle modulation -what you need to be familiar with
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79. Summary (cont’d)
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80. Summary (cont’d) Bandwidth:
Actual minimum bandwidth from Bessel table:
b) Approximate minimum bandwidth using Carson’s rule:
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81. Summary (cont’d) Multitone modulation (equation in general):
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82. Summary (cont’d)
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83. END OF ANGLE MODULATION
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84. Exercise 1
Determine the deviation ratio and worst-case bandwidth for an FM signal with a maximum frequency deviation 25 kHz and maximum modulating signal 12.5 kHz.
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85. Exercise 2
For an FM modulator with 40-kHz frequency deviation and a modulating-signal frequency 10 kHz, determine the bandwidth using both Carson’s rule and Bessel table.
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86. Exercise 3
For an FM modulator with an unmodulated carrier amplitude 20 V, a modulation index, m = 1, and a load resistance of 10-ohm, determine the power in the modulated carrier and each side frequency, and sketch the power spectrum for the modulated wave.
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87. Exercise 4
A frequency modulated signal (FM) has the following expression:
The frequency deviation allowed in this system is 75 kHz. Calculate the:
Modulation index
Bandwidth required, using Carson’s rule
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