chapter 4 · chapter 4 amplitude modulation. ... define am concepts ... modulation index, voltage...
TRANSCRIPT
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Chapter 4
Amplitude Modulation
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Communication System Chart
Communication
System
Continuous Wave Digital Wave
Amplitude
Modulation
(AM)
Pulse
Modulation
(PM)
Angle
Modulation
Frequency
Modulation
(FM)
Analogue Pulse
Modulation
Digital Pulse
Modulation
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What is modulation?
“Modulation is defined as the process of modifying a carrier
wave (radio wave) systematically by the modulating signal
(audio)”
This process makes the signal suitable for the transmission and
compatible with the channel. The resultant signal is called the
modulated signal
In the other words, it is the process of changing/varying one of
the parameters of the carrier wave by the modulating signal
Introduction
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Modulation is operation performed at the transmitter to achieve efficient and reliable information transmission
For analogue modulation, it is frequency translation method caused by changing the appropriate quantity in a carrier signal
It involves two waveforms:
A modulating signal/baseband signal – represents the message
A carrier signal – depends on type of modulation
Introduction
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Introduction
Analogue modulations - frequency translation
methods caused by changing the appropriate
quantity in a carrier signal.
MODULATIONModulated
signal
Carrier
Baseband
signal
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Introduction
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•Once this information is received, the low frequency information
must be removed from the high frequency carrier.
•This process is known as “ Demodulation”.
Introduction
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Types of Modulation
Three main type of modulations:
Analog Modulation
Amplitude modulation
Example: Double sideband with carrier (DSB-WC), Double sideband suppressed carrier (DSB-SC), Single sideband suppressed carrier (SSB-SC), Vestigial sideband (VSB)
Angle modulation (frequency modulation & phase modulation)
Example: Narrow band frequency modulation (NBFM), Wideband frequency modulation (WBFM), Narrowband phase modulation (NBPM), Wideband phase modulation (NBPM)
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Types of Modulation
Pulse Modulation
Carrier is a train of pulses
Example: Pulse Amplitude Modulation (PAM), Pulse width modulation (PWM) , Pulse Position Modulation (PPM)
Digital Modulation
Modulating signal is analog Example: Pulse Code Modulation (PCM), Delta Modulation
(DM), Adaptive Delta Modulation (ADM), Differential Pulse Code Modulation (DPCM), Adaptive Differential Pulse Code Modulation (ADPCM) etc.
Modulating signal is digital (binary modulation) Example: Amplitude shift keying (ASK), frequency Shift Keying
(FSK), Phase Shift Keying (PSK) etc.
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Summary of Modulation Techniques
v(t) = V sin )2( ftASK FSK PSK
Digital Modulation
AM FM PM
Analogue Modulation
Volt Hertz Radians
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•Changing of the amplitude produces
Amplitude Modulation signal
•Changing of the frequency produces
Frequency Modulation signal
•Changing of the phase produces
Phase Modulation signal
Types of Modulation
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Learning Outcomes
Define AM concepts
Calculate the AM voltage distribution,
modulation index, voltage ,power
distribution
Calculate and draw AM in time and
frequency domain, bandwidth
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Revision..
Why do we need modulation?
What are the types of modulation?
What is AM?
What is bandwidth?
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Basic Amplitude Modulation
• Amplitude Modulation is the process of changing the Amplitude of a relatively high frequency carrier signal in accordance with the amplitude of the modulating signal (Information).
The carrier amplitude varied linearly by the modulating signal which usually consist of a range of a audio frequencies. The frequency of the carrier is not affected
Application of AM - Radio broadcasting, TV pictures
(video), facsimile transmission
Frequency range for AM - 535 kHz – 1600 kHz
Bandwidth - 10 kHz
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Amplitude Modulation
Various forms of Amplitude Modulation
• Conventional Amplitude Modulation (Alternativelyknown as Full AM or Double Sideband Large carriermodulation (DSBLC) /Double Sideband Full Carrier(DSBFC)
• Double Sideband Suppressed carrier (DSBSC)modulation
• Single Sideband (SSB) modulation
• Vestigial Sideband (VSB) modulation
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Amplitude Modulation ~ DSBFC (Full AM)
“Amplitude Modulation is the process of changing the
amplitude of the radio frequency (RF) carrier wave by the amplitude variations of modulating signal”
The carrier amplitude varied linearly by the modulating signal which usually consist of a range of a audio
frequencies. The frequency of the carrier is not affected
Application of AM - Radio broadcasting, TV pictures
(video), facsimile transmission
Frequency range for AM - 535 kHz – 1600 kHz
Bandwidth - 10 kHz
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17
Basic Amplitude Modulation
Envelope
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AM Envelope
Carrier
Envelope is the original modulating
signal
•Wave and the shape of the Modulated Wave is called AM Envelope.
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Amplitude Modulation – What really happened?? (you are not required to memorized this)
carrier
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We now know how AM wave looks like,
but how do we represent it
mathematically?
Can you write the general equation of a
sinusoid wave?
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The expression of voltage in the electric circuit is given
by :
or
V = Amplitude of the signal in Volts
f = The signal frequency in Herzt
(2ft + ) = The phase of the signal in radian
AM wave equation
)2cos()(
)2sin()(
ftVtv
ftVtv
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An unmodulated modulating signal :
vm (t) = Em sin (2fmt)
Or vm (t) = Vm sin (2fmt)
22
AM wave equation
Em = Vm= peak modulating signal amplitude(volts)
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AM Modulation
Envelope of the modulating signal varies above &
below the peak carrier amplitude
In general Em < Ec, otherwise distortion will occur.
The modulating signal values adds or subtracts from
the peak value of the carrier.
This instantaneous value either top or bottom voltage
envelope (new expression for Vm) :
)2sin(1
1
tfvvv
vvv
mmc
mc
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v1
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An unmodulated carrier (carrier signal) is described by the following equation :-
vc (t) = Ec sin (2fct)
Or vc (t) = Vc sin (2fct)
25
AM wave equation
Ec = Vc = peak carrier amplitude (volts)
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26
AM Concepts
Figure 3-3: Amplitude modulator showing input and output signals.
(Low frequency)
(High frequency)
(nonlinear devices)
carrier
Modulation x carrier
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The modulated wave can be expressed as :-
Vam(t) =[Ec + Em sin (2fmt)] (sin 2fct) .........(1)
WHERE:
Ec + Em sin (2fmt) = Amplitude of the modulated wave
Em = peak change in the amplitude of the envelope
fm = frequency of the modulating signal
27
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Expanding eq (1) we get:
28
AM wave equation
)2........()2sin()2sin()2sin( tftfEtfEV cmmccam
Carrier signalModulating
signal
Later we will see how this equation can be further improved to make it more
meaningful
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2
9
AM wave equation
)2)........(2sin()]2sin([ tftfEEV cmmcam
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AM Concepts
In AM, it is particularly important that the
peak value of the modulating signal be
less than the peak value of the carrier.
Vm < Vc
Distortion occurs when the amplitude of
the modulating signal is greater than the
amplitude of the carrier.
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The amplitude-modulated wave can then be expressed as
)cos()()cos()( ttvtVtv cmccAM
)cos()()( ttvVtv cmcAM
)cos()cos()( ttVVtv cmmcAM
tV
VtVtv m
c
mccAM cos1)cos()(
tmtVtv maccAM cos1)cos()(
Amplitude Modulation ~ DSBFC (Full AM)
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where notation m is termed the modulation index. It is
simply a measurement for the degree of modulation and
bears the relationship of Vm to Vc
c
ma
V
Vm
Therefore the full AM signal may be written as
tmtVtv maccAM cos(1)cos()(
Amplitude Modulation ~ DSBFC (Full AM)
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Modulation Index and Percentage of
Modulation
modulation index (m) is a value that describes the
relationship between the amplitude of the modulating signal and the amplitude of the carrier signal.
Percentage of modulation.
c
m
E
Em
100c
m
E
EM
modulating factor or
coefficient, or degree of
modulation.
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modulation index (m) can also calculate it using
34
Modulation Index and Percentage of
Modulation
mc
mc
EEV
EEV
min
max
minmax
minmax
minmax
minmax
21
21
VV
VV
VV
VVm
where
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• The modulating signal (information signal) is often a complex form consists of many sinusoidal wave with different Amplitude and Frequencies;
v(t) = V1sin(2f1t) + V2sin(2f2t) + V3sin(2f3t)+V4sin(2f4t) + V5sin(2f5t) + ….
• Thus, after modulation, the output wave will be in the form of :
vam(t) = Ecsin(2fct) - ½ m1Ec cos[2(fc+fm1)t] + ½m1Ec cos[2(fc-fm1)t] - ½ m2Ec cos[2(fc+fm2)t] +½ m2Ec cos[2(fc-fm2)t] - ½ m3Ec cos[2(fc+fm3)t]+ ½ m3 Ec cos[2(fc-fm3)t] - …
• The Total Modulation Index will be :
m = sqrt (m12 + m2
2 + m32 + mn
2)
Modulation of complex signal
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Modulation Index for Multiple
Modulating Frequencies Two or more sine waves of different, uncorrelated
frequencies modulating a single carrier is calculated
by the equation:
m m1
2m2
2
Modulation Index for Multiple Modulating Frequencies
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Consider
these
envelopes:
Do they
look the
same?
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Modulation Index and Percentage of
Modulation
Overmodulation and Distortion
The modulation index should be a number
between 0 and 1.
If the amplitude of the modulating voltage is
higher than the carrier voltage, m will be
greater than 1, causing distortion.
If the distortion is great enough, the
intelligence signal becomes unintelligible.
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Modulation Index and Percentage of
Modulation
Overmodulation and Distortion
Distortion of voice transmissions produces
garbled, harsh, or unnatural sounds in the
speaker.
Distortion of video signals produces a
scrambled and inaccurate picture on a TV
screen.
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Over Modulation
http://www.williamson-labs.com/480_am.htm
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Modulation Index and Percentage of
Modulation
Figure : Distortion of the envelope caused by overmodulation where the
modulating signal amplitude Vm is greater than the carrier signal Vc.
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AM Modulation
Draw AM wave in time domain and
frequency domain
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Voltage Distribution
An unmodulated carrier (carrier signal) is described by the following equation :-
Vc (t) = Ec sin (2fct)
The Amplitude of the AM Wave varies proportional to the amplitude of the modulation signal, and the maximum of the modulated wave equal to Ec + Em.
Thus the amplitude of the modulated wave can be expressed as :-
Vam(t) =[Ec + Emsin(2fmt)] sin (2fct)
Ec + Emsin(2fmt) Amplitude of modulated wave.
Em= Peak Change in the Amplitude of Envelope
fm= Frequency of Modulating signal
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Voltage Modulation
• Since Em = mEc and by developing the equation for modulated wave, the final equation of the modulated wave can be expressed in term of its Carrier Component and Side FrequenciesComponent (usf & lsf):-
Where Ecsin(2fct) carrier signal (V)
upper side frequency signal (V)
lower side frequency signal (V)
• Carrier wave is 90˚ out of phase with the upper and lower side frequencies
• The upper and lower side frequencies are 180 ˚ out of phase with each other
])(2cos[2
])(2cos[2
)2sin( tffmE
tffmE
tfEV mcc
mcc
ccam
])(2cos[2
tffmE
mcc
])(2cos[2
tffmE
mcc
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The frequency domain provides an alternative
description of signal in which the time axis is
replaced by a frequency axis.
Frequency Domain
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The relationship between the time
and frequency domains
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Sidebands and
the Frequency Domain
Side frequencies, or sidebands are generated as
part of the modulation process and occur in the
frequency spectrum directly above and below the
carrier frequency.
• Single-frequency sine-wave modulation generates two
sidebands.
• Complex wave (e.g. voice or video) modulation generates a
range of sidebands.
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Sidebands and
the Frequency Domain
Frequency
Amplitude
fLSB fC fUSB
fUSB = fc + fmfLSB = fc - fm
2
musblsb
EEE
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Sidebands and
the Frequency Domain
Figure : The AM wave is the
algebraic sum of the
carrier and upper and
lower sideband sine
waves.
(a) Intelligence or modulating
signal.
(b) Lower sideband.
(c ) Carrier.
(d ) Upper sideband.
(e ) Composite AM wave.
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Bandwidth
Signal bandwidth is an important characteristic of any
modulation scheme
In general, a narrow bandwidth is desirable
Bandwidth is calculated by:
mfB 2
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Bandwidth
Bandwidth is the difference between the upper and lower sideband frequencies.
BW = fUSB−fLSB
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Sidebands and the Frequency
Domain
Example:
A standard AM broadcast station is allowed to transmit modulating frequencies up to 5 kHz. If the AM station is transmitting on a frequency of 980 kHz, what are sideband frequencies and total bandwidth?
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54
fUSB = fc +fm =980 + 5 = 985 kHz
fLSB = fc -fm = 980 – 5 = 975 kHz
BW = fUSB – fLSB = 985 – 975 = 10 kHz
Or
BW = 2 (5 kHz) = 10 kHz
1. Highlight and identify important information in the question: fm
fc2. Use the formulas to solve the problem:
A standard AM broadcast station is allowed to transmit modulating frequencies up to 5 kHz. If the AM station is transmitting on a frequency of 980 kHz, what are sideband frequencies and total bandwidth?
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EXAMPLE :
AM DBSFC Modulator with a carrier frequency, fc = 100 kHz and maximum modulating signal frequency, fm of 10 kHz, determine the following :
a. LSB & USB
b. Bandwidth
c. Upper and Lower side frequencies if the modulating signal is a single frequency of 5kHz.
d. Draw the output frequency spectrum
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Solution:
Frequency
Lower side band Upper side bandCarrier
fc-fm(max fc+m(maxfcfLSF
fUSF
100kHz95kHz 105kHz90kHz 110kHz
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If fm consists of a range frequencies f1 to f2, the component of the sidebands become:
Upper sideband (USB) range is from (fc+f1) to (fc+f2)
Lower sideband (LSB) range is from (fc-f2) to (fc-f1)
Bandwidth for this case,B = (fc+f2) - (fc-f2)
= 2f2
AM spectrum when the modulating signal is a baseband signal from frequency f1 to f2
f1 f2 fc-f2 fc-f1 fc+f1 fc+f2
Amplitude,V Amplitude,V
Baseband signal lower sideband upper sideband
Modulatedsignal
freq freq
Amplitude Modulation
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For example, if voice signal with the band of frequency of
0 – 4 kHz is transmitted using a carrier of 100 kHz, the
modulated signal consists of
Carrier signal with frequency of 100 kHz
upper side band with frequency of range of 100 – 104 kHz
lower side band with frequency of range 96 – 100 kHz
The bandwidth is 104 – 96 = 8 kHz
Amplitude Modulation
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Given the first input to AM Modulator is 500 kHz Carrier signal
with Amplitude of 20V. The second input to AM Modulator is the
10kHz modulating signal with ± 7.5 Vp. Determine the following :-
a) USB & LSB
b) Modulation Index and percent modulation, M
c) Peak Amplitude of modulated carrier and Upper & Lower side
frequency voltage
d) Maximum & Minimum Amplitude of the envelope, Vmax and Vmin
e) Draw output in frequency domain & time domain
59
Group Activity
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(a) Upper and lower side frequencies:
(b) Modulation Index and percent modulation, M
60
Solution
%5.37100375.0
375.020
5.7
M
E
Em
c
m
kHzf
kHzf
lsb
usb
49010500
51010500
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(c) Peak Amplitude of modulated carrier and Upper & Lower side
frequency voltage
We can find Elsb and Eusb by using equation:
Thus
61
Solution (c)-method 1
pcc VulatedunEulatedE 20)mod()(mod
pm
usblsb VE
EE 75.32
5.7
2
2
musblsb
EEE
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(c) Peak Amplitude of modulated carrier and Upper &
Lower side frequency voltage
Let’s say Em is unknown. Em can be found from
Thus
62
Solution (c)- method 2
pc
usblsb VmE
EE 75.32
)20)(375.0(
2
cm
c
m mEEE
Em
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(d) Maximum & Minimum Amplitude of the
envelope, Vmax and Vmin
63
Solution
pmc
pmc
VEEV
VEEV
5.125.720
5.275.720
min
max
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(e) frequency domain
64
Solution
f (kHz)
Amplitude (Vp)
fLSB =490 fC = 500 fUSB = 510
3.75
20
3.75
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(e) time domain
65
Solution
Vmax=27.5 Vp Vmin =12.5 Vp
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Frequency
Amplitude
fLSB fC fUSB
How to
calculate AM
power ???
PT ????
Pc
PUSBPLSB
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AM Power
The AM signal is a composite of the
carrier and sideband signal voltages.
Each signal produces power in the
antenna.
Total transmitted power (PT) is the sum
of carrier power (Pc ) and power of the
two sidebands (PUSB and PLSB).
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AM Power
Power in a transmitter is important, but the most important power measurement is that of the portion that transmits the information
Power in an AM transmitter is calculated according to the formula at the right
Pt Pc 1m 2
2
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Measuring AM signal power
The greater the percentage of modulation, the higher the
sideband power and the higher the total power transmitted.
Power in each sideband is calculated
PSB = PLSB = PUSB = Pcm2 / 4
Maximum power appears in the sidebands when the carrier is
100 percent modulated.
Pc = (Vc )2 / 2R
where Pc = carrier power (W)
Vc =peak carrier voltage(V)
R= load resistance (Ohm)
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Measuring AM signal power
In reality it is difficult to determine AM
power by measuring the output voltage.
However, antenna current is easy to
measure and output power can be
expressed
where IT is measured RF current and R is antenna
impedance
22 where 1
2T T T c
mP I R I I
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AC average power dissipation
Recall that the average power dissipated
by resistor R is with a sinusoidal source
of amplitude Vpk is given
2
22pkrms
/ 2
2
pkV VVP
R R R
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AM signal power
Since the vAM is composed of three sinusoids
the total average power dissipated by the antenna R is
given
LSB USB
2 2 2
2 2 2
/ 2 / 2 2 / 2 2
2 8 8
T c
c m m
c m m
P P P P
V V V
R R R
V V V
R R R
AM sin 2 sin 2 ( ) sin 2 ( )2 2
m mc c c m c m
V Vv V f t f f t f f t
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AM signal power
Remembering that the modulation index
m = Vm /Vc we can write
The common term is the just the carrier
power, thus the total power can also be
written
2 2 2 2 2 2
12 8 8 2 4 4
c c c cT
V mV mV V m mP
R R R R
2
12
T C
mP P
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AM power efficiency
Therefore given the equation for power of
an AM waveform, the efficiency is:
It can be seen from this equation that the
efficiency of AM modulation increases as
the modulation index, μ, increases.
%1002
2
2
m
mh
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An AM transmitter has a carrier power of 30 W. The
percentage modulation is 85%. Calculate (a) the total
power, and (b) the power in one sideband.
Example Problem 1
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Time (sec)
Vo
ltag
e (V
)
0 1000 2000 3000 4000 5000 60000
0.1
0.2
0.3
0.4
0.5
Frequency (Hz)
Vo
ltag
e (V
)
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AM power efficiency
From the previous example, what percentage of the total
power was dedicated to transmitting the carrier?
Is any information conveyed by the carrier itself?
How could we maximize the power in the sidebands?
PT= 42.75 W
PUSB = 5.4 WPLSB = 5.4 W
Pc = 30 W
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AM power efficiency
Sideband power is maximized by setting m
= 1.
For m = 1, what percentage of the total
power is dedicated to the sidebands?
2
12
T c
mP P
2
4c
mP
2
4c
mP
cP
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AM power efficiency
At maximum modulation, the sideband power is at most
33% of the total transmitted power.
2
12
T c
mP P
2
4c
mP
2
4c
mP
cP
Percentage modulation (% m)
Per
cen
tag
e o
f to
tal
po
wer
(%
PT)
Power in sidebands (PSB
)
Power in carrier (Pc)
100 90 80 70 60 50 40 30 20 10 00
20
40
60
80
100
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AM power efficiency
Two-thirds of the power is wasted in the carrier.
Further, 100% modulation only occurs at peaks in the
modulating signal, thus the average sideband power is
considerably worse than the ideal.
0 0.5 1 1.5 2 2.5 3
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Time (sec)
Vo
ltag
e (V
)
Speech as a modulating signal100% modulation only occurs
at peaks
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Improving on AM
Besides the 67% power loss due to the carrier,
the sidebands contain redundant information.
To maximize the efficiency of AM we need to
Suppress the carrier
Eliminate one of the sidebands
AM modulated speech signal
Upper and lower
sidebands contain the
same information.
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Why is still widely used?
AM is still widely used because it is simple
and effective.
AM broadcast radio
CB radio (11m range)
TV broadcasting
Air traffic control radios
Garage door opens, keyless remotes
Aircraft VHF Communications Transceiver
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Types of AM
1) Double sideband full carrier (DSBFC)
- Contains USB, LSB and Carrier
- This is the most widely used type of AM modulation. In fact, all radio channels in the AM band use this type of modulation.
2) Double sideband suppressed carrier (DSBSC)
- Contains only USB & LSB
- A circuit that produces DSBSC is Balanced modulator
3) Single sideband (SSB)
- In this modulation, only half of the signal of the DSBSC is used
- Contains either LSB or USB
- Produce efficient system in term of power consumption and bandwidth
4) Vestigial Sideband (VSB):
- This is a modification of the SSB to ease the generation and reception of the signal.
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EXAMPLE :
For AM DSBFC wave with an unmodulated
carrier voltage, Vc = 10 Vp , a load resistance
of 10 and modulation index of 1, determine
the following :
a. Power of the carrier, and sideband
frequencies (Plsf & Pusf)
b. Total Power of sideband, PT
c. Draw Power Spectrum
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EXAMPLE :
An AM Transmitter has a carrier power output of 50W. Determine
the total power that produced 80% modulation.
SOLUTION :
1. Total Power is defined as :
PT = Pc[1 + (m2 /2)]
Thus,
PT = (50 W)[1 + ((0.8)2 /2)]
= 66 W
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EXAMPLE:
• For AM DSBFC transmitter with an unmodulated
carrier Power, Pc = 100 W is modulated
simultaneously with 3 other modulating signals with
coefficient index of m1 = 0.2, m1 = 0.4, m1 = 0.5,
determine the following :-
a. Total Modulation Index or Coefficient
b. Upper and Lower sideband power
c. Total transmitted power
m m1
2m2
2