ANGLE MODULATION EKT343 Principle of Communication
Engineering1
Slide 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.
EKT343 Principle of Communication Engineering2
Slide 3
Contd 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 EKT343 Principle of
Communication Engineering3
Slide 4
Contd 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. EKT343 Principle of Communication
Engineering4
Slide 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 EKT343 Principle of
Communication Engineering5
Slide 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 EKT343 Principle of Communication
Engineering6
Slide 7
Principles of FM Frequency deviation (f d ) 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.
Slide 8
Principles of FM EKT343 Principle of Communication Engineering8
Carrier Modulating Signal FM signal
Slide 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.
Slide 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.
Slide 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.
Slide 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.
Slide 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.
Slide 14
Principles of Phase Modulation Figure: Phase modulation of a
carrier by binary data produces PSK.
Slide 15
Mathematical analysis of FM Mathematical analysis: Let message
signal: And carrier signal: EKT343 Principle of Communication
Engineering15
Slide 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 EKT343 Principle of Communication
Engineering16
Slide 17
Mathematical analysis of FM Thus, we get the FM wave as: Where
modulation index for FM is given by EKT343 Principle of
Communication Engineering17
Slide 18
Mathematical analysis of FM Therefore: K 1 deviation
sensitivities Hz/V EKT343 Principle of Communication
Engineering18
Slide 19
Example 1 (FM) Determine the peak frequency deviation (f) and
modulation index (m) for an FM modulator with a deviation
sensitivity K 1 = 5 kHz/V and a modulating signal, EKT343 Principle
of Communication Engineering19
Slide 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: EKT343 Principle of Communication Engineering20
Slide 21
PM (contd) 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 m p =
Modulation index of phase modulation K is a constant and called
deviation sensitivities of the phase EKT343 Principle of
Communication Engineering21
Slide 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, EKT343 Principle of Communication
Engineering22
Slide 23
Summary of Mathematical Equation for FM and PM Summary of
Mathematical Equation for FM and PM EKT343 Principle of
Communication Engineering23 Tomasi Electronic Communications
Systems, 5e Copyright 2004 by Pearson Education, Inc. Upper Saddle
River, New Jersey 07458 All rights reserved.
Slide 24
Modulation Index and Sidebands 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.
Slide 25
Modulation Index and Sidebands Modulation Index The ratio of
the frequency deviation to the modulating frequency is known as the
modulation index (m f ). 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.
Slide 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.
Slide 27
FM&PM (Bessel function) Thus, for general equation: EKT343
Principle of Communication Engineering27
Slide 28
Bessel function EKT343 Principle of Communication
Engineering28
Slide 29
B.F. (contd) 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 f = modulation index EKT343 Principle of
Communication Engineering29
Slide 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 /2 = 1.57, or m f < /2. NBFM is
widely used in communication. It conserves spectrum space at the
expense of the signal-to-noise ratio.
Slide 31
B.F. (contd) EKT343 Principle of Communication Engineering
31
Slide 32
Bessel Functions of the First Kind, J n (m) for some value of
modulation index EKT343 Principle of Communication Engineering
32
Slide 33
Representation of frequency spectrum EKT343 Principle of
Communication Engineering33
Slide 34
Example 3 For an FM modulator with a modulation index m = 1, a
modulating signal v m (t) = V m sin(21000t), and an unmodulated
carrier v c (t) = 10 sin(2500kt). Determine the number of sets of
significant side frequencies and their amplitudes. Then, draw the
frequency spectrum showing their relative amplitudes. EKT343
Principle of Communication Engineering34
Slide 35
Comparison NBFM&WBFM EKT343 Principle of Communication
Engineering35 WBFMNBFM Modulation indexgreater than 10less than 1
Freq deviation75 kHz5 kHz Modulation frequency 30 Hz- 15 kHZ3 kHz
SpectrumInfinite no of sidebands and carrier Two sidebands and
carrier Bandwidth15 x NBFM 2( *fm (max)) 2 fm NoiseMore
suppressedLess suppressed ApplicationEntertainment &
Broadcasting Mobile communication
Slide 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
n1 EKT343 Principle of Communication Engineering36
Slide 37
FM Bandwidth (contd) Estimation of transmission b/w; Assume m f
is large and n is approximate m f + 2; thus B fm =2(m f + 2)f m =
(1) is called Carsons rule EKT343 Principle of Communication
Engineering37
Slide 38
Example 4 For an FM modulator with a peak frequency deviation,
f = 10 kHz, a modulating-signal frequency f m = 10 kHz, V c = 10 V
and a 500 kHz carrier, determine Actual minimum bandwidth from the
Bessel function table. Approximate minimum bandwidth using Carsons
rule. Plot the output frequency spectrum for the Bessel
approximation. EKT343 Principle of Communication Engineering38
Slide 39
Deviation Ratio (DR) The worse case modulation index which
produces the widest output frequency spectrum. Where f (max) = max.
peak frequency deviation f m(max) = max. modulating signal
frequency EKT343 Principle of Communication Engineering39
Slide 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. EKT343 Principle of Communication
Engineering40
Slide 41
Angle Modulation Part 2 Power distribution of FM Generation
& Demodulation of FM Noise in FM FM Threshold Effect Nonlinear
Effect Application of FM EKT343 Principle of Communication
Engineering41
Slide 42
FM Power Distribution As seen in Bessel function table, it
shows that as the sideband relative amplitude increases, the
carrier amplitude,J 0 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. EKT343
Principle of Communication Engineering42
Slide 43
FM Power Distribution (contd) 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, m f, 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. EKT343 Principle of Communication
Engineering43
Slide 44
Average Power The average power in unmodulated carrier The
total instantaneous power in the angle modulated carrier. The total
modulated power EKT343 Principle of Communication
Engineering44
Slide 45
Example 6 For an FM modulator with a modulation index m = 1, a
modulating signal v m (t) = V m sin(21000t) and an unmodulated
carrier v c (t) = 10sin(2500kt) Determine the unmodulated carrier
power for the FM modulator given with a load resistance, R L = 50 .
Determine also the total power in the angle-modulated wave. EKT343
Principle of Communication Engineering45
Slide 46
Quiz For an FM modulator with modulation index, m = 2,
modulating signal, v m (t) = V m cos(22000t) and an unmodulated
carrier, v c (t) = 10 cos(2800kt) Assume, R L =50 a) Determine the
number of sets of significant sidebands. b) Determine their
amplitudes. c) Draw the frequency spectrum showing the relative
amplitudes of the side frequencies. d) Determine the bandwidth. e)
Determine the total power of the modulated wave. EKT343 Principle
of Communication Engineering46
Slide 47
Generation of FM Two major FM generation: i) Direct method:
i)straight forward, requires a VCO whose oscillation frequency has
linear dependence on applied voltage. ii)Advantage: large frequency
deviation iii)Disadvantage: the carrier frequency tends to drift
and must be stabilized. iv)Common methods: i)FM Reactance
modulators ii)Varactor diode modulators EKT343 Principle of
Communication Engineering47
Slide 48
1) Reactance modulator Generation of FM (contd) EKT343
Principle of Communication Engineering48
Slide 49
2) Varactor diode modulator Generation of FM (contd) EKT343
Principle of Communication Engineering49
Slide 50
Generation of FM (contd) ii) Indirect method: i.Frequency-up
conversion. ii.Two ways: a.Heterodyne method b.Multiplication
method iii.One most popular indirect method is the Armstrong
modulator EKT343 Principle of Communication Engineering50
Slide 51
EKT343 Principle of Communication Engineering51 Wideband
Armstrong Modulator
Slide 52
A complete Armstrong modulator is supposed to provide a 75kHz
frequency deviation. It uses a balanced modulator and 90 o 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. Armstrong Modulator EKT343
Principle of Communication Engineering52
Slide 53
Generation of FM and PM EKT343 Principle of Communication
Engineering53
Slide 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. EKT343 Principle of Communication
Engineering54
Slide 55
FM detection (contd) 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.
EKT343 Principle of Communication Engineering55
Slide 56
PLL Demodulator EKT343 Principle of Communication Engineering56
Phase detector VCO Low pass filter Amplifier FM input Vc(t) f vco V
0 (t) fifi
Slide 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. EKT343 Principle of Communication Engineering57
Slide 58
PLL Demodulator Let instantaneous freq of FM Input, f i (t)=f c
+k 1 v m (t), and the VCO output frequency, f VCO (t)=f 0 + k 2 V c
(t); f 0 is the free running frequency. For the VCO frequency to
track the instantaneous incoming frequency, f vco = f i ; or ???
EKT343 Principle of Communication Engineering58
Slide 59
PLL Demodulator f 0 + k 2 V c (t)= f c +k 1 v m (t), so, If VCO
can be tuned so that f c =f 0, then Where Vc(t) is also taken as
the output voltage, which therefore is the demodulated output
EKT343 Principle of Communication Engineering59
Slide 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. EKT343 Principle of Communication
Engineering60
Slide 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. EKT343
Principle of Communication Engineering61
Slide 62
Noise in FM(Contd) 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: = f m 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 EKT343 Principle of Communication
Engineering62
Slide 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.
EKT343 Principle of Communication Engineering63
Slide 64
Noise-Suppression Effects of FM EKT343 Principle of
Communication Engineering64 Figure 5-11: An FM signal with
noise.
Slide 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 transmitters pre-emphasis circuit. Pre-emphasis provides more
amplification of only high-frequency components. EKT343 Principle
of Communication Engineering65
Slide 66
Noise-Suppression Effects of FM EKT343 Principle of
Communication Engineering66 Preemphasis circuit.
Slide 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. EKT343 Principle of Communication
Engineering67
Slide 68
Noise-Suppression Effects of FM EKT343 Principle of
Communication Engineering68 Deemphasis circuit.
Slide 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 EKT343 Principle of Communication
Engineering69
Slide 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. EKT343 Principle of Communication Engineering70
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.
Slide 71
Nonlinear Effect in FM 1. Strong nonlinearity; intentionally
introduced in a controlled manner. It is introduced for particular
application e.g. square law modulators, hard-limiters and frequency
multipliers. 2. 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 EKT343 Principle of
Communication Engineering71
Slide 72
Transfer characteristic of communication channel is given by
Where We know that EKT343 Principle of Communication
Engineering72
Slide 73
After filtering through bandpass filter, the fm signal output
Effect of nonlinearities: nonlinear nature of channel changes the
amplitudes of the FM signal EKT343 Principle of Communication
Engineering73
Slide 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. EKT343 Principle of Communication
Engineering74
Slide 75
Frequency Modulation Versus Amplitude Modulation Major
applications of AM and FM
Slide 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. EKT343 Principle of
Communication Engineering76
Slide 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.
EKT343 Principle of Communication Engineering77
Slide 78
Summary of angle modulation -what you need to be familiar with
EKT343 Principle of Communication Engineering78
Slide 79
Summary (contd) EKT343 Principle of Communication
Engineering79
Slide 80
Summary (contd) Bandwidth: a) Actual minimum bandwidth from
Bessel table: b) Approximate minimum bandwidth using Carsons rule:
EKT343 Principle of Communication Engineering80
Slide 81
Summary (contd) Multitone modulation (equation in general):
EKT343 Principle of Communication Engineering81
Slide 82
Summary (contd) EKT343 Principle of Communication
Engineering82
Slide 83
END OF ANGLE MODULATION EKT343 Principle of Communication
Engineering83
Slide 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. EKT343 Principle of
Communication Engineering84
Slide 85
Exercise 2 For an FM modulator with 40-kHz frequency deviation
and a modulating- signal frequency 10 kHz, determine the bandwidth
using both Carsons rule and Bessel table. EKT343 Principle of
Communication Engineering85
Slide 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.
EKT343 Principle of Communication Engineering86
Slide 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
Carsons rule EKT343 Principle of Communication Engineering87