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<b>Up:</b> <a name="tex2html59" href="http://www.media.mit.edu/physics/pedagogy/fab/fab_2002/help_pages/networking_resources/more%20networking/robotics.eecs.berkeley.edu/_sastry/ee20/modulation/node1.html"> Analog Modulation Schemes</a>
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<br> <hr> <p>
</p><h2><a name="SECTION00013000000000000000"> Frequency Modulation</a></h2>
<p>
FM is a so called angle modulation scheme, it was inspired by phase
modulation but has proved to be more useful partly for its ease of
generation and decoding.
The main advantages of FM over AM are:
</p><ol><li> Improved signal to noise ratio (about 25dB) w.r.t. to man made
interference.
</li><li> Smaller geographical interference between neighboring stations.
</li><li> Less radiated power.
</li><li> Well defined service areas for given transmitter power.
</li></ol>
Disadvantages of FM:
<ol><li> Much more Bandwidth (as much as 20 times as much).
</li><li> More complicated receiver and transmitter.
</li></ol>
<p>
In this scheme the frequency of the modulating signal is changed in
proportion to the <b>message signal <img src="ECS%20Web%20Site_files/_8834_tex2html_wrap140.gif" align="bottom"></b>. Thus the signal that is
transmitted is of the form
</p><p><img src="ECS%20Web%20Site_files/_8834_displaymath142.gif" align="bottom"></p><p>
Here the signal </p><p><img src="ECS%20Web%20Site_files/_8834_displaymath144.gif" align="bottom"></p><p> is assumed to be normalized so that
the maximum of the integral is 1 and </p><p><img src="ECS%20Web%20Site_files/_8834_displaymath146.gif" align="bottom"></p><p> is called the
frequency deviation of the modulation scheme. The index of modulation
of an FM signal of the form </p><p><img src="ECS%20Web%20Site_files/_8834_displaymath150.gif" align="bottom"></p><p> is defined to be
</p><p><img src="ECS%20Web%20Site_files/_8834_displaymath148.gif" align="bottom"></p><p>
Figures <a href="http://www.media.mit.edu/physics/pedagogy/fab/fab_2002/help_pages/networking_resources/more%20networking/robotics.eecs.berkeley.edu/_sastry/ee20/modulation/node4.html#figfm1">3</a>, <a href="http://www.media.mit.edu/physics/pedagogy/fab/fab_2002/help_pages/networking_resources/more%20networking/robotics.eecs.berkeley.edu/_sastry/ee20/modulation/node4.html#figfm2">4</a>, and <a href="http://www.media.mit.edu/physics/pedagogy/fab/fab_2002/help_pages/networking_resources/more%20networking/robotics.eecs.berkeley.edu/_sastry/ee20/modulation/node4.html#figfm3">5</a>
are examples of what FM signals look like in the time domain
for a message signal of the form </p><p><img src="ECS%20Web%20Site_files/_8834_displaymath150.gif" align="bottom"></p><p>
</p><p>
</p><p><a name="61"> </a><a name="figfm1"> </a><img src="ECS%20Web%20Site_files/_11271_figure56.gif" align="bottom">
<br><strong>Figure 3:</strong> FM modulation with modulating frequency 1, carrier frequency
10 and modulation index 2<br>
</p><p>
</p><p>
In general the determination of the frequency content of an FM
waveform is complicated, but when </p><p><img src="ECS%20Web%20Site_files/_8834_displaymath158.gif" align="bottom"></p><p> is small, for a sinusoidal
signal </p><p><img src="ECS%20Web%20Site_files/_8834_displaymath144.gif" align="bottom"></p><p>, the bandwidth of the FM signal is
</p><p><img src="ECS%20Web%20Site_files/_18523_displaymath342.gif" align="bottom"></p><p>
On the other hand when </p><p><img src="ECS%20Web%20Site_files/_8834_displaymath158.gif" align="bottom"></p><p> is large, the bandwidth is determined
(empirically) to be
</p><p><img src="ECS%20Web%20Site_files/_18523_displaymath346.gif" align="bottom"></p><p>
Your FM dial goes from 88 MHz to 108 MHz (this range is in between the
frequency ranges for the TV channels 1-6, and 7-12.
For a typical radio station, </p><p><img src="ECS%20Web%20Site_files/_8834_displaymath158.gif" align="bottom"></p><p> varies from about 150 at low
frequencies like 50 Hz
to 3.75 at high frequencies (20 KHz), and a <em>very rough</em> bandwidth
figure is 200 KHz. Thus, KDFC 102.5 on your FM dial goes from
102.4 MHz to 102.6 MHz.
</p><p>
</p><p><a name="67"> </a><a name="figfm2"> </a><img src="ECS%20Web%20Site_files/_11271_figure62.gif" align="bottom">
<br><strong>Figure 4:</strong> FM modulation with modulating frequency 2, carrier frequency
10 and modulation index 2<br>
</p><p>
</p><p>
</p><p><a name="72"> </a><a name="figfm3"> </a><img src="ECS%20Web%20Site_files/_11271_figure67.gif" align="bottom">
<br><strong>Figure 5:</strong> FM modulation with modulating frequency 1, carrier frequency
10 and modulation index 5<br>
</p><p>
</p><p>
Try to puzzle over how you might try to <b>demodulate</b> FM
(think differentiation!).
</p><p>
<br> </p><hr><a name="tex2html60" href="http://www.media.mit.edu/physics/pedagogy/fab/fab_2002/help_pages/networking_resources/more%20networking/robotics.eecs.berkeley.edu/_sastry/ee20/modulation/node5.html"><img alt="next" src="ECS%20Web%20Site_files/next_motif.gif" align="bottom"></a> <a name="tex2html58" href="http://www.media.mit.edu/physics/pedagogy/fab/fab_2002/help_pages/networking_resources/more%20networking/robotics.eecs.berkeley.edu/_sastry/ee20/modulation/node1.html"><img alt="up" src="ECS%20Web%20Site_files/up_motif.gif" align="bottom"></a> <a name="tex2html54" href="http://www.media.mit.edu/physics/pedagogy/fab/fab_2002/help_pages/networking_resources/more%20networking/robotics.eecs.berkeley.edu/_sastry/ee20/modulation/node3.html"><img alt="previous" src="ECS%20Web%20Site_files/previous_motif.gif" align="bottom"></a> <br>
<b> Next:</b> <a name="tex2html61" href="http://www.media.mit.edu/physics/pedagogy/fab/fab_2002/help_pages/networking_resources/more%20networking/robotics.eecs.berkeley.edu/_sastry/ee20/modulation/node5.html"> Digital Modulation Schemes</a>
<b>Up:</b> <a name="tex2html59" href="http://www.media.mit.edu/physics/pedagogy/fab/fab_2002/help_pages/networking_resources/more%20networking/robotics.eecs.berkeley.edu/_sastry/ee20/modulation/node1.html"> Analog Modulation Schemes</a>
<b> Previous:</b> <a name="tex2html55" href="http://www.media.mit.edu/physics/pedagogy/fab/fab_2002/help_pages/networking_resources/more%20networking/robotics.eecs.berkeley.edu/_sastry/ee20/modulation/node3.html"> Amplitude Modulation</a>
<br> <hr> <p>
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<p></p><address>
<i> S Sastry <br>
Sun Apr 20 16:50:27 PDT 1997</i>
</address>
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