Transcript Amplitude/Phase Modulation

Amplitude/Phase Modulation
Baseband and carrier
communications
• The term baseband refers to a band of
frequencies of signal generated by a
information source.
• In telephony, baseband signal is 0Hz-3.4kHz
• In TV, it is 0Hz to 4.3 MHz
Baseband and carrier
communications
• In baseband communication, baseband signal
is transmitted without modulation. It cannot
be transmitted through radio link.
• In carrier communication, one of the basic
parameters (amplitude, frequency and
phase)of a sinusoidal carrier of high frequency
wc is varied in proportion to the baseband
signal m(t)
AM: Double side band DSB
In AM, the amplitude (Ac) of the carrier Ac sin ct   
is varied according to the message signal m(t).
If the carrier amplitude is made proportional
to the carrier signal,
The modulated signal is
1
• m(t ) cosct     2 M (  c )  M (  c )
M (  c ) is the shifted to left by 
M (  c ) is the shifted to right by 
c
c
• B is the BW of m(t ) , the BW of the modulated
signal is 2 B
• We observe that the modulated signal
spectrum centered at c is composed of two
part: the portion that lies above c is called
USB and the portion that lies below c is called
LSB.
• For the reason it is called double sideband
suppressed carrier (DSB-SC)
In order to avoid the overlap in the spectrum c  2B
Demodulation DSB-SC
• The process of recovering the baseband signal
from the modulated signal is called
demodulation. In time domain,
1
2
e(t )  m(t ) cos c t  [m(t )  m(t ) cos 2c t ]
2
Demodulation DSB-SC
• In time domain, 2
1
e(t )  m(t ) cos c t  [m(t )  m(t ) cos 2c t ]
2
• In frequency domain,
1
1
E ( )  M ( )  [ M (  2c )  M (  2c )]
2
4
• At the output of the LPF
1
1
m(t )  M ( )
2
2
Problem 4.1
• If m(t )  cos ct , Find DSB-SC signal and Sketch
its spectrum. Identify USB and LSB.
• Find that m(t )  cos ct can be find at the
receiver from the modulated signal.
AM with carrier
• Limitation of SC scheme
– Frequency and phase synchronism is required
– Sophisticated receiver must be required.
• The alternative is to transmit a carrier A cos ct
• In this scheme, the transmitter needs to
transmit much larger power
• The Tx signal can be given by
 AM (t )  A cos ct  m(t ) cos ct  [ A  m(t )] cos ct
1
 AM (t )  [ M (  c )  M (  c )]  A [ (  c )   (  c )]
2
Amplitude Modulation
• The condition for envelope detection of the
[ A  m(t )]  0 for all t
AM signal
• If m(t )  0 and A=0 also satisfy the above
condition
• Let m p (t ) be the peak amplitude of m(t )
m(t )  m p (t )
• This condition is equivalent to A  m p (t )
• The min. carrier amplitude required for
envelope detection is m p (t )
Modulation index
• The modulation index   m p (t ) / A
0   1
Problem
• Sketch  AM (t ) for modulation indices of 0.5
and 1, when m(t )  A cos mt
Sideband and carrier power
• Carrier term does not carry information, and
hence the carrier power is wasted
 AM (t )  A cos ct  m(t ) cos ct  carrier  sidebands
• The carrier power Pc is the mean sq. value of
A cos ct which is A2 / 2
• The sideband power Ps is the mean sq. value
2
m
(
t
)
cos

t
m
(t ) / 2
of
c which is
• The power efficiency
Ps
m 2 (t )

 2
100%
2
Pc  Ps A  m (t )
• For the special case of tone modulation
2
2
m(t )  A cos mt
m (t )  A / 2
• Hence

Ps
A / 2


 2
100% 
100%
2
2
Pc  Ps A  A / 2
2 
2
  1,max  33%
2
Problem
• Find the power efficiency for   .5 and   0.35
• The voltage across the
terminal bb is
bb (t )  [c cos ct  m(t )]w(t )
 [c cos c t  m(t )]
1 2 
1

 2    cos c t  3 cos 3c t 



2
c

  cos c t  m(t ) cos c t  other 

2

Other terms are suppressed by BPF
• If an AM signal is applied to a diode and a resistor
circuit, the –ve part of the AM wave will be
suppressed. The output across the resistor is a ½
wave rectified version of AM signal the AM signal is
multiplied by w(t). Hence the rectified o/p is
vR  [ A  m(t )] cos ct w(t )
1 2 
1

 [ A  m(t )] cos ct    cos ct  cos 3c t  ..
2

3



1


[ A  m(t )]  other
• The o/p of LPF is 1 [ A  m(t )] . The first term can be
blocked by a capacitor
Single-sideband suppressed-carrier
transmission
• The information represented by the modulating signal is contained
in both the upper and the lower sidebands. Since each modulating
frequency fc produces corresponding upper and lower sidefrequencies
• fc + fi and fc − fi it is not necessary to transmit both side-bands.
Either one can be suppressed at the transmitter without any loss of
information.
Advantages
• Less transmitter power.
• Less bandwidth, one-half that of Double-Sideband (DSB).
• Less noise at the receiver.
• Size, weight and peak antenna voltage of a single-sideband (SSB)
transmitters is significantly less than that of a
standard AM transmitter.
Vestigial sideband (VSB)
• A vestigial sideband (in radio communication) is a sideband that has been
only partly cut off or suppressed. Television broadcasts (in analog video
formats) use this method if the video is transmitted in AM, due to the
large bandwidth used. It may also be used in digital transmission, such as
the ATSC standardized 8-VSB. The Milgo 4400/48 modem (circa 1967) used
vestigial sideband and phase-shift keying to provide 4800-bit/s
transmission over a 1600 Hz channel.
• The video baseband signal used in TV in countries that use NTSC or ATSC
has a bandwidth of 6 MHz. To conserve bandwidth, SSB would be
desirable, but the video signal has significant low frequency content
(average brightness) and has rectangular synchronizing pulses. The
engineering compromise is vestigial sideband modulation. In vestigial
sideband the full upper sideband of bandwidth W2 = 4 MHz is
transmitted, but only W1 = 1.25 MHz of the lower sideband is transmitted,
along with a carrier. This effectively makes the system AM at low
modulation frequencies and SSB at high modulation frequencies. The
absence of the lower sideband components at high frequencies must be
compensated for, and this is done by the RF and IF filters.
Advantages/disadvantages
Advantages of Amplitude Modulation, AM
There are several advantages of amplitude modulation, and some of these reasons
have meant that it is still in widespread use today:
• It is simple to implement
• it can be demodulated using a circuit consisting of very few components
• AM receivers are very cheap as no specialized components are needed.
Disadvantages of amplitude modulation
Amplitude modulation is a very basic form of modulation, and although its simplicity is
one of its major advantages, other more sophisticated systems provide a number
of advantages. Accordingly it is worth looking at some of the disadvantages of
amplitude modulation.
• It is not efficient in terms of its power usage
• It is not efficient in terms of its use of bandwidth, requiring a bandwidth equal to
twice that of the highest audio frequency
• It is prone to high levels of noise because most noise is amplitude based and
obviously AM detectors are sensitive to it.
• Noise power is proportional to the modulated
signal bandwidth (sideband).
• Finding the modulation scheme that will
reduce the BW.
• In FM carrier freq is varied proportional to the
baseband signal.
• The carrier freq is varied with time
w(t )  c  km(t )
• Where k is an arbitrary constant. If m p is the
peak amplitude, then the max and min values
of the carrier freq will be w(t )  c  kmP
• Hence the spectral components would remain
within this band with a BW2 km p .
• The FM BW was found to be always greater
than or equal to AM BW.
• A sine wave is
 (t )  A cos  (t )
•  (t ) is the generalized
angle and it is function
of t.
• The generalized angle of
conventional sine wave
is  (t )  ct   0
• For small angle
 (t )  A cos(ct  0 )
• The instantaneous frequency at any instant
d
i 
dt
• The technique in which the angle of carrier
wave is varied with modulating signal is called
angle modulation or exponential modulation
• In PM the angle  (t ) is varied linearly with
information signal
 (t )  c t   0  k p m(t )
• When  0  0
 (t )  ct  k p m(t )
• The resulting PM wave
 PM (t )  A cos(ct  k p m(t ))
• The instantaneous frequency i (t ) is given by
d
i (t ) 
 c  k p mˆ (t )
dt
• If i (t ) is varied linearly with the modulating
signal, the modulation is called FM.
i (t )  c  k f m(t )
• The angle t
 (t )   [c t  k f m( )]d  c t  k f

• The FM wave is
 FM (t )  A cos(c t  k f
t
 m( )d )

t
 m( )d

• In PM it is directly proportional to m(t )
• In FM it is directly proportional to integral of m(t )
• We have an infinite no of possible ways of generating
measure of information signal. If we restrict the
choice to a linear operator, the generalized angle
modulated carrier can be written as
h( )  k p (t )
t
 EM (t )  A cos[c t  (t )]  A cos[c t   m( )h(t   )d ]
