analog communication lecture 12
TRANSCRIPT
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FM Bandwidthand FM Generation
Lesson 12EEE 352 Analog Communication Systems
Mansoor KhanEE Department
CIIT Islamabad Campus
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Frequency Modulation
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Frequency Modulation
• The magnitude and direction of the
frequency shift (Δf) is proportional to the
amplitude of the modulating signal.
• The rate at which the frequency changes
are occurring is equal to the frequency of
the modulating signal (fm).
• (Δf) is called the frequency deviation.
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Phase Modulation
• The magnitude and direction of the phase shift (Δө)
is proportional to the amplitude of the modulating
signal.
• The rate at which the phase changes are occurring
is equal to the frequency of the modulating signal
(fm).
• (Δө) is called the phase deviation
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Mathematical Analysis
For Phase: e = Ec cos[ωct + KpEicos(ωit)]
For Frequency: e = Ec cos[ωct + (KfEi/ ωi)sin(ωit)]
Kp = Deviation Sensitivity of the Phase Modulator
Kf = Deviation Sensitivity of the Frequency Modulator
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Frequency Modulation Waveform
Mathematical Analysis
In FM, the message signal m(t) controls the frequency fc of the carrier. Consider the
carrier
then for FM we may write:
FM signal ,where the frequency deviation
will depend on m(t).
Given that the carrier frequency will change we may write for an instantaneous
carrier signal
where i is the instantaneous angle = and fi is the instantaneous frequency.
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Bessel Function
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Examples from the graph
= 0: When = 0 the carrier is unmodulated and J0(0) = 1, all other Jn(0) = 0, i.e.
= 2.4: From the graph (approximately)
J0(2.4) = 0, J1(2.4) = 0.5, J2(2.4) = 0.45 and J3(2.4) = 0.2
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Significant Sidebands – Spectrum.
As may be seen from the table of Bessel functions, for values of n above a certain
value, the values of Jn() become progressively smaller. In FM the sidebands are
considered to be significant if Jn() 0.01 (1%).
Although the bandwidth of an FM signal is infinite, components with amplitudes
VcJn(), for which Jn() < 0.01 are deemed to be insignificant and may be ignored.
Example: A message signal with a frequency fm Hz modulates a carrier fc to produce
FM with a modulation index = 1. Sketch the spectrum.
n Jn(1) Amplitude Frequency
0 0.7652 0.7652Vc fc
1 0.4400 0.44Vc fc+fm fc - fm
2 0.1149 0.1149Vc fc+2fm fc - 2fm
3 0.0196 0.0196Vc fc+3fm fc -3 fm
4 0.0025 Insignificant
5 0.0002 Insignificant
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Significant Sidebands – Spectrum.
As shown, the bandwidth of the spectrum containing significant
components is 6fm, for = 1.
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Significant Sidebands – Spectrum.
The table below shows the number of significant sidebands for various modulation
indices () and the associated spectral bandwidth.
No of sidebands 1% of
unmodulated carrier
Bandwidth
0.1 2 2fm
0.3 4 4fm
0.5 4 4fm
1.0 6 6fm
2.0 8 8fm
5.0 16 16fm
10.0 28 28fm
e.g. for = 5,
16 sidebands
(8 pairs).
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Carson’s Rule for FM Bandwidth.
An approximation for the bandwidth of an FM signal is given by
BW = 2(Maximum frequency deviation + highest modulated
frequency)
)(2Bandwidth mc ff Carson’s Rule
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Narrowband and Wideband FM
From the graph/table of Bessel functions it may be seen that for small , ( 0.3)
there is only the carrier and 2 significant sidebands, i.e. BW = 2fm.
FM with 0.3 is referred to as narrowband FM (NBFM) (Note, the bandwidth is
the same as DSBAM).
For > 0.3 there are more than 2 significant sidebands. As increases the number of
sidebands increases. This is referred to as wideband FM (WBFM).
Narrowband FM NBFM
Wideband FM WBFM
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For FM Modulator with frequency deviation of 10
kHz, modulating signal frequency of 10 kHz, Carrier
amplitude voltage of 50V and Carrier frequency of
500 kHz, determine the following:
(a) Minimum Bandwidth using Bessel table
(b) Minimum Bandwidth using Carson’s rule
(c) Amplitudes of the side frequencies and plot the
output frequency spectrum
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a)From Bessel function table, m=1 yields three sets of
significant sidebands. Thus bandwidth is
b) Approx. minimum bandwidth is given by Carson’s
rule. So
1kHz10
kHz10
mf
fm
Hz60)103(2 kkHzB
Hz40)1010(2 kkHzkHzB
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c)
VJ
VJ
VJ
VJ
1)50(02.0
5.5)50(11.0
12)50(24.0
5.38)50(77.0
3
2
1
0
38.5V
12V12V
5.5V5.5V
1V1V
500 510 520 530490480470
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Armstrong Indirect FM Transmitter
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Demodulation of FM (cont)
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Bandpass Limiter
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