### AMPLITUDE MODULATION

```Signal Encoding Techniques
(modulation and encoding)
Analog
data to analog signal
(AM, FM, PM)
Digital
data to analog signal
Analog
data to digital signal
(PCM, DM)
Digital
data to digital signal
(line codes)
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Analog Signals
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Digital Signals
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By Ya
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Analog and Digital Transmission
AMPLITUDE MODULATION
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
Modulation


The process by which some characteristics of a carrier
wave is varied in accordance with an informationbearing signal.
Continuous-wave modulation
Amplitude modulation
 Frequency modulation


AM modulation family
Amplitude modulation (AM)
 Double sideband-suppressed carrier (DSB-SC)
 Single sideband (SSB)
 Vestigial sideband (VSB)

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AMPLITUDE MODULATION
Carrier wave: is a waveform (usually sinusoidal) that is modulated (modified)
with an input signal for the purpose of conveying information. This carrier wave
is usually a much higher frequency than the input signal.
1.

DEFINING AM
A carrier wave whose amplitude is varied in
proportion to the instantaneous amplitude of a
modulating voltage
GENERATING THE AM
nonlinear device: diode or transistor biased in its
nonlinear region
2.
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3. ANALYSIS OF THE AM WAVE
vc  Vc sin 2f c t
m
m
v  Vc sin 2f c t  Vc cos 2 ( f c  f s )t  Vc cos 2 ( f c  f s )t
2
2
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4. Different Carriers and AM
Carriers are spaced at 20 kHz, beginning at 100kHz.
Each carrier is modulated by a signal with 5kHz
bandwidth. Is there interference from sideband overlap?
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5. MODULATION INDEX AND SIGNAL POWER
Vm
Vmax  Vmin
m

Vc
Vmax  Vmin
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Moduiation Index and Power
2
carr
2
V
2
c
(Vc / 2 )
V
Pc 


R
R
2R
PLSB  PUSB
2
Vc
m


2R
4
2
C
2
2
2
PT
m  2(  1)
PC
V
m
m
PT 
(1 
)  Pc (1 
)
2R
2
2
PT
m
 1
Pc
2
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Current Calculations
2
IT
m
 1
Ic
2
Example
A carrier of 1000 W is modulated with a resulting
modulation index of 0. 8. What is the total power?
What is the carrier power if the total power is 1000 W
and the modulation index is 0.95?
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6.2 Double Sideband Suppressed Carrier
(DSBSC)
When the carrier is reduced, this is called doublesideband suppressed-carrier AM, or DSB-SC. If the
carrier could somehow be removed or reduced, the
transmitted signal would consist of two informationbearing sidebands, and the total transmitted power
would be information
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6.3 Single-Sideband (SSB)

suppressing the carrier and one of the sidebands
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6.4 Filtering the SSB LSB or USB

Dual Conversion: up-converting the modulating
frequency twice and selecting the upper or lower
sideband for transmission.
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AM: Features and Drawbacks:
the AM signal is greatly affected by noise
impossible to determine absolutely the original
signal level
conventional AM is not efficient in the use of
transmitter power
AM is useful where a simple, low-cost
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Angle Modulation
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ANGLE MODULATION:
The intelligence of the modulating signal can be
conveyed by varying the frequency or phase of the
carrier signal. When this is the case, we have
angle modulation, which can be subdivided into
two categories: frequency modulation (FM), and
phase modulation (PM).
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Frequency Modulation. The carrier's
instantaneous frequency deviation from its
unmodulated value varies in proportion to the
instantaneous amplitude of the modulating signal.
eFM  Ac sin(ct  m f sin mt )
Phase Modulation. The carrier's instantaneous
phase deviation from its unmodulated value
varies as a function of the instantaneous
amplitude of the modulating signal;
ePM  Ac sin(ct  m sin mt )
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FIGURE 4-1 The FM and PM waveforms for sine-wave modulation: (a) carrier
wave; (b) modulation wave; (c) FM wave; (d) PM wave. (Note: The derivative of
the modulating sine wave is the cosine wave shown by the dotted lines. The
PM wave appears to be frequency modulated by the cosine wave.)
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MODULATION INDEX

modulation index for an FM signal
mf 

fm
δ = maximum frequency deviation of the carrier caused
by the amplitude of the modulating signal
fm = frequency of the modulating signal
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FREQUENCY ANALYSIS OF THE FM WAVE
eFM  Ac J 0 sin  ct
 Ac {J 1 (m f )[sin(c  m )t  sin(c  m )t ]}
 Ac {J 2 (m f )[sin(c  2m )t  sin(c  2m )t ]}
 Ac {J 3 (m f )[sin(c  3m )t  sin(c  3 m )t ]}
 ..., etc

where: eFm = the instantaneous amplitude of the
modulated FM wave
Ac = the peak amplitude of the carrier
Jn = solution to the nth order Bessel function for a
modulation index mf.
mf = FM modulation index, Δf/fm
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Spectral components of a carrier of frequency, fc, frequency modulated by
a sine wave with frequency fm
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FM signal characters
• The FM wave is comprised of an infinite number of
sideband components
• bandwidth of an FM signal must be wider than that of
an AM signal
• As the modulation index increases from mf = 0, the
spectral energy shifts from the carrier frequency to
an increasing number of significant sidebands.
• Jn(mf) coefficients, decrease in value with increasing
order, n.
• negative Jn(mf) coefficients imply a 1800 phase
inversion.
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Carrier Frequency Eigenvalues

in some cases the carrier frequency component, JO, and
the various sidebands, Jn go to zero amplitudes at specific
values of m. These values are called eigenvalues.
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Bandwidth Requirements for FM

The higher the modulation index, the greater the
required system bandwidth
BW  2(n  f m )
where n is the highest number of significant
(least 1%, or -40 dB; (20 log 1/100 ), of the voltage of the unmodulated carrier)
sideband components and fm is the highest
modulation frequency.
Carson's Rule
BW  2(  f m )  2 f m (1  m f )
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Amplitude versus frequency spectrum for various modulation indices (fm
fixed, & varying): (a) mf = 0.25; (b) mf = 1; (c) mf = 2; (d) mf = 5; (e) mf = 10.
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Warren Hioki
Telecommunications,
Fourth Edition
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Upper Saddle River, New Jersey 07458
FIGURE 4-6
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•
The maximum permissible carrier deviation, δ, is ±75
kHz
•
Modulating frequencies (voice or music) is ranging from
50 Hz to 15 kHz
•
The modulation index can range from as low as 5 for fm
= 15 kHz (75 kHz/15 kHz) to as high as 1500 for fm = 50
Hz (75 kHz/50 Hz).
•
The ±75-kHz carrier deviation results in an FM
bandwidth requirement of 150 kHz for the receiver.
•
A 25-kHz guard band above and below the upper and
lower FM sidebands.
•
Total bandwidth of one channel is 200Hz.
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Narrowband FM (NBFM)




NBFM uses low modulation index values, with a
much smaller range of modulation index across all
values of the modulating signal.
An NBFM system restricts the modulating signal to
the minimum acceptable value, which is 300 Hz to
3 KHz for intelligible voice.
10 to 15 kHz of spectrum.
Used in police, fire, and Taxi radios, GSM, amateur
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POWER IN THE FM WAVE


power of the unmodulated carrier
Vcrms
PT 
R
For a modulated carrier
2
PT  PJ 0  PJ1  PJ 2  PJ 3  ...  PJ n

2
J0
V
R
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
2
J1
2V
R

2
J2
2V
R

2
J3
2V
R
 ... 
2
Jn
2V
R
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FM NOISE
 Increased
bandwidth of an FM – to enhance the signalto-noise ratio (SNR). Advantages of FM over AM.
 To
take this advantage, large mf is necessary– high
order sidebands are important – wider bandwidth is
required.
 Phase
Analysis of FM Noise
VN
  sin
Vc
1
where α = the maximum phase deviation of the carrier frequency caused by the
noise
VN = noise voltage
Vc= carrier voltage
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Phasor addition of noise on an FM signal’s carrier frequency causes a phase
shift, whose maximum value is .
Warren Hioki
Telecommunications,
Fourth Edition
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Upper Saddle River, New Jersey 07458
The ratio of carrier voltage to noise voltage,
Vc
Vn
is the SNR (voltage)
Vc
SNR 
VN
1
  sin
SNR
1
α represents the equivalent modulation index
produced by the noise.
 N    fm
SNRFM
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

N
39
• The effect of noise on an FM carrier signal is
directly proportional to the modulation frequency fm.


SNR 

 N   fm
Voice, data, and music contain many frequencies,
which are distributed throughout the given
modulation passband. Therefore, the SNR is not
uniform throughout.
To maintain a flat SNR, some techniques are
employed.
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