Transcript Linear Modulation_part 1

CHAPTER 2
AMPLITUDE MODULATION (AM)
& DEMODULATION
AMPLITUDE MODULATION (AM)
Sub-topics:
 Modulation Techniques: An Overview
 AM Principles
 The AM Envelope
 AM Frequency Spectrum and Bandwidth
 Modulation Index and Percent of Modulation
 The Mathematical Representation and Analysis
of AM
 AM Power Distribution
 Various types of AM Methods or Schemes
Modulation Techniques:
An overview
 Communications electronics is largely the study
of various modulation techniques and the
modulator and demodulator circuits. It covers
transmission, reception and processing the
information between two or more locations.
 Two basic types of electronic communications
systems: analog (energy Tx and Rx in analog
form) and digital (energy Tx and Rx in digital
form).
Cont’d…
 Direct transmission Vs. Broadband transmission.
Telephone sys
Video over coaxial cable
Long-distance communication??
 It is often impractical to propagate info signals
over a metallic systems or fiber cables or thru
earth’s atmosphere directly, hence necessary to
encode the info onto a higher-freq carrier signal.
Generic Block Diagram of a Comm. System
Tx End
SOURCE
TX
MOD
TX
Channel
DESTINATION
RX
Rx End
DEMOD
Definition
 Modulation is a process of changing some
property (amplitude, frequency or phase) of the
higher frequency signal in accordance with the
information signal.
 The information signal (voice, video or digital
data) is usually called the modulating signal and
the higher frequency being modulated is called
the carrier (usually a sine wave) or modulated
wave.
Why modulation is necessary in
communications?
 It is extremely difficult to radiate low-freq signals
thru earth’s atmosphere (atm) in the form of EM
energy: antenna length.
 Signal propagates with greater efficiency at
higher frequencies.
 The information signals always occupy the same
freq band: interference, use multiplexing.
A standard voice-quality transmission – 3 kHz
Microwaves and satellite radio – 30 MHz
AM Principles
Amplitude modulation (AM) is a process of
changing the amplitude of the high
frequency carrier in proportion with the
instantaneous value of the modulating
signal.
AM is a process of translating information
signal from low band frequency to high
band frequency.
AM is a linear analog modulation process
Cont’d…
 Inexpensive, low quality form of modulation
 Applications of AM:
Commercial broadcasting – audio & video signals
Two way mobile radio communication
 Amplitude of the carrier signal varies with the
information signal. An increase in the modulating
signal amplitude causes the amplitude of the
carrier to increase.
 The modulated signal consist of carrier signal,
upper sideband and lower sideband signals.
The AM Envelope
 AM double-sideband full carrier (AM DSBFC) is
the most commonly used and the oldest and
simplest form of AM modulation.
 Sometimes called conventional AM or simply
AM.
 The outline of the positive and negative peaks of
the carrier frequency re-create the exact shape
of the modulating signal is known as envelope.
 Note that the repetition rate of the envelope is
equal to the frequency of the modulating signal.
AM Generation Waveforms
AM Frequency Spectrum and Bandwidth
 An AM modulator is a non-linear device.
 Nonlinear mixing results in a complex output
envelope consists of the carrier frequency and
the sum (fc + fm) and difference (fc – fm)
frequencies (called cross-products).
 The cross-products are displaced from the
carrier frequency by fm on both sides of it.
 AM modulated wave contains no frequency
component of fm.
Frequency spectrum of an AM DSBFC
Wave
Bandwidth (BW)
The BW of an AM DSBFC wave is equal to
the difference between the highest upper
side frequency and lowest lower side
frequency:
BW = [fc + fm(max)] – [fc – fm(max)]

= 2fm(max)
For efficiency transmission the carrier and
sidebands must be high enough to be
propagated thru earth’s atm.
Example 1
 For a conventional AM modulator with a carrier
freq of fc = 100 kHz and the maximum
modulating signal frequency of fm(max) = 5 kHz,
determine:
a) Freq limits for the upper and lower sidebands.
b) Bandwidth.
c) Upper and lower side frequencies produced
when the modulating signal is a single-freq 3kHz tone.
d) Draw the output freq spectrum.
Modulation Index and Percent of
Modulation
 Used to describe the amount of amplitude
change (modulation) present in an AM
waveform.
 Percentage modulation (%m) is simply the
modulation index (m) stated as a percentage.
 Moe specifically percent modulation gives the
percentage change in the amplitude of the
output wave when the carrier is acted on by a
modulating signal.
Cont’d…
 Mathematically, the modulation index is
m = modulation index
Vm = peak change in the amplitude output
waveform (sum of voltages from upper and
lower side frequencies)
Vc = peak amplitude of the unmodulated
carrier
m
Vm
Vc
 And the percentage of modulation index is
Vm
%m
x 100 %
Vc
Determining modulation index from Vmax
and Vmin
Cont’d…
 If the modulating signal is a pure, single-freq
sine wave and the process is symmetrical
then the modulation index can be derived as
1
follows:
V 
(V  V )
m
m ax
m in
2
1
Vc 
(Vm ax  Vm in )
2
 Therefore,
1
(Vmax  Vmin )
(V  Vmin )
m 2
 max
1
(Vmax  Vmin )
(Vmax  Vmin )
2
Cont’d…
 Since the peak change in of modulated output
wave Vm is the sum of the usf and lsf voltages
hence,
Vm  Vusf  Vlsf
where Vusf  Vlsf
 Then
Vusf  Vlsf
1
(V
 Vm in )
Vm 2 m ax


2
2
1
 (V m ax  Vm in )
4
Vusf = peak amplitude
of the lower side
frequency (volts)
Vlsf = peak amplitude
of the upper side
frequency (volts)
Cont’d…
From the modulated wave displayed in the
previous slide, the maximum and minimum
values of the envelope occurs at
+Vmax = Vc + Vusb + Vlsb
+Vmin = Vc – Vusb – Vlsb
-Vmax = - Vc - Vusb - Vlsb
-Vmin = - Vc + Vusb + Vlsb
% modulation of AM DSBFC envelope
Cont’d…
For proper AM operation, Vc ≤ Vm means
that 0≤ m ≤ 1.
If Vc > Vm means that m > 1 leads to
severe distortion of the modulate wave.
If Vc = Vm the percentage of modulation
index goes to 100%, means the maximum
information signal is transmitted. In this
case, Vmax = 2Vc and Vmin = 0.
Example 2
Suppose that Vmax value read from the
graticule on an oscilloscope scree is 4.6
divisions and Vmin is 0.7 divisions.
Calculate the modulation index and
percentage of modulation.
Example 3
 For the AM waveform shown in Figure below,
determine
a) Peak amplitude of the upper and lower side
frequencies.
b) Peak amplitude of the unmodulated carrier.
c) Peak change in the amplitude of the envelope.
d) Modulation index.
e) Percent modulation.
AM Envelope for Example 3
The Mathematical Representation and
Analysis of AM
 Representing both the modulating signal Vm(t) and the
carrier signal Vc(t) in trigonometric functions.
 The AM DSBFC modulator must be able to produce
mathematical multiplication of these two analog
signals.
v m (t )  Vm sin (2f m t )
v am (t )  [Vc  Vm sin (2f m t )] sin (2f c t )
vc (t )  Vc sin (2f c t )
Cont’d…
 Substituting Vm = mVc gives:
v am (t )  [Vc  mVc sin (2f m t )] sin (2f c t )
 [1  m sin (2f m t )] Vc sin (2f c t )
Constant +
mod. signal
Unmodulated
carrier
Cont’d…
 The constant in the first term produces the
carrier freq while the sinusoidal component in
the first term produces side bands frequencies
v am (t )  Vc sin (2f c t )  [mVc sin (2f m t )] [sin (2f c t )]
 Vc sin (2f c t ) 
Carrier frequency 
signal (volts)
mVc
cos[2 ( f c  f m )t ]
2
mVc
cos[2 ( f c  f m )t ]
2
Lower side frequency
signal (volts)
Upper side frequency
signal (volts)
Cont’d…
From the equation it is obvious that the
amplitude of the carrier is unaffected by
the modulation process.
The amplitude of the side frequencies
depend on the both the carrier amplitude
and modulation index.
At 100% modulation the amplitudes of side
frequencies are each equal to one-half the
amplitude of the carrier.
Generation of AM DSBFC envelope showing the
time-domain of the modulated wave, carrier and
sideband signals
Voltage spectrum for an AM DSBFC wave
Example 4

a)
b)
c)
d)
e)
One input to a conventional AM modulator is a 500kHz carrier with an amplitude of 20 Vp. The second
input is a 10-kHz modulating signal that is of sufficient
amplitude to cause a change in the output wave of
±7.5 Vp. Determine
Upper and lower side frequencies.
Modulation index and percentage modulation.
Peak amplitude of the modulated carrier and the upper
and lower side frequency voltages.
Maximum and minimum amplitudes of the envelope.
Expression for the modulated wave.
AM Power Distribution
 In any electrical circuit, the power dissipated is
equal to the voltage squared (rms) divided by
the resistance.
 Mathematically power in unmodulated carrier is
2
(V / 2 ) 2 Vc
Pc  c

R
2R
Pc = carrier power (watts)
Vc = peak carrier voltage (volts)
R = load resistance i.e antenna (ohms)
Cont’d
 The upper and lower sideband powers will be
Pus b
(mV c / 2) 2 m 2Vc
 Plsb 

2R
8R
2
 Rearranging in terms of Pc,
Pus b
m2
 Plsb 
4
 Vc 2  m 2


Pc
 2R 
4


Cont’d…
 The total power in an AM wave is
Pt  Pc  Pusb  Plsb
 Substituting the sidebands powers in terms of PC yields
m2
m2
Pt  Pc 
Pc 
Pc
4
4
m2
m2
 Pc 
Pc  Pc [1 
]
2
2
 Since carrier power in modulated wave is the same as
unmodulated wave, obviously power of the carrier is
unaffected by modulation process.
Power spectrum for AM DSBFC wave
with a single-frequency modulating signal
Cont’d…
 With 100% modulation the maximum power in
both sidebands equals to one-half the carrier
power.
 One of the most significant disadvantage of AM
DSBFC is with m = 1, the efficiency of
transmission is only 33.3% of the total
transmitted signal. The less wasted in the carrier
which brings no information signal.
 The advantage of DSBFC is the use of relatively
simple, inexpensive demodulator circuits in the
receiver.
Example 5
 For an AM DSCFC wave with a peak
unmodulated carrier voltage Vc = 10 Vp,
a load resistor of RL = 10  and m = 1,
determine
a) Powers of the carrier and the upper and
lower sidebands.
b) Total sideband power.
c) Total power of the modulated wave.
d) Draw the power spectrum.
Amplitude modulation with digital signal
 Digital signal i.e binary data may also used to
amplitude modulate a carrier.
 Figure below shows a binary signal modulating a
sine wave carrier .
 In Amplitude Shift Keying (ASK), carrier switches
between two different levels. Binary ‘1’ produces
a maximum carrier amplitude and binary ‘0’
produces a lower-value carrier.
 A special case of ASK is On-off Keying (OOK) in
which the carrier is simply switched on and off.
Amplitude modulation of a carrier with
binary information: ASK and OOK