AMPLITUDE MODULATION
Lecture Notes by:
Modulation Theory
What is MODULATION?
- A process by which a low frequency signal is made to change a property of a higher frequency signal to allow effective transmission and reception of the desired information.
- A process of imposing information contained in lower-frequency signal onto a higher frequency signal.
-The low frequency signal is called the modulating signal and the high frequency signal is called the carrier.
Why modulate?
1.) Direct transmission of low-frequency information signal would cause to interference problem since the resulting radio waves would all be at the same frequency range.
2.) Transmitting low-frequency information signal in free space is not practical since it will require a very high antenna.
Modulation Theory
Types of Modulation
A. Analog Modulation
I. Amplitude Modulation II. Angle Modulation
a.) Frequency Modulation b.) Phase Modulation B. Digital Modulation
fmt
2
sin
Vm
)
(
t
Vm
fct
2
sin
Vc
)
(
t
Vc
Amplitude Modulation
What is AMPLITUDE MODULATION?
-Type of analog modulation wherein the amplitude of the carrier signal is varied or changed according to the instantaneous amplitude of the
modulating signal.
- Process of modulation wherein the information is imposed on the carrier, causing the amplitude of the carrier to vary in accordance with the
modulating signal. Note that the carrier frequency remains constant during the modulation process.
Amplitude Modulation
MATHEMATICAL DESCRIPTION OF AN AM SIGNAL
Let:
fct
2
sin
A
)
(
t
AM
V
where: VAM is the Amplitude Modulated signal A is the instantaneousamplitude of the AM signal
fmt
2
sin
Vm
Vc
A
sin2 fmt Vc Vm 1 Vc A
fct
2
sin
fmt
2
sin
Vc
Vm
1
Vc
)
(
t
AM
V
but Vm / Vc is the modulation index, m.Amplitude Modulation
1
m
sin
2
fmt
sin
2
fct
Vc
)
(
t
AM
V
fct
2
sin
fmt]
2
sin
mVc
[Vc
)
(
t
AM
V
fct
2
sin
fmt
2
sin
mVc
fct
sin2
Vc
)
(
t
AM
V
Note: cos(X Y) 2 1 Y) -cos(X 2 1 Y sin X sin Let : fmt 2 Y and fct 2 X
fm)t
(fc
cos2
2
mVc
-fm)t
-(fc
cos2
2
mVc
fct
2
sin
Vc
)
(
t
AM
V
2 Vc ) rms ( C V 2 2 2 mVc ) rms ( LSB V ) rms ( USB V ; mVc ) pk ( LSB V ) pk ( USB V Amplitude Modulation
FREQUENCY SPECTRUM OF AN AM SIGNAL
BANDWIDTH = 2 fm
PERCENT MODULATION, %M AND MODULATION INDEX, m
- show the relationship between amplitudes of the modulating signal and carrier. Also referred to as
modulation factor or depth of modulation.
100
x
Vc
Vm
M
%
Vc
Vm
m
Amplitude Modulation
Vmin
Vmax
Vmin
-Vmax
m
where:Vmax is the maximum peak value of the AM wave Vmin is the minimum peak value of the AM wave
Amplitude Modulation
a) Undermodulation - %M < 100%, m < 1, Vm < Vc (practical)
b) 100% modulation - m = 1, Vm = Vc (ideal)
Three (3) degrees of modulation :
c) Over modulation – %M > 100%, m > 1, Vm > Vc (with distortion)
Amplitude Modulation
POWER CONTENT OF AN AM SIGNAL
USB LSB T
Pc
P
P
P
Where:PT = total transmitted power or total modulated power in Watts
PLSB, PUSB = lower and upper sideband power in Watts
Pc = unmodulated carrier power in Watts. Carrier
power remains the same, regardless of percent modulation.
Pc
2
m
US B
P
LS B
P
4
Pc
m
Pc
m
Pc
P
2 2 T
4
4
2
2 Tm
1
Pc
P
Amplitude Modulation
CALCULATION OF VOLTAGE IN AM SYSTEMS
2
m
1
Vc
v
2 T
where:vT = total transmitted voltage or total voltage of the modulated wave
Ic = unmodulated carrier voltage
Amplitude Modulation
CALCULATION OF CURRENTS IN AM SYSTEMS
m
1
Ic
I
2 T
2
where:IT = total transmitted current or total current of the modulated wave
Ic = unmodulated carrier current
m = modulation index
EFFICIENCY OF TRANSMISSION
-ratio of the total sideband power to the total transmitted power
SB T LSB USB T SB
P
%
100
x
P
P
P
100
x
P
P
(eta)
%
100
x
m
2
m
(eta)
%
2 2
m22Pc 4 Pc 2 m 4 Pc 2 m LSB P USB P SB P where:MODULATION BY A COMPLEX INFORMATION SIGNAL OR BY SEVERAL INFORMATION SIGNAL
Amplitude Modulation
The total modulating signal, The total modulation index, The total transmitted power, The total sideband power,
... 2 3 Vm 2 2 Vm 2 1 Vm t Vm ... 2 3 m 2 2 m 2 1 m t m 2 2 t m 1 Pc T P 2 Pc 2 t m t S B P
Amplitude Modulation
FORMS OF AMPLITUDE MODULATION TRANSMISSION
1. Double Sideband, Full Carrier Transmission (DSBFC) or A3 - Standard AM transmission
- Component of the AM wave being transmitted: USB, LSB and carrier signal - In conventional AM systems, at least two thirds of the transmitted power is in
the carrier. There is no information in the carrier; the sidebands contain the information. Also the information contained in the upper sideband is
identical to the information contained in the lower sideband.
USB LSB
T
Pc
P
P
P
2. Double Sideband, Suppressed Carrier Transmission (DSBSC)
- Component of the AM wave being transmitted: USB and LSB signals - Produced by balanced modulator
USB LSB
T
P
P
P
Amplitude Modulation
3. Single sideband, Full Carrier Transmission or H3E emission
- Form of amplitude modulation in which the carrier is transmitted at full power, but only one sideband is transmitted
USB T LSB T
Pc
P
or
P
Pc
P
P
4. Single Sideband, Suppressed Carrier Transmission (SSBSC) or J3E emission
- Form of amplitude modulation in which the carrier is totally suppressed and only one sideband is transmitted.
- It reduces the amount of power and bandwidth necessary to transmit a given amount of information.
- Used for radio communication.
USB T LSB T
P
or
P
P
P
5. Single sideband, Reduced Carrier Transmission or R3E
- Form of amplitude modulation in which one sideband is totally removed and the carrier voltage is reduced to approximately 10% of its unmodulated amplitude
Amplitude Modulation
6. Two independent sidebands, with an attenuated or suppressed carrier Transmission or B8E
- Also known as ISB (independent sideband emission).
- A form of amplitude modulation in which a single carrier frequency is independently modulated by two different modulating signals.
- Used for HF point to point radiotelephony 7. Vestigial Sideband Transmission or C3F
- Used for TV video transmission
- A form of amplitude modulation in which the carrier and one complete sideband are transmitted, but only part of the second sideband is
transmitted.
- Picture carrier and only a small vestige of the lower sideband is transmitted to conserve bandwidth.
8. Amplitude Compandored Single Sideband (ACSSB)
- recently developed AM system in which the speech signal is compressed at the transmitter and expanded at the receiver.
Amplitude Modulation
100
x
n
suppressio
without
power
Total
n
suppressio
during
saved
Power
S AVING
POWER
%
PERCENTAGE POWER SAVING
SINGLE SIDEBAND TRANSMITTER RATING
R
V
PK 22
PEP
Where: PEP = peak envelope power (W) Vpk = peak voltage (V)
SAMPLE PROBLEM:
1. An audio signal whose mathematical representation is 25 sin 21000t modulates a carrier described as 75 sin 2150000t. Determine the following:
a) sketch of the modulating signal b) sketch of the carrier
c) sketch of the AM wave
d) modulation index and percent modulation
e) instantaneous voltage equation of the AM signal f) frequency spectrum of the AM signal
g) bandwidth
2. An antenna transmit an AM signal having a total power content of 15KW. Determine the power being transmitted at the carrier and at each sideband when the %M is 85% and find the efficiency of transmission.
3. An AM signal contains 4000W at the carrier frequency and 1000 W in each of its sidebands. Determine the following:
a) total power of the AM signal b) %M and m
c) total power of the AM signal when the %M is changed to 70%
4. When a broadcast transmitter is 50% modulated, its total antenna current is 12 A. What is the carrier unmodulated current? What will be the total modulated current when the modulation depth is increased to 0.9?
5. A certain transmitter radiates 9KW with the carrier unmodulated, and 12KW when the carrier is sinusoidally modulated. Calculate the modulation index. If another sine wave, corresponding to 30% modulation, is transmitted simultaneously, determine the total modulation index and total radiated power. 6. The antenna current of an AM broadcast transmitter, modulated to a depth of
40% by an audio signal, is 10 A. It is increased to 12 A as a result of the simultaneous modulation by another sine wave. Determine the following:
a) Carrier current
b) Total modulation index
c) Modulation index due to the second wave
7. A SSB transmission contains 800W. This transmission is to replaced by a DSBFC AM signal with the same power content. Determine the power being transmitted at the carrier and at each sideband when the %M is 85%. Find the efficiency of transmission.
8. A SSB signal contains 10KW. How much power is contained in the sideband and how much at the carrier?
9. A 500 W carrier is modulated to a depth of 75%. Calculate the total power in the modulated wave in the following form of AM transmission.
a) DSBFC b) DSBSC c) SSBFC d) SSBSC
