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EE 324 - Communication Systems EE 384 - Engineering Systems: Dr. Himal A. Suraweera

This document discusses communication systems courses EE 324 and EE 384 taught by Dr. Himal A. Suraweera. It covers topics on frequency modulation including: the proportionality constant in FM known as frequency deviation, representing FM signals as integrals, narrowband FM vs wideband FM, and how a narrowband FM signal can be generated using a product modulator that divides a carrier wave into two paths. The document also compares phase modulation and frequency modulation, and discusses how the average power of PM and FM signals is given by a specific equation regardless of the message signal.

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62 views11 pages

EE 324 - Communication Systems EE 384 - Engineering Systems: Dr. Himal A. Suraweera

This document discusses communication systems courses EE 324 and EE 384 taught by Dr. Himal A. Suraweera. It covers topics on frequency modulation including: the proportionality constant in FM known as frequency deviation, representing FM signals as integrals, narrowband FM vs wideband FM, and how a narrowband FM signal can be generated using a product modulator that divides a carrier wave into two paths. The document also compares phase modulation and frequency modulation, and discusses how the average power of PM and FM signals is given by a specific equation regardless of the message signal.

Uploaded by

bhathiyaeng
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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EE 324 Communication Systems

EE 384 Engineering Systems


Dr. Himal A. Suraweera

Figure 1: Rotating phase concept of exponential


modulation (adopted from [2])

The proportionality constant,


frequency deviation.

( ) is called the

It represents the maximum shift of


the carrier frequency, .

relative to

Since

With integration we have

Now if we take such that


FM wave form as

, we can write the

Note: The message signal must not have a DC


component (average). Else the integral will
diverge as time (t) goes to infinity.
Condition,
ensures that
However, we can also have
to ensure
the bandpass nature of the frequency
modulated signal,
.

PM versus FM comparison
Recall that
PM signal:
FM signal:
These representations indicate that by integrating
or differentiating, a phase modulator can produce
frequency modulation and vice versa. We show this
graphically as follows:

Figure 2: Relationship between PM and FM

Table 1: Comparison between PM and FM


(adopted from [2])
Regardless of the message signal m(t), the average
power of a PM or FM signal is given by

Frequency modulation was first thought of as a way


of bandwidth reduction!!
How this was erroneously assumed:
Suppose one modulates the frequency by swinging
it over a range of + or 100 Hz. Then the
transmission bandwidth will be 200 Hz regardless of
the message bandwidth!

This argument is totally wrong. We have to


understand the difference between instantaneous
frequency and spectral frequency.

Figure 3: Illustrative examples of PM and FM


signals (adopted from [2])

Narrowband FM vs Wideband FM
FM signal is a nonlinear function of the message
signal

Therefore frequency modulation is a nonlinear


process
The spectrum of a FM signal is not related to
the message signal, m(t) in a simple way
How can we handle the spectral analysis of FM
signals?
To make things simple, we consider two cases
as follows:
1) Single tone modulation, that produces a
narrowband FM signal
2)Single tone modulation, but this time the FM
signal is wideband
These cases are sufficient to establish an
empirical relationship between the transmission
bandwidth of an FM signal and the message
signal bandwidth.
Consider a sinusoidal modulating signal given by

The instantaneous frequency of the resulting FM is


given by

where

(frequency deviation) represents the


maximum deviation of the instantaneous
frequency of the FM signal from the carrier
frequency.
It is proportional to the amplitude of the
message signal, but is independent of its
frequency.
Now, the angle of the FM signal can be
expressed as

The ratio of and the message signals


frequency is called the modulation index ( ) of
the FM signal. Mathematically, we have

With this definition we can write

and the FM signal becomes

Now depending on the value of the modulation


index, , we will differentiate two cases of FM:
1.Narrowband FM, for which is small
compared to one radian
2. Wideband FM, for which is large compared
to one radian

Narrowband FM
Let us expand

Using (using

), we get

Now assuming that is small compared to one


radian, we have the following approximation:
and

(Since

and

Therefore, we have

for small x)

Figure 4: Block diagram of a method for


generating narrowband FM (adopted from [1])
We see that
The carrier wave is divided into two parts:
One path is direct; other path is -90 degree
phase-shifted.
A product modulator, that generates a DSBSC signal
The difference between the carrier and the
DSB-SC signal produces the narrowband FM
signal

References
[1] Simon Haykin, Communication Systems, 4th Edition
[2] A. Bruce Carlson, Communication Systems, 4th Edition

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