Transcript Chapter 4 Notes

TEL312 Electronic Communications Fundamentals
Modulation
Modulation is the process by which information (message) is transformed
Into waveforms that are compatible with the characteristics of the channel.
Baseband Modulation (for digital modulation) is to use certain pulse waveforms to
Carry information.
Bandpass Modulation: the desired Information signal modulates a sine wave (or
Carrier).
TEL312 Electronic Communications Fundamentals
Why Modulate?
• Improve transmission efficiency.
e.g. – 3kHz voice, wavelength is c/f which is about 60 miles. Using
a 60 mile antenna is impractical.
• Allows efficient usage of bandwidth
e.g. Allows multiple signals to use one channel (FDMA)
• Help minimize interference effects
e.g. Spread Spectrum Techniques
• Simplify design to meet circuit design requirements
e.g. Intermediate Frequency (IF) can help simplify filter and amplifier
design at different frequencies.
TEL312 Electronic Communications Fundamentals
Analog Modulation
TWO MAIN TYPES OF MODULATION SCHEMES ( BOTH BANDPASS):
AM – Amplitude Modulation
y(t )  Ac  Amm(t )cos(2f ct )
If m(t) is sinusoidal, we have tone-modulated AM:
y(t )  Ac  Am cos(2f mt )cos(2f ct )
FM – Frequency Modulation:
t

y (t )  Ac cos  2 f c t  2 f d  m( )d 
0


where A c is thecarrieramplitude, A m is themessage amplitude,
f c is thecarrierfrequency, f d is thefrequencydeviationof theFM signal
f m is the tonefrequencyof themessage
m(t)is themessage signal
TEL312 Electronic Communications Fundamentals
AM – Amplitude Modulation
(Ref. Tomasi, Chapter 4 – 6)
•
THREE MAJOR TYPES OF Amplitude MODULATION
•
Conventional Amplitude Modulation
Full AM, also known as Double Sideband Transmitted Carrier AM (DSB-TC)
•
Double Sideband Suppressed carrier (DSB-SC) modulation
•
Single Sideband (SSB) modulation
TEL312 Electronic Communications Fundamentals
AM Type I – DSB-TC AM
s (t )   Ac  Am cos(2f mt )cos(2f c t )
where
carrier  Ac cos(2f c t )
m essage  m(t )  Am cos(2f mt )  Am cos(mt )
TEL312 Electronic Communications Fundamentals
DSB-TC AM GENERATION
Special case: message is a tone
sc (t )  Ac cosct
m(t )  Am cosmt
Modulator
Carrier signal
y(t )  Ac (1  m cos(mt )) cos(ct )
A c is t heAM carrieramplit ude, A m is t hemessage amplit ude,
A'c is t hecarriersignal amplit ude
m is t hemodulat ionindex
m(t )is t hemessage signal, s c (t ) is t hecarriersignal
y(t )is t heDSB - T C signal
TEL312 Electronic Communications Fundamentals
Frequency Translation of AM DSB-TC
m Ac
m Ac
s(t )  Ac cos wct 
cos(wc  wm )t 
cos(wc  wm )t


2

 2
carrier
USB
LSB
TEL312 Electronic Communications Fundamentals
Modulating Index (m)
a measurement for the degree of modulation and bears the relationship of the ratio of Am to Ac
Am
m 
.
Ac
what is the degree of modulation required to establish a desirable AM communication link?
to maintain
m  1.0(100%)
IF m  1.0(100%) , envelope
distortion will occur and the waveform is said to be over-modulated.
Under this circumstances,
Ac is large enough, resulting the non-proportionality of
s(t ) to sm (t )
----hence distortion of the desire message signal!!
TEL312 Electronic Communications Fundamentals
In practice, the modulation index of an AM signal can be computed from Amax and Amin.
1.5
1
0.5
Amin
0
Amax
-0.5
-1
-1.5
0
5
10
15
20
25
30
35
40
45
Amax : is half the peak-to-peak value of the AM signal Amax(pk-pk) /2
Amin : is half the peak-to-peak value of the AM signal Amin(pk-pk) /2
Am : is half the difference of Amax and Amin .
Ac : is half the sum of Amax and Amin.
The values for Amax and Amin can be obtained directly from the oscilloscope.
The evaluation of the modulation index m can be achieved by invoking the following expression:
A
A
A
m
max
min
m

A
A
A
c
max
min
TEL312 Electronic Communications Fundamentals
Power distribution in full AM
The power in a sinusoidal signal is proportional to the square of its amplitude.
Transmitted power = the carrier power + the power in the sidebands
Pc  kAc2
Carrier power :
Sideband power:
Total transmitted power:
PUSB  PLSB
 mA 
 k c 
 2 
2
Ptotal  Pc  PUSB  p LSB

m2 m2 

 kA 1 

4
4


2
c


m2 
m2 
  Pc 1 

 kA 1 
2
2




2
c
where
k
is the proportionality constant
TEL312 Electronic Communications Fundamentals
•The power in the sidebands depends upon the value of the modulation index.
•The greater the percentage of modulation, the higher the sideband power.
•Maximum power appears in the sidebands when the carrier is 100% (m=1) modulated.
•The power in each respective sideband , is given by
2
PUSB  PLSB
Ac
Pc
k

4
4
Each sideband is one-fourth, or 25 percent, of the carrier power.
Since there are two sidebands, their power put together to give
50 percent of the carrier power.
TEL312 Electronic Communications Fundamentals
Power Efficiency
sidebandspower
Power Efficiency 
total power
2
2
m /2
m


2
2
1 m / 2 2  m
When m  1, p.e.  1 / 3.
TEL312 Electronic Communications Fundamentals
Generation of AM – DSB-TC (Square law Modulator)
BPF
sm (t )
sc (t )
+
v1 ( t )
Nonlinearity
(square-law)
Square law of nonlinearity:
where
a1 and a 2
v2 (t )
at
f c +2B
v2 (t )  a1v1 (t )  a2 v12 (t )
are constants.
v o (t )
TEL312 Electronic Communications Fundamentals
v1 (t )  sc (t )  sm (t )  Ac cos(wc t )  sm (t )
Hence
2a
v2 (t )  a1 Ac( 1  2 sm(t))cos(wc t)  a1sm(t)  a2 sm2 (t)  a2 Ac2 cos2 wc t

a1
unwanted terms (remo ved by filtering)


Desired AM signal
By lettinga1  1 & a2  1 /(2 Ac )
vo  Ac 1  m cos(wmt ) cos(wc t )
TEL312 Electronic Communications Fundamentals
Detection of AM – DSB-TC
Square-Law Detector
Although above is described as a modulator,
it can also be used as a demodulator provided that the BPF is replaced
by a low pass filter (LPF) with cutoff frequency at (i.e. bandwidth of ) and
a local carrier signal oscillator.
TEL312 Electronic Communications Fundamentals
Envelope Detector