Upload
jumanne-ally
View
219
Download
0
Tags:
Embed Size (px)
DESCRIPTION
AM Modulation
Citation preview
DIT
Dar es Salaam institute of Technology (DIT)
ETU 07123
Introduction to Communication System
Ally, J
DIT
Analogue Modulation
DIT
Introduction to Modulation Definitions
Analog modulation
Both the message signal and the transmitted signal are analog signals
Two classes: amplitude modulation, angle modulation
Three signals:
Message signal: the information signal to be modulated and transmitted
Carrier signal c(t) : high frequency sinusoidal signal
Modulated signal: the signal to be transmitted, or the signal obtained after modulation
DIT
Modulation It is the process of facilitating the transfer of
information over a medium.
This is done by changing one or more the parameters of a signal including power, frequency, phase and amplitude depending on the requirement of the transmission system.
DIT
Baseband, Passband
Baseband: refers to the signals and systems before modulation, which have frequencies/bandwidth much lower than the carrier frequency
Passband: refers to the signals and systems after (including) modulation, which have frequencies/bandwidth around the carrier frequency
Baseband signal: is usually the message signal
Passband signal: is usually the modulated signal, or transmitted signal
Baseband and Passband signals
DIT
Baseband and Bandpass Signals Baseband signal is the original signal having the original
frequencies when delivered by transmitters.
In Baseband communication, signals are transmitted without modulation.
Bandpass signal is a signal which is modulated by one of the modulation schemes.
Demodulation is the process of extracting the baseband message from the carrier so that it may be processed and interpreted by the intended receiver
DIT
Message signal m(t) modifies: Amplitude: AM linear modulation Phase: PM Frequency: FM Example Compare signal waveforms
( )A t
( ) ( )f t d t dtNon-linear modulation)(t
DIT
Concept of Modulation
DIT
Checkpoints for studying each modulation
Modulated signal (time-domain)
Spectrum (frequency-domain)
Parameters: bandwidth, power, etc
Modulator and demodulator (Principles, block diagrams or circuits)
Major properties (advantages/disadvantages over other modulations)
DIT
List of modulation methods we will learn
Amplitude modulation methods and applications1. AM (amplitude modulation): AM radio, short wave
radio broadcast, 2. DSBSC (double sideband suppressed carrier AM):
data modem, Color TV’s color signals 3. SSB (single sideband AM): telephone4. VSB (vestigial sideband AM): TV picture signal
Angle modulation methods and applications1. FM (frequency modulation): FM radio broadcast, TV
sound signal, analog cellular phone2. PM (phase modulation): not widely used, except in
digital communication systems (but that is different)
DIT
Amplitude Modulation (AM) AM (conventional amplitude modulation)
Amplitude Modulation (AM) is the one which the amplitude of a sinusoidal carrier is varied in accordance with an incoming message signal
Modulated signal Carrier: Message signal: m(t) AM modulated signal
where ka, is a constant called the amplitude
sensitivity of the modulator responsible forthe generation of the modulated signal s(t).
DIT
Time-Domain descriptionThe standard form of an AM wave is defined by
The amplitude of the time function multiplying is called the envelope of AM wave s(t).
The envelope of s(t) has essentially the same shape as the baseband signal m(t) provided that two requirements are satisfied:
1. The amplitude of is always less than unity, that is, for all t 2. The carrier frequency fc, is much greater than the highest frequency
component W (message bandwidth) of the message signal m(t), that is
(a) Baseband signal m(t) (b) AM wave for (c) AM wave for
tf c2cos
DIT
Frequency-Domain descriptionThe Fourier transform of the AM wave s(t) is given by
(a) Spectrum of baseband signal
(b) Spectrum of AM wave
DIT
Generation of AM Waves Multipliers difficult to build in hardware AM waves typically generated using a nonlinear device to obtain the
desired multiplication Square law modulator sums carrier c(t) and information m(t) signals,
then squares them using a nonlinear device. Unwanted terms are filtered out with a bandpass filter.
Switched modulation sums c(t) and m(t) then passes sum through a switch, which approximately multiplies it by a periodic square wave. This generates the desired signal plus extra terms that are filtered out.
m(t)
+
Accos(2fct+
Squareor Switch BPF
s(t)
DIT
Modulation IndexThe degree of modulation is an important parameter and is known as the modulation index. It is the ratio of the peak amplitude of the modulating signal, Am to the peak amplitude of the carrier signal, Ac
(a) Under Modulation (ka < 1)
(b) Ideal Modulation (ka = 1)
(c) Over Modulation (ka > 1)
c
ma A
Ak
DIT
Over Modulation http://www.williamson-labs.com/480_am.htm
DIT
Detection of AM waves There are two devices for the detection of AM waves, namely, the
square-law detector and the envelope detector
Square law detector, squares signal and then passes it through a LPF Residual distortion proportional to m2(t) Non-coherent (carrier phase not needed in RX) Envelope detection simple alternative method
+ Square-law devices
Square-law devicesBPF LPFm(t)
tfA cc 2cos
S(t) m’(t)
DIT
Explanation
Diode D1 cut the negativeportion of AM signal s(t)
When signal after D1 is positive,C is charged.When signal after D2 is 0,C is discharged.
Overall effect: y(t) remains approximatelyas the envelope of s(t)
m(t) can be detected from y(t)using capacitor to remove d.c.1.
Very important: this isEnvelope Detector.
DIT
Bandwidth of AM signal BT = 2W
AM signal’s bandwidth is twice message bandwidth
This is also transmitted signal bandwidth, or required minimum channel bandwidth Bc
Negative frequency contents of m(t) becomes visible in positive frequency
Upper sideband (USB):
Lower sideband (LSB):
Transmission power: PT = PM + Pcarrier
= PUSB + PLSB + Pcarrier
Wfff cc
cc ffWf
DIT
AM Power Distribution In any electrical circuit, the power dissipated is
equal to the voltage squared divided by the resistance.
Mathematically, power in an unmodulated carrier:
The upper and lower sideband powers is given by:
The total power in AM wave is equal to:
RAP c
c 2
2
482
2/ 2222ccc
lsbusbP
RA
RAPP
21
244
2222 c
cc
ccclsbusbct PPPPPPPPPP
DIT
AM – Modulation EfficiencyDefinition : The modulation efficiency is the percentage of the total power of the modulated signal that conveys information.
Only “Sideband Components” – Convey information
Modulation Efficiency:
1001 2
2
tm
tmE
Voltage Spectrum of the AM signal:
Translated version of message signal
ccccc ffMffffMffA
fS 2
)(
Carrier line spectral component
DIT
Major Properties of AM Advantages
Simplicity in implementation, especially in receiver and transmitter The major reason that AM was the first & most popular
broadcasting methods during early days Disadvantages
Waste power and bandwidth Carrier components wastes a major portion power, but
carrier does not have message information Both USB and LSB are transmitted, which carry the same
message information
DIT
Ways for AM improvement
To enhance power efficiency Reduce/remove carrier: DSB-SC Remove one/partial sideband: SSB, VSB
To enhance bandwidth efficiency Remove one/partial sideband: SSB, VSB Multiplex two message signals together: QAM
Cost for the improvement More expensive implementation The simple envelope detector is no longer applicable
DIT
Double-Sideband Suppressed-carrier (DSB-SC) In the standard form of Amplitude Modulation (AM), the carrier wave
c(t) is completely independent of the message signal m(t), which means that the transmission of the carrier wave represents a waste of power.
To overcome this shortcoming , we may suppress the carrier component from the modulated wave, resulting in double-sideband suppressed carrier (DSB-SC) modulation.
Thus, by suppressing the carrier, we obtain a modulated wave that is proportional to the product of the carrier wave and the message signal.
DIT
Time-Domain Description The standard form of a DSB-SC wave is defined by
This modulated wave undergoes a phase reversal whenever the message signal m(t) crosses zero, as illustrated in figure below
(a) Baseband signal (b) DSB-SC modulated wave
tmtcts
tmtfAts cc 2cos
DIT
The Fourier transform of the DSB-SC wave s(t) is given by
(a) Spectrum of message signal
(b) Spectrum of DSB-SC modulated wave
Frequency-Domain Description
DIT
Generation of DSB-SC Waves A DSB-SC modulated wave consists simply of the product of the
message signal and the carrier wave. A device achieving this requirement is called a Product Modulator.
Remove inefficient constant term
Modulated signal is
Can also use ring modulator: diodes and inductors
DIT
Coherent Detection of DSB-SC Modulated Wave The baseband signal m(t) can be uniquely recovered from a DSB-
SC wave s(t) by first multiplying s(t) with a locally generated sinusoidal wave and then low-pass filtering the product
It is assumed that the local oscillator output is exactly coherent or synchronized, in both frequency and phase, with the carrier wave c(t) used in the product modulator to generate s(t).
This method of demodulation is known as coherent detection or synchronous detection.
DIT
Coherent Detection of DSB-SC Modulated Wave-2 We find that the product modulator output is:
The first term represents a DSB-SC modulated signal with a carrier frequency 2fc, whereas the second term is proportional to the baseband signal m(t).
the first term is removed by the low-pass filter, this requirement is satisfied by choosing fc > W. At the filter output we then obtain a
signal given by
The demodulated signal is therefore proportional to m(t) when the phase error is a constant.
DIT
Coherent Detection of DSB-SC Modulated Wave-3 The amplitude of this demodulated signal is maximum when and it is minimum (zero) when
As long as the phase error is constant, the detector provides an undistorted version of the original baseband signal m(t).
In practice, however, we usually find that the phase error varies randomly with time, due to random variations in the communication channel. The result is that at the detector output, the multiplying factor also varies randomly with time, which is obviously undesirable.
Therefore, provision must be made in the system to maintain the local oscillator in the receiver in perfect synchronism, in both frequency and phase, with the carrier wave used to generate the DSB-SC modulated signal in the transmitter.
The resulting system complexity is the price that must be paid for suppressing the carrier wave to save transmitter power.
cos
DIT
Costas Loop (DSB-SC Demodulator)Goal: Maintain
-90o
Phase-shifter
Product Modulator
Product Modulator
VoltageControlled Oscillator
Low-passfilter
Low-passfilter
Phasediscriminator
tmtfA cc 2cos
tfc2cos
tfc2sin
tmsin21
tmcos21
I-channel
Q-channel
DIT
Costas Loop One method of obtaining a practical synchronous receiver system, suitable
for demodulating DSB-SC waves, is to use the Costas loop.
This receiver consists of two coherent detectors supplied with the same input signal, namely, the incoming DSB-SC wave Accos(2πfct)m(t), but with individual local oscillator signals that are in phase quadrature with respect to each other.
The frequency of the local oscillator is adjusted to be the same as the carrier frequency fc, which is assumed known a priori.
The detector in the upper path is referred to as the in-phase coherent detector or I-channel, and that in the lower path is referred to as the quadrature-phase coherent detector or Q-channel.
These two detectors are coupled together to form a negative feedback system designed in such a way as to maintain the local oscillator synchronous with the carrier wave.
DIT
Double Side Band Suppressed CarrierPower in a AM signal is given by
21
21 2222 tmAAts cc
Discrete carrier power Sideband power
Discrete carrier power can be eliminated (Suppressing carrier )if m(t) is assumed to have a zero DC level
Then ttmAts cc cos)()(
Spectrum
ccc ffMffMAfS
2)(
Since no power is wasted in carrier the efficiency is
Power
21 222 tmAts c
%1001002
2
tm
tmE
DIT
Noise in AM Receivers
Power in s(t) is 0.5Ac2Pm
Power in n(t) is N0B
SNR=Pm/Pn= Ac2Pm/(2N0B)= Ps/(N0B) (SNR at the receiver input)
Power in m(t) is 0.25Ac2Pm (half the power in s(t))
Power in n(t) is 0.5N0B (PSD 0.25N0 over BW 2B)
SNR=Pm´/Pn´= Ac2Pm/(2N0B)= Ps/(N0B) (SNR at the receiver output)
ProductModulato
r
m´(t)+ n´(t)
Accos(2fct+
s(t)=Accos(2fct+m(t) +
n(t)LPF1
White Gaussian noise (AWGN)
-B B
DIT
Single-SideBand (SSB) Modulation Standard AM and DSB-SC Modulation are wasteful of
bandwidth because they both require a transmission bandwidth equal to twice message the message bandwidth.
This means that insofar as the transmission of information is concerned, only one sideband is necessary, and no information is lost.
Thus the channel needs to provide only the same bandwidth as the message signal, a conclusion that is intuitively satisfying.
When only one sideband is transmitted, the modulation is referred to as single-sideband modulation
DIT
Single Sideband Modulation(2) Only transmits upper or lower sideband of AM and DSBSC The transmitted signal can be written in terms m(t) and the
Hilbert Transform of m(t) Use same demodulator as DSBSC SSB has half the SNR of DSBSC for half the transmit
power: no SNR gain SSB can introduce significant distortion at DC where the
sidebands meet: not good for TV signals
USB LSBM(f)
0 fc-fcB-B
USB
LSB)]2sin()()2cos()([
2)( tftmtftmAts chc
c
DIT
Baseband Representation of Modulated Signals
Baseband signal representation is a compact way to represent passband signals.
All passband signals at carrier frequency fc can be written as s(t) = sI(t) cos(2fct) + sQ(t) sin(2fct).
sI(t) is called the in-phase signal component; sQ(t) is called the quadrature signal component.
The sine and cosine are orthogonal signals, can be used to separate out the in-phase and quadrature components from s(t).
We define as the baseband signal representation. Then which is a compact way to represent and analyze passband signals.
DIT
Generating of SSB modulated wave by phase discrimination method
The phase discrimination method of generating an SSB modulated wave involves two separate simultaneous modulation processes and subsequent combination of the resulting modulation products.
The system uses two product modulators, I and Q, supplied with carrier waves in phase quadrature to each other.
The incoming baseband signal m(t) is applied to product modulator I, producing a modulated DSBSC wave that contains reference phase sidebands symmetrically spaced about carrier frequency fc.
The hilbert transform mh(t) of m(t) is applied to product modulator Q, producing DSBSC modulated wave that containssideband having identical amplitude spectra to those of modulator I, but with phase spectra such that vector addition or subtraction of the two modulator outputs results in cancellation of one setof sidebands and reinforcement of the other set.
The use of plus sign yields SSB wave with only the upper sideband, whereas the use of minus sign yields SSB wave with only upper sideband.
DIT
Block diagram for generating of SSB modulated wave by phase discrimination method
-90o
Phase-shifter
I
Q
Oscillator
In-phase path
Quadrature path
Wide-band
-90o
Phase-shifter
tfA cc 2cos
tfA cc 2sin
ModulatingWave m(t)
Hilbert transform m~(t)
+
+-
SSB wave
DIT
Demodulation of SSB wave To recover the baseband signal m(t) from the SSB wave s(t), we
have to shift the spectrum by the amounts so as to convert the transmitted sideband back into the baseband signal.
This can be accomplished using coherent detection, which involves applying the SSB wave s(t), together with locally generated carrier , assumed to be of unit amplitude for convenience, to a product modulator and then low-pass filtering the modulator output.
cf
tfc2cos
,
Product Modulator
Low-pass filter
SSB waves(t)
tfc2cos
v(t) vo(t)
DIT
Demodulation of SSB wave (2) The product modulator output is given by
The first term is the desired message signal. The second term represents an unwanted components in the product modulator output that is removed by low-pass filtering.
The detection of SSB modulated waves assume perfect synchronization between the local carrier and that in the transmitter both in frequency and phase. The effect of a phase error Ф in the locally generated carrier wave is to modify the detector output as follows
tstftv c2cos
tftmtftmAtmA
tftmtftmtfA
cccc
cccc
4sin~4cos41
41
2sin~2cos2cos21
sin~41cos
41 tmAtmAtv cco
DIT
Demodulation of SSB wave (3) Owing to the phase error Ф, the detector output
vo(t) contains not only the message signal m(t) but also its Hilbert transform mh(t).
Consequently, the detector output suffers from phase distortion. This phase distortion is usually not serious with voice communications because the human ear is relatively insensitive to phase distortion.
In the transmission of music and video signals, on the other hand, phase distortion in the form of a constant phase difference in all components can be intolerable.
DIT
Vestigial Side-Band (VSB) Modulation Single-sideband modulation is well-suited for the
transmission of voice because of the energy gap that exists in the spectrum of voice signals between zero and a few hundred hertz.
When the message signal contains significant components at extremely low frequencies i.e. television signals, the upper and lower sidebands meet at the carrier frequency. This means SSB modulation is inappropriate for the transmission of television signals.
This difficulty suggests another scheme known as vestigial sideband modulation (VSB), which is a compromise between SSB and DSBSC modulation.
DIT
Vestigial Sideband VSB is similar to SSB but it retains a small portion (a vestige) of the
undesired sideband to reduce DC distortion. Transmits USB or LSB and vestige of other sideband
Reduces bandwidth by roughly a factor of 2
VSB signals are generated using standard AM or DSBSC modulation, then passing modulated signal through a band-pass filter i.e. it is the special design of the band-pass filter that distinguishes VSB modulation from SSB modulation.
Demodulation uses either standard AM or DSBSC demodulation
VSB used for image transmission in TV signals
USB
DIT
Generation of VSB modulated wave The transmission bandwidth of VSB modulation is given by
where W is the message bandwidth, and f, is the width of the vestigial sideband
To generate a VSB modulated wave, we pass a DSBSC modulated wave through a sideband shaping filter.
The exact design of this filter depends on the desired spectrum of the VSB modulated wave.
the VSB modulated wave is described in the time domain as
This is the desired representation representation for a VSB modulated wave containing a vestige of the lower sideband. The component 0.5Acm(t) constitutes the in-phase component of this VSB modulated wave, and 0.5AcmQ(t) constitutes the quadrature components.
tftmA
tftmA
ts cQc
cc 2sin
22cos
2
DIT
Scheme for generation and demodulation of a VSB modulated wave
Block diagram of VSB modulator
Block diagram of VSB demodulator
ProductModulator
SidebandShaping
filter
tfA cc 2cos
m(t) DSBSC VSB waves(t)
ProductModulator
Low-passfilter
tfA cc 2cos
v(t)VSB waves(t)
tvo
DIT
Envelope detection of a VSB wave plus carrier
In commercial television broadcasting, a sizable carrier is transmitted together with the modulated wave.
This makes it possible to demodulate the incoming modulated wave by an envelope detector in the receiver.
In commercial television broadcasting, the vestigial
sideband occupies a width of about 1.25 MHz, or about one-quarter of a full sideband.
This has been determined empirically as the width of vestigial sideband required to keep the distortion due to mQ(t) within tolerable limits when when the percentage modulation is nearly 100.