Amplitude Modulation

AMPLITUDE MODULATIONLecture Notes by:

Engr. Analene M. Nagayo

Modulation TheoryWhat 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

fmt2 sin Vm )( tVm

fct2 sin Vc )( tVc

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 ModulationMATHEMATICAL DESCRIPTION OF AN AM SIGNAL

Let:

fct2 sin A)( tAMV

where:

VAM is the Amplitude

Modulated signal

A is the instantaneous

amplitude of the AM signal

fmt2 sin Vm Vc A

fmt2 sin

Vc

Vm 1 Vc A

fct2 sin fmt2 sin Vc

Vm 1 Vc )(

tAMV but Vm / Vc is the

modulation index, m.


fct2 sin fmt2 sin m 1 Vc )( tAMV

fct2 sin fmt]2 sin mVc [Vc )( tAM

V

fct2 sinfmt 2 sin mVc fctsin2 Vc )( tAM

V

Note: Y) cos(X 2

1 - Y)-cos(X

2

1 Y sin Xsin

Let :

fmt2 Y andfct 2 X

fm)t(fccos22

mVc -fm)t-(fccos2

2

mVc fct 2 sin Vc )( tAMV

2

Vc)rms(CV

222

mVc)rms(LSBV)rms(USBV ;

mVc)pk(LSBV)pk(USBV


Amplitude ModulationFREQUENCY 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.

100x Vc

Vm M%

Vc

Vm m


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


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)


POWER CONTENT OF AN AM SIGNAL

USBLSBT PP Pc 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. Pc2

m USBP LSBP

4

Pcm

Pcm

Pc P 22

T44

2

2

T

m 1 Pc P

Amplitude ModulationCALCULATION 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

m = modulation index

Amplitude ModulationCALCULATION OF CURRENTS IN AM SYSTEMS

m

1 Ic I 2

T2

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

LSBUSB

T

SB P%100 x P

P P 100x

P

P (eta) %

100x m 2

m (eta) %

2

2

2

Pc2

m

4

Pc2

m

4

Pc2

m LSBP USBP SBP where:

MODULATION BY A COMPLEX INFORMATION SIGNAL OR BY SEVERAL

INFORMATION SIGNAL


The total modulating signal,

The total modulation index,

The total transmitted power,

The total sideband power,

......23Vm2

2Vm21Vm tVm

......23m2

2m21m tm

2

2tm

1 Pc TP

2

Pc2tm

tSBP

Amplitude ModulationFORMS 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.

USBLSBT PP Pc P

2. Double Sideband, Suppressed Carrier Transmission (DSBSC)

- Component of the AM wave being transmitted: USB and LSB signals

- Produced by balanced modulator

USBLSBT PP P


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

USBTLSBT P Pc Por P Pc 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.

USBTLSBT PPor 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 Modulation6. 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.


100x nsuppressiowithout power Total

nsuppressio during savedPower SAVING POWER %

PERCENTAGE POWER SAVING

SINGLE SIDEBAND TRANSMITTER RATING

R

VPK

2

2 PEP

Where: PEP = peak envelope power (W)

Vpk = peak voltage (V)

R = load resistance (ohms)

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

REFERENCES

Electronic Communication Systems Through

Advanced by W. Tomasi

Communication Electronics by L. Frenzel

Lecture Notes in Principles of Communication

by A.H. Ballado and M.M. Sejera

Electronic Communication Systems by

G. Kennedy

Documents

Amplitude Modulation