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EE 324: Communication Systems

Dr. Himal A. Suraweera

Continuous Wave Modulation

The purpose of a communication system is to transmit information-bearing signals through a communication channel.

Figure: Basic Block Diagram of a Communication System

Transmitter (source):process the input signal to produce a transmittedsignal to match the characteristics of the channel

Channel: is the medium that connects the transmitter and the receiver

(destination)

Receiver:operates on the output signal of the channel and decodes the

signal to extract the message sent by the source

Information carrying signalsare referred to as baseband signals In general shifting of the range of frequencies of the basebandsignals are achieved using a process called modulation

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Modulation involves two wave forms:

A message signalo In the audio frequency range (2020,000 Hz). In AM broadcasting(1005000 Hz)

A carrier waveo In the US, commercial AM radio is broadcast on a carrier wave of520 kHz to 1710 kHz, while the FM band is 87.5 MHz to 108 MHz.

Why we need modulation?

There are several good reasons that we need to modulate baseband

signals as follows:

1. Modulation for Efficient Transmission Line-of-sight propagation requires transmit antennas whose physicaldimensions at least 1/10th of the signals wavelength

Figure: Wavelength of a sine wave

Examples:

Unmodulated audio signals down to 100 Hz require an antenna length of

300m!

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Submarine communications use very low frequencies (76 Hz in the US

and 82 Hz in Russia) a wavelength of 3,658.5 kms! Obviously, the usual

half-wavelengthdipole antenna cannot be constructed

On the other hand, at high frequencies better efficiency with reasonable

size antennas

2. Modulation to overcome Hardware limitationsCost and availability of hardware issues can be avoided. Modulation

permits a designer to place the signal in some frequencies to avoid

hardware limitations.

3. Modulation to reduce noise and interference A simple method to overcome noise effects is to increase the

signal power which is not desirable!

Wideband modulation techniques such as FM can suppress bothnoise and interference.

Therefore allows a designer to tradeoff between wideband widthto low power

4. Modulation for frequency assignmentObvious benefit of modulation is that it can be used for frequency

assignment

If there is no modulation, only one radio can transmit at a giventime in a given place!

http://en.wikipedia.org/wiki/Dipole_antennahttp://en.wikipedia.org/wiki/Dipole_antenna

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In this course, we will study two types of continuous-wave modulation

systems:

1. Amplitude modulation

2. Angle modulation (phase modulation and frequency modulation)

Properties of sinusoidal waves

Figure: Sinusoids

1.Wavelength2.Frequency3.Amplitude4.Phase

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Figure: Illustration of AM and FM signals produced by a single sine

wave

Amplitude Modulation

In amplitude modulation, the amplitude of the sinusoidal carrier wave

is linearlyvaried according to the amplitude of baseband signal.

Let us consider a sinusiodal carrier defined by

According to the above definition we can represent the AM wave as a

function of time as follows:

is called the amplitude sensitivity(modulation index).

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In order for the envelope of the AM modulated signals(t) to have the

same shape as the message signal m(t):

1. The amplitude of must be always less than one.

Mathematically we have:

for all t

The condition is called overmodulationand results in

phase distortion (envelope can not be recovered)

Note: is referred to as the percentage modulation

2. The carrier frequency must be much larger than the message

bandwidth

The carrier oscillates more rapidly compared to the message signal and

hence m(t) can be visualized!

Exercise:Show that we can calculate using the following formula

given by

where and are the maximum and minimum positive voltages

of the AM modulated signal.

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Average transmitted power of the AM signal

Average transmitted power is given by

Now apply

to yield

Now, if the message has no dc value, i.e.,

and

we have

Now we re-express the above expression as:

with

= power of the unmodulated carrier

= power per sideband

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Due to the constraint we can further show that

Remark:At least 50% of the power of the AM signal resides in the

unmodulated carrier which does not convey any message signal

Example: A transmitter puts out a total power of 25 Watts of 30% AM

signal. How much power is contained in the carrier and each of thesidebands? (Assume that

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Figure: Illustration of % modulation effects on the amplitude

modulation

Frequency spectrum of the AM signal

We can find the Fourier transform of the AM signal to find the

frequency spectrum

How to obtain this expression?

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Fourier transform is a linear operator. Hence we have

Next we write

And employ the frequency translation property

to obtain the Fourier transform of the second term

as

Figure: Spectrum of the AM signal

(Adapted from Simon Haykin, Communication Systems, 4th

Edition)

The spectrum consists of twoparts:

1. Carrier signal2. Message signal

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Remarks:

As a result of AM modulation, the spectrum of the message signalfor negative frequenciesW to 0 becomes completely visible in the

positive frequencies.

Hence the transmission bandwidth is given by

As a double check we see that:

Example: A 500 KHz carrier is amplitude modulated by an audio

signal which contains all frequencies in the range 300 Hz to 5 kHz.

(a)What are the frequency bands which are output?(b)What is the output bandwidth?(c)Draw the spectral diagram of these signals.

Limitations of AM modulation

Amplitude modulation is a wasteful of power! Amplitude modulation is a wasteful of bandwidth!We trade the system complexity for improved use of communication

resources.

E.g. we may use a fairly simple envelope detector for AM

demodulation

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References

[1] Simon Haykin, Communication Systems, 4th

Edition

[2] A. Bruce Carlson, Communication Systems, 4th

Edition