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EELE 3370
Communications I
Amplitude Modulations and Demodulations
Dr. Talal Skaik 2016
Islamic University of Gaza
Electrical Engineering Department
1
Introduction
2
Modulation is a process that moves the message signal into
a specific frequency band that is dictated by the physical
channel.
We will study classic analog modulations:
Amplitude modulation and Angle modulation
Communication systems that does not use modulation –
baseband communications
Communication systems that use modulation –
carrier communications
Dr. Talal Skaik IUG 2016
Baseband vs Carrier Communications
3
Baseband Communications
The baseband is the frequency band of the original signal.
Example: Telephones: 300–3700 Hz
Baseband signals such as audio and video contain
significant low-frequency content.
They cannot be effectively be transmitted over radio
(wireless) link.
Baseband communication usually requires wire (single,
twisted pair, coax).
Dr. Talal Skaik IUG 2016
Baseband vs Carrier Communications
4
Carrier Communications oCarrier communication uses modulation to shift spectrum of signal. oWireless communication requires frequencies higher than baseband. oIn carrier communication, the signal modulates a sinusoidal carrier. oThe signal modifies the amplitude, frequency, or phase of carrier.
s(t) = A(t) cos(ωct +φ (t))
◮ Amplitude modulation: A(t) is proportional to m(t) ◮ Frequency modulation: frequency is proportional to m(t) ◮ Phase modulation: φ(t) is proportional to m(t)
Frequency and phase modulation are called angle modulation.
Dr. Talal Skaik IUG 2016
Double Sided Amplitude Modulation
5
The carrier amplitude is changed in proportional to the message
signal.
At the same time, angular frequency ωc and the phase θc remains
constant ( assume phase θc = 0).
If carrier amplitude A is made directly proportional to the
modulating signal m(t), then modulated signal is:
m(t) cos ωct (shifts spectrum of m(t) to carrier frequency
If
1
22
c c c
m( t ) M ( f )
then
m( t ) cos( f t ) M ( f f ) M ( f f )
Dr. Talal Skaik IUG 2016
Double Sided Amplitude Modulation
6 Dr. Talal Skaik IUG 2016
• If the bandwidth of m(t) is B Hz, then the modulated signal has a
bandwidth of 2B Hz.
• The modulated signal spectrum centered at ±fc (or ωc rad/s)
consists of two parts:
a portion that lies outside ±fc and is know as upper sideband (USB)
A portion that lies inside ±fc is known as Lower Sideband (LSB)
• The modulated signal does not contain a discrete component of the
carrier frequency fc.
• This modulation process does not introduce sinusoid at fc and as a
result, it is called Double-sideband, suppressed-carrier (DSB-SC
modulation).
Double Sided Amplitude Modulation
7 Dr. Talal Skaik IUG 2016
• The relationship of B to fc is of interest:
• From fig c, if fc ≥ B, thus avoiding overlap of modulated spectra
centered at ±fc .
• If fc < B, the two copies of message spectra overlap and the
information of m(t) is distorted during modulation. This will make
it impossible to recover m(t) from m(t)cos ωct.
Double Sided Amplitude Modulation
8
Examples: ◮ AM radio: B = 5 KHz, 550 ≤ fc ≤ 1600 KHz
◮ FM: B = 200 KHz, 87.7 ≤ fc ≤ 108.0 MHz
◮ US television: B = 6 MHz, 54 ≤ fc ≤ 862 MHz
Dr. Talal Skaik IUG 2016
• DSB-SC modulation shifts spectrum to right and left by fc.
• To recover original signal m(t) from the modulated signal, it is necessary to retranslate the spectrum to its original position (Demodulation)
• If modulated signal spectrum in fig c (previous figure) is shifted to the left and to the right by fc and multiplied by half, we obtain:
• The figure contains the desired baseband spectrum plus and unwanted spectrum at ±2fc.
• The unwanted spectrum can be suppressed by a low-pass filter.
DSB-SC Demodulation
9 Dr. Talal Skaik IUG 2016
• Demodulation consists of multiplication of the incoming modulated signal m(t)cos ωct by a carrier cosωct followed by a low pass filter.
• This can be verified in the time domain by observing e(t):
DSB-SC Demodulation
10
2 12
2
1 12 2
2 4
c c
c c
e( t ) m( t ) cos t m( t ) m( t ) cos t
E ( f ) M ( f ) M ( f f ) M ( f f )
Dr. Talal Skaik IUG 2016
• The spectrum of the second component in E(f), being a signal with
carrier frequency 2fc, is centered at ±2fc.
• This component is suppressed by low-pass filter.
• On the other hand, the desired component (1/2)M(f), being a low-pass
spectrum (centered at f = 0) passes through the filter unharmed, resulting
in (½)m(t).
• You can get rid of the inconvenient fraction ½ in the output by using a
carrier 2cosωct instead of cosωct
• This method of recovering the baseband signal is called synchronous
detection or coherent detection where we use a carrier of exactly the
same frequency(same phase) as the carrier used for modulation.
Demodulation
11
1 1
2 22 4
c cE ( f ) M ( f ) M ( f f ) M ( f f )
For a baseband signal: m(t) = cos ωmt = cos 2πfmt
Find the DSB-SC signal, and sketch its spectrum. Identify the upper
and lower sidebands (USB and LSB). Verify that the DSB-SC
modulated signal can be demodulated by the demodulator shown
previously (synchronous detection or coherent detection)
[This case is called tone modulation because the modulating signal is a
pure sinusoid or tone, cos ωmt ]
Example
12 Dr. Talal Skaik IUG 2016
Example
13 Dr. Talal Skaik IUG 2016
Example
14 Dr. Talal Skaik IUG 2016
15 Dr. Talal Skaik IUG 2016
Multiplier Modulators
• Modulation is achieved directly by using an analog multiplier
whose output is proportional to the product of two signals m(t)
and cos ωct.
• Typically, the multiplier is obtained from a variable-gain
amplifier in which the gain parameter is controlled by one of
the signals e.g m(t).
• When cos ωct is applied to the input of the amplifier, the output
is proportional to m(t)cos ωct.
Modulators
16 Dr. Talal Skaik IUG 2016
Non-Linear Modulator
Modulation is achieved through nonlinear devices such as a
semiconductor diode or a transistor.
• Let the input-output characteristics of either of the nonlinear
elements be approximated by a power series:
y(t) = a x(t) + b x2(t)
• where x(t) and y(t) are the input and output of the nonlinear element.
Modulators
17 Dr. Talal Skaik IUG 2016
Modulators
18 Dr. Talal Skaik IUG 2016
Non-Linear Modulator
• Passing z(t) through a bandpass filter tuned to ωc, the signal
am(t) is suppressed and the desired modulated signal
4bm(t)cosωct can pass through the system without distortion
• Because the cos ωct does not appear at the z(t), this setup is
called balanced circuit.
• The nonlinear modulator is an example of a class of modulators
known as balanced modulator.
• Because m(t) appears in z(t), it is called single balance
modulator, however, m(t) is removed through bandpass filter.
Modulators
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Switching Modulators • multiplication operation for modulation is replaced by a simple
switching operation.
• Multiplication of the signal by a sinusoid can be replaced by multiplication the signal by any periodic signal w(t) with fundamental radian frequency ωc.
• The periodic signal can be expressed as:
• Hence
Modulators
20
0
n c n
n
w ( t ) C cos( n t )
0
n c n
n
m( t ) w ( t ) C m(t) cos( n t )
Dr. Talal Skaik IUG 2016
• This shows that the spectrum of the product m(t)w(t) is the spectrum
M(f) shifted to ±fc, ±2fc, ……… ±nfc….
• Passing the signal through bandpass filter of bandwidth 2B Hz and
tuned to fc will result c1m(t) cos(ωct+θ1).
• For a square wave centered at t = 0. Then
• Then m(t) w(t) is given by
Switching Modulators
21
0
n c n
n
m( t ) w ( t ) C m(t) cos( n t )
1 2 1 13 5
2 3 5c c cw ( t ) cos t cos t cos t
1 2 1 13 5
2 3 5c c cm(t)w ( t ) m( t ) m( t ) cos t m( t ) cos t m( t ) cos t
Dr. Talal Skaik IUG 2016
• The signal m(t)w(t) consists of m(t) and an infinite number of modulated signals with angular frequency ωc, 3ωc, 5ωc…..
• Spectrum of m(t)w(t) consists of m(t) shifted by ±fc, ±3fc ….. (with decreasing relative weight).
• We are only interested in m(t)cosωct, hence the signal m(t)w(t) is passed through a bandpass filter of bandwidth 2B Hz centered at ±fc
• This will suppress all spectra components not centered at ±fc to yield the desired modulated signal (2/π)m(t)cos ωct as shown in fig (d).
Switching Modulators
22
1 2 1 13 5
2 3 5c c cm(t)w ( t ) m( t ) m( t ) cos t m( t ) cos t m( t ) cos t
Dr. Talal Skaik IUG 2016
Switching Modulators
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Switching Modulators
24 Dr. Talal Skaik IUG 2016
• The advantage of this scheme is that multiplication of a signal by a
square pulse train is in reality a switching operation.
• It involves switching the signal m(t) on and off periodically and can
be implemented using simple switching element.
• Example is the diode bridge modulator driven by a sinusoid
Acos ωct to produce the switching action.
Switching Modulators
25
•When the signal cos ωct is of a
polarity that will make terminal c
positive with respect to d, all diodes
conduct.
•terminals a and b have the same potential and are effectively shorted.
Dr. Talal Skaik IUG 2016
• During the next half-cycle, terminal d is positive with respect to c and all four diodes off, thus opening terminal a and b.
• This therefore acts as a switch.
• Terminals a and b open and close periodically with carrier frequency fc when a sinusoid A cos ωct is applied across c and d.
Switching Modulators
26 Dr. Talal Skaik IUG 2016
• To obtain m(t)cos wct, terminals a and b are connected in series or across (parallel) to m(t) as shown below:
• This is called series bridge diode modulator and the shunt bridge diode modulator.
• The switching on and off periodically with fc results in switched signal m(t)w(t) which when bandpassed yields modulated signal (2/π)m(t)cosωct
Switching Modulators
27 Dr. Talal Skaik IUG 2016
• This another switching modulator.
• During the positive half-cycles of the carrier, diodes D1 and D3
conduct and D2 and D4 are off.
• Terminal a is therefore connected to c and terminal b to d.
Ring Modulators
28 Dr. Talal Skaik IUG 2016
• During negative half-cycles of the carrier, D1 and D3 are off, D2 and
D4 are conducting
• Terminal a and d are connected and so is b and c.
• Output is proportional to m(t) during positive half-cycle and to –m(t)
during the negative half-cycle.
Ring Modulators
29 Dr. Talal Skaik IUG 2016
• In effect, m(t) is multiplied by a square pulse w0(t) shown below:
Ring Modulators
30 Dr. Talal Skaik IUG 2016
• The Fourier series of w0(t) is given by:
• When m(t)w0(t) is passed through a bandpass filter tuned to ωc, the filter output will be (4/π)m(t)cos ωct.
Ring Modulators
31
4 1 13 5
3 5c c cw ( t ) cos t cos t cos t
4 1 13 5
3 5
i 0
c c c
and v (t) = m(t)w ( t )
m( t ) cos t m( t ) cos t m( t ) cos t
Dr. Talal Skaik IUG 2016
• The Ring modulator circuit has two inputs: m(t) and cos ωct
• The input to the bandpass filter does not contain either of these inputs
• As a result, this circuit is an example of a double balanced modulator.
Ring Modulators
32 Dr. Talal Skaik IUG 2016
• Frequency mixer or converter: is used to change the carrier angular
frequency of a modulated signal m(t)cos ωct from ωc to ωI
• This is achieved by multiplying m(t) cos ωct by 2cos ωmixt, where
ωmix = ωc+ ωI or ωc-ωI and bandpass filtering the product.
• The product x(t) is:-
Frequency Mixer or Converter
33
2 c mix
c mix c mix
x ( t ) m( t ) cos t cos t
m( t ) cos t cos t
Dr. Talal Skaik IUG 2016
• If ωmix = ωc-ωI then
• If ωmix = ωc+ωI then
Frequency Mixer or Converter
34
c mix c mixx ( t ) m( t ) cos t cos t
2I c Ix ( t ) m( t ) cos t cos t
2I c Ix ( t ) m( t ) cos t cos t
Dr. Talal Skaik IUG 2016
• When a bandpass filter tuned to ωI is applied at the output,
m(t) cos ωIt will be passed and the other spectra will be suppressed.
• As a result, carrier frequency ωc has been translated to ωI from ωC.
• The operation of frequency mixing/conversion is known as
heterodyning.
Frequency Mixer or Converter
35 Dr. Talal Skaik IUG 2016