Communication Systems, 5e
Chapter 4: Linear CW Modulation
A. Bruce Carlson
Paul B. Crilly
© 2010 The McGraw-Hill Companies
Chapter 4: Linear CW Modulation
•
•
•
•
•
Bandpass signals and systems
Double-sideband amplitude modulation
Modulation and transmitters
Suppressed-sideband amplitude modulation
Frequency conversion and demodulation
© 2010 The McGraw-Hill Companies
Linear CW Radios
Modulation
• Conventional AM
– Multiply and sum
– Nonlinearity
• DSB
– Multiply
– AM sum and difference
Demodulation
• Conventional AM
– Noncoherent Envelope
Detector
– Coherent Multiply w/ carrier
and highpass filter
– Complex Mix & HPF
• DSB
– Coherent Multiply
3
AM Transmission - Blocks
• How do you make an AM signal?
xt 

s t 
Ac
st   Ac  1    xt   cos2  f c  t 
cos2  f c  t 
s t   Ac  1    cos2  f m  t   cos2  f c  t 
4
AM Transmission - Nonlinear
• Another way to make an AM signal
NLt   a1  xt   cos2  f c  t   a2  xt   cos2  f c  t 
2

 a1  xt   cos2  f c  t   a2  xt   2  xt   cos2  f c  t   cos2  f c  t 
2
2
 a1  xt   a2  xt   a1  a2  2  xt   cos2  f c  t   a2  cos2  f c  t 
2


2
a2
a
2
 a1  xt   a2  xt   a1  a2  2  xt   cos2  f c  t   2  cos2  2 f c  t 
2
2
st   a 1  a 2  2  x t   cos2  f c  t 
5
AM modulator example
tank circuit
(a) the concept, (b) practical circuit.
Note in (b) how the message and carrier source are superimposed
onto the gate circuitry.
© 2010 The McGraw-Hill Companies
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Envelope detection
(a) Circuit; (b) Waveforms
In-class example for homework
- Picking R’s and C’s
7
SW CAD IV
• Solution for Envelope Detect
– AMGen_EnvDM
– AMGen_EnvDMv2
– PostEnv_Filter
8
Coherent AM Demodulator
• Pilot carrier in modulated signal
– Filter isolates the pilot
– Mix by phase-coherent pilot
– Note: a better method uses a phase-lock loop (coming soon)
9
AM Mixing and Filter
st   Ac  amt   cos2  f c  t     nt 
r t   Ac  amt   cos2  f c  t     nt  cos2  f c  t   t 
r t   Ac  amt   cos2  f c  t     cos2  f c  t   t   nt   cos2  f c  t   t 
Ac
 amt   cos   t   cos2  2  f c  t   t   nt   cos2  f c  t   t 
2
A

y t   r t   ht    c  amt   cos   t   ht   nt   cos2  f c  t   t  ht 
2

r t  
• Any phase or frequency error components of the
local oscillator can effect demodulation
10
AM Mixing and Filtering
• Non-coherent  Unknown Phase (a r.v)
– You must use a diode or rectifier. Demodulation occurs
at an intermediate frequency and not at baseband.
– can be done for AM/DSB w/ carrier
• Coherent  phase/freq. is known and zeroed!
– must be done for DSB-SC.
cos   t   1
y t   r t   ht  
0
n  2
   t   
Ac
 amt   ht   nt   cos2  f c  t  ht 
2
y t   r t   ht  
Ac
 amt   nt   cos2  f c  t  ht 
2
11
Frequency Demodulation
• Non-Coherent Demodulation
– An unknown phase, find another way …
– Envelope detection, lose ½ the signal power
– Advanced version, use a diode bridge rectifier instead
of a single diode
• Coherent Demodulation
– A known phase, filter and your done.
– The carrier frequency can be used to provide a local
oscillator, after very narrowband filtering
12
Oscillator Errors
• Automatic Fine Tuning (AFT) error
r t   Ac  1    mt   cos2  f c  t    cos2   f c  f e   t   
r t   Ac  1    mt   cos2  f e  t   cos2  2  f c  f e   t  2   
Ac
 1    mt   cos2  f e  t  ht 
2
A
A
y t   r t   ht   c  cos2  f e  t   c    mt   cos2  f e  t 
2
2
A
A
Y  f   c    f  f e     f  f e   c    M  f  f e   M  f  f e 
4
4
y t   r t   ht  
– DC term not completely removed
– message amplitude slowly oscillates
(gets louder and softer periodically
13
Single Sideband Modulation
•
Standard amplitude modulation produces a modulated output signal
that has twice the bandwidth of the baseband signal. Single-sideband
modulation avoids this bandwidth doubling, and the power wasted on a
carrier, at the cost of device complexity.
•
SSB was pioneered by telephone companies in the 1930s for use over
long-distance lines, as part of a technique known as frequency-division
multiplexing (FDM). This enabled many voice channels to be sent
down a single physical circuit. The use of SSB meant that the channels
could be spaced (usually) just 4,000 Hz apart, while offering a speech
bandwidth of nominally 300 – 3,400 Hz.
•
Amateur radio operators began to experiment with the method
seriously after World War II. It has become a de facto standard for
long-distance voice radio transmissions since then.
From Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Single-sideband_modulation
14
SSB Signal Generation
• First Method
– Generate a DSB Signal
– Filter out either the
upper or lower sideband
15
Second Method
Weaver’s SSB modulator
x cos t   cos2  f 2  t   h t   x t   cos2  f1  t 
x sin t   sin 2  f 2  t   h t   x t   sin 2  f1  t 
16
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Weaver Modulator Math
(ignoring filter)
xc t   xcos t   xsin t 
 cos2  f 2  t   ht   xt   cos2  f1  t 
 sin 2  f 2  t   ht   xt   sin 2  f1  t 
x t 

 x t 
x c t   
 cos2  f 2  f1   t  
 cos2  f 2  f1   t 
2

 2
x t 

 x t 

 cos2  f 2  f1   t  
 cos2  f 2  f1   t 
2

 2
• Using the upper plus signs …

W W 

x c t   x t   cos 2   f c 
   t 
2
2  


Matlab
example
SSB_Weaver
• Adding the filter:
The lowpass filter only passes one of the sidebands!
17
Weaver Modulator Spectrum
• Complex Mix
• Baseband LPF
• Complex Mix – then keep the real part
18
Equivalent Complex Operation
x c t 
xt 
exp j  2  f1  t 
exp j  2  f 2  t 
xc t   exp j  2   f c  f1   t   ht   xt   exp j  2  f1  t 
• Complex Mixing of signal band to “zero”
intermediate frequency (IF)
• LPF replaces IF LPF or HPF at IF frequency
• Complex up conversion from “zero” IF to RF
19
fs/4 Weaver Modulation in DSP
• What would happen if we modulated by fs/4

f n
 n 

n
exp  j  2  s    exp  j 
   j 
4 fs 
2 


• Even samples are purely real
• Odd samples are purely imaginary
• A low pass filter then removes “the other sideband”



f n 
  n 

x ZIF t   h t    x t   exp  j  2  s    h t    x t   exp  j 

4 f s 
2 





 h t   x t    j
n

20
Vestigial Sideband (VSB)
• When there is frequency content near 0 Hz, the
SSB filter will “leak” an unwanted sideband
• If you can’t stop it … invent a scheme that uses it!
• Allow 0 Hz crossover to exist, but make it
complementary about zero
– When recreating the opposite sideband (complex
conjugate), the response around zero sums to unity!
21
VSB Spectrum at Fc
• Allow Fc Hz
crossover to exist, but
make it
complementary about
zero
– When recreating the
opposite sideband
(complex conjugate),
the response around
zero sums to unity!
– Figure 4.4-8
22
Uses of VSB
• NTSC Television
– 4 MHz USB with 1.25 MHz LSB
– no longer broadcast after 2009
https://en.wikipedia.org/wiki/NTSC
23
Broadcast Television
• Advanced Television Systems Committee (ATSC)
– North American Standard
– HD TV using 8-VSB
– cable TV may use 16-VSB or 256-QAM
• Digital Video Broadcast-Terrestrial (DVB-T)
– much of the rest of the world (not China, Japan, South
& Central America and a few others)
– Based on direct broadcast satellite TV system
• Aside: it is all about line counts and repetition
rates.
– 720p: 720 lines @ 25 or 30 freames per second
– 1080p: 1125 lines @ 25 or 30 freames per second
24
Circuits and Systems
•
•
•
•
•
Passive Bandpass Filter
Ring Modulator
Square wave instead of sine wave
Weaver Modulator
Phase Shift SSB Generation (Hilbert Transform)
25