Transcript EE 3760 chapter 7

Band Limited Signals:
Sending Analog Data with Band Limited Signals
Based on Chapter 5 of William Stallings, Data and
Computer Communication
Kevin Bolding
Electrical Engineering
Seattle Pacific University
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Analog Signals
No. 1
Pulse Trains vs. Band-Limited Signals
Pulse Trains consume the
entire bandwidth of the
transmission medium
Line coding uses pulse trains
to send digital data
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Band-Limited signals are
waves (compositions of sine
waves) and constrained to a
specified band of a medium’s
bandwidth
Band-limited signals may be
used to send analog or
digital data
Analog Signals
No. 2
Modulation
Modulation is the process of
combining a signal wave
and a carrier wave
Carrier wave has frequency fc,
which must be greater than the
modulating wave’s frequency, fm
Modulation allows the engineer to move the base frequency of a band
Allows the use of higher-frequency media
Makes frequency-division multiplexing possible
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Analog Signals
No. 3
cos 2f ct
Amplitude Modulation
Generate a signal by modulating
the amplitude of the carrier with
the signal wave
Signal
x(t )
Carrier
s(t )  [1  na x(t )]cos2f ct
Modulation Index
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Analog Signals
No. 4
Multiplying Sine/Cosine Waves
cos 2f ct
If the signal x(t) is a single cosine
wave, we get (with a modulation
index of 1):
1 cos2f xt
s(t )  [1  cos2f xt ] cos2f ct
s(t )  cos2f ct  cos2f xt  cos2f ct
s (t )
1
1
s(t )  cos 2f c t  cos 2 ( f c  f x )t  cos 2 ( f c  f x )t
2
2
Sum
Carrier
Difference
pwr
Spectrum
Analyzer view
0
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Analog Signals
fc- fx
fc
fc+ fx
No. 5
f
AM Signal Spectrum
M(f)
Bandpass
Filter
(Fc to Fc+B)
Signal
BW: B
Signal
Carrier
Fc
0
• Modulating signal covers a
B
Carrier
Fc
f
S(f)
band from 0Hz to B
• Carrier signal is
concentrated at Fc
Lower
sideband
Upper
sideband
• Combined signal has bandwidth
of 2B, centered at Fc
• Includes a large amount of power
at Fc
• Sending just one sideband
reduces the bandwidth to B
• Filtering out the carrier
reduces the power required
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0
Fc-B
Fc
Fc+B
f
S(f)
Single
Sideband
0
Analog Signals
Fc-B
Fc
Fc+B
No. 6
f
Power of an AM Signal
Modulation Index
Carrier Power
 na2 
Pt  Pc 1  
2 

Total Power
Note: Largest practical modulation index is 1
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Analog Signals
No. 7
AM Detection
Vin
Vout
• To Detect
(Demodulate) an AM
Signal:
• Rectify it to remove
the negative portion
of the waveform
• Low pass filter using
a simple RC filter
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Analog Signals
No. 8
Frequency/Phase Modulation
cos 2f ct
Generate a signal by modulating
the frequency/phase of the carrier
with the signal wave
Carrier
x(t )
Angle Offset
s(t )  Ac cos[2f ct  (t )]
For phase modulation:
Signal
(t )  np x(t )
For frequency modulation:
(t )  n f x(t )
Signal
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Analog Signals
No. 9
FM/PM Signal Spectrum
• FM/PM frequencies vary according to an analog
signal
• Analog signal --> Unlimited precision
• Unlimited bandwidth needed
• Some practical limits
• Maximum frequency deviation DF is proportional to
maximum amplitude in the modulating signal
• Carson’s rule for FM bandwidth requirement:
BT  2DF  2B works well
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Analog Signals
No. 10