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Chapter 2

- Amplitude Modulation

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

Revision..

- Why do we need modulation?
- What are the types of modulation?
- What is AM?
- What is bandwidth?

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). - It is a low quality form of modulation
- Amplitude Modulation is the simplest and earliest

form of transmitters

Basic Amplitude Modulation

Envelope

AM Envelope

- Wave and the shape of the Modulated Wave is

called AM Envelope.

Envelope is the original modulating signal

Carrier

Amplitude Modulation What really happened??

(you are not required to memorized this)

carrier

- 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?

AM wave equation

- 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
- (2?ft ?) The phase of the signal in radian

AM wave equation

- An unmodulated modulating signal
- vm (t) Em sin (2?fmt)
- Or vm (t) Vm sin (2?fmt)

Em Vm peak modulating signal amplitude(volts)

- Envelope of the modulating signal varies above

below the peak carrier amplitude - In general Em lt 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)

(No Transcript)

AM wave equation

- An unmodulated carrier (carrier signal) is

described by the following equation - - vc (t) Ec sin (2?fct)
- Or vc (t) Vc sin (2?fct)

Ec Vc peak carrier amplitude (volts)

AM Concepts

(Low frequency)

carrier

(nonlinear devices)

Modulation x carrier

(High frequency)

Figure 3-3 Amplitude modulator showing input and

output signals.

AM wave equation

- The modulated wave can be
- expressed as -
- Vam(t) Ec Em sin (2?fmt) (sin 2?fct)

.........(1) - WHERE
- Ec Em sin (2?fmt) Amplitude of the modulated

wave - Em peak change in the amplitude of the envelope

- fm frequency of the modulating signal

AM wave equation

- Expanding eq (1) we get

Carrier signal

Modulating signal

Later we will see how this equation can be

further improved to make it more meaningful

AM wave equation

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 lt Vc
- Distortion occurs when the amplitude of the

modulating signal is greater than the amplitude

of the carrier.

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.

modulating factor or coefficient, or degree of

modulation.

Modulation Index and Percentage of Modulation

- modulation index (m) can also calculate it using

where

Modulation Index for Multiple Modulating

Frequencies

Modulation Index for Multiple Modulating

Frequencies

- Two or more sine waves of different, uncorrelated

frequencies modulating a single carrier is

calculated by the equation

- Consider these envelopes
- Do they look the same?

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.

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.

http//www.williamson-labs.com/480_am.htm

Over Modulation

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.

- Draw AM wave in time domain and frequency domain

Frequency Domain

- The frequency domain provides an alternative

description of signal in which the time axis is

replaced by a frequency axis.

The relationship between the time and frequency

domains

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.

Sidebands and the Frequency Domain

(No Transcript)

Sidebands and the Frequency Domain

- Figure The AM wave is the algebraic sum of the

carrier and upper and lower sideband sine waves. - Intelligence or modulating signal.
- (b) Lower sideband.
- (c ) Carrier.
- (d ) Upper sideband.
- (e ) Composite AM wave.

Bandwidth

- Signal bandwidth is an important characteristic

of any modulation scheme - In general, a narrow bandwidth is desirable
- Bandwidth is calculated by

Bandwidth

- Bandwidth is the difference between the upper and

lower sideband frequencies. - BW fUSB-fLSB

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?

Solution to Example 1

fm

1. Highlight and identify important information

in the question

- 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?

fc

2. Use the formulas to solve the problem

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

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

Solution

Lower side band

Upper side band

Carrier

Frequency

100kHz

95kHz

105kHz

90kHz

110kHz

fc

fUSF

fc-fm(max

fcm(max

fLSF

Group Activity

- 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 - - USB LSB
- Modulation Index and percent modulation, M
- Peak Amplitude of modulated carrier and Upper

Lower side frequency voltage - Maximum Minimum Amplitude of the envelope, Vmax

and Vmin - Draw output in frequency domain time domain

Solution

- Upper and lower side frequencies
- Modulation Index and percent modulation, M

Solution (c)-method 1

- (c) Peak Amplitude of modulated carrier and Upper

Lower side frequency voltage - We can find Elsb and Eusb by using equation
- Thus

Solution (c)- method 2

- (c) Peak Amplitude of modulated carrier and Upper

Lower side frequency voltage - Lets say Em is unknown. Em can be found from
- Thus

Solution

- (d) Maximum Minimum Amplitude of the envelope,

Vmax and Vmin

Solution

- (e) frequency domain

20

3.75

3.75

Solution

- (e) time domain

Vmax27.5 Vp

Vmin 12.5 Vp

How to calculate AM power ???

Pc

PT ????

PUSB

PLSB

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).

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

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)

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

AC average power dissipation

- Recall that the average power dissipated by

resistor R is with a sinusoidal source of

amplitude Vpk is given

AM signal power

- Since the vAM is composed of three sinusoids

the total average power dissipated by the

antenna R is given

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

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.

Example Problem 1

- 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.

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

Pc 30 W

PUSB 5.4 W

PLSB 5.4 W

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?

AM power efficiency

- At maximum modulation, the sideband power is at

most 33 of the total transmitted power.

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.

100 modulation only occursat peaks

Speech as a modulating signal

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

Upper and lower sidebands contain the same

information.

AM modulated speech signal

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

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.

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

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 Pc1 (m2 /2)
- Thus,
- PT (50 W)1 ((0.8)2 /2)
- 66 W

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

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