Transcript chapter2 - Elearning-KL

CHAPTER 2
Amplitude Modulation
Objectives: After completing this chapter, you will be able to;
1.
Calculate the modulation index and percentage of
modulation of an AM signal given the amplitudes of
the carrier and modulating signals.
2. Define over modulation and explain how to alleviate
its effects.
3. Explain how the power is distributed between the
carrier and the sideband.
4. Compare time-domain, freq-domain of AM signal.
5. Explain DSB and SSB and state the main advantages of
SSB over conventional AM.
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Introduction
 To carry the information signal to a destination, we
need a carrier.
 Carrier signal has the higher frequency than the
information signal.
 AM is the first to used this technique and it became
the basis for a variety of more sophisticated schemes
such as television broadcasting and long-distance
telephony.
Base band signal is the modulating signal/original
information signal either in a digital or analog form
(intelligent/message) in communication system
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Example: voice signal (300Hz – 3400Hz
WHAT IS MODULATION?
Modulation is the process of varying a carrier
signal in order to use that signal to convey
information.
WHAT is Carrier Signal?
A carrier signal or carrier wave or carrier is a
waveform (usually sinusoidal) that is modulated
(modified) to represent the information to be
transmitted. This carrier wave is usually of much
higher frequency than the modulating signal (the
signal which contains the information).
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WHAT IS AM?
Amplitude Modulation (AM) is a form of
modulation in which the amplitude of a carrier
wave is varied in direct proportion to that of a
modulating signal.
OR
The information signal (modulating signal)
causes the amplitude of a carrier signal to vary
with time.
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Full Carrier AM
 AM signals can be displayed either in timedomain or frequency domain.
 Time-domain signals, voltage or currents
variations that occur over time, are what displayed
on the screen of an oscilloscope.
 Using trigonometric functions, we can express
the sine-wave carrier with the simple expression;
c = Vc sin 2fc t
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Full Carrier AM
Information /
Modulating
Signal
+
Carrier
Signal
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Full Carrier AM
Modulation
Envelope
+
Carrier
Wave
0
-
Amplitude Modulation Wave
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Full Carrier AM
Figure shows the modulated carrier, AM
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Full Carrier AM
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Full Carrier AM
 AM can also be presented in frequency
domain form. Usually we can get the frequency
spectrum using Spectrum Analyzer.
 Amplitude modulation results in two sidebands.
The frequencies above the carrier frequency
constitute what is referred to as the "upper
sideband"; those below the carrier frequency,
constitute the "lower sideband."
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Full Carrier AM
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Frequency-domain Display
 The modulating signal usually is more complex
than a “single sine-wave tone”.
 In this case, multiple upper and lower
sidebands are produced by the AM process.
 Eg: A voice signal consists of many sine wave
components of different frequencies mixed
together.
 Recall that voice frequencies occur in 300Hz –
3kHz. Therefore, voice signals produce a range
of freq above and below the carrier frequencies.
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Frequency-domain Display
3 kHz
3 kHz
Lower
Sidebands
fc – fm
Upper
Sidebands
fc
fc+fm
• Let say, fc = 2800 kHz., then the max and min of sidebands
frequencies are,
fUSB = fc + fm = 2.8 MHz + 3 kHz = 2803 kHz.
fLSB = fc – fm = 2.8 MHz – 3 kHz = 2797 kHz.
• The total B.W = fUSB – fLSB = 2803 kHz–2797 kHz = 6 kHz
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Frequency-domain Display
• We can also get B.W by using,
B.W = 2 x fm
*fm – max modulating freq.
Eg: A standard AM broadcast station is allowed to
transmit modulating frequencies up to 5 kHz. If
the AM station is transmitting on a freq of 980
kHz, compute the max and min sidebands and
total bandwidth.
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Full Carrier AM
 The carrier is almost always the sine wave but
modulating signal (info.signal) can be anything music,
voice, audio, etc signals.
 In this subject , we are going use the sine wave to
represent the modulating and carrier signals.
 A sine-wave modulating signal can be expressed with
similar formula;
m = Vm sin 2fm t
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Full Carrier AM
Information or
Modulating signal
AM signal
Modulator
 m =Vm sin 2fm t
VAM = Vc sin 2fc t + (Vm
sin 2fm t)( sin 2fc t)
Carrier signal
Vc=Vc sin 2fc t
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Modulation Index & Percentage of Modulation
What is Modulation Index??
Modulation index, m, is used to describe the ratio of maximum
voltage to minimum voltage in the modulated signal.
m=
Vm
OR
m = Vmax - Vmin
Vc
Vmax + Vmin
 In order for undistorted AM to occur, the modulating signal
voltage Vm must be less than the carrier voltage Vc.
 If the modulating signal is equal in magnitude to the
carrier, then m = 1
 When m = 0, no modulation of the carrier is performed. If
m is greater than 1, the carrier is actually cut off for some
period of time, and unwanted harmonics are created at the
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transmitter output.
What is
Percentage of Modulation??
By multiplying the modulation index by 100 gives
the percentage of modulation.
Eg: m = 0.8333 and the percentage of modulation
is 0.8333 x 100% = 83.33%
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100% Modulation
Here, the maximum voltage (Vmax) is 2 V and the
minimum (Vmin) is 0 V. From the modulation index
formula:
m=
2-0
2+0
= 1.0
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50% Modulation
Here, the maximum voltage (Vmax) is 3 V and
the minimum (Vmin) is 1 V. From the
modulation index formula:
m=
3-1
3+1
= 0.5
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25% Modulation
Here, the maximum voltage (Vmax) is 1.25 V and
the minimum (Vmin) is 0.75 V. From the modulation
index formula:
m=
1.25 - 0.75
1.25 + 0.75
= 0.25
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150% Modulation
Here, the maximum voltage (Vmax) is 2.5 V and the
minimum (Vmin) is -0.5 V. From the modulation
index formula:
Clipping of
Envelope no longer the
same shape as original
modulating signal
m=
2.5 - (-0.5)
2.5 + (-0.5)
(-ve) peaks)
= 1.5
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AM Power
 In radio transmission, the AM signal is amplified by a
power amplifier and fed to the antenna which is almost pure
resistance.
 The AM signal is really a composite of several signals
voltages, namely the carrier and the two sidebands, and
each of theses signals produces power in the antenna.
 The total transmitted power PT is;
PT = PC + PLSB + PUSB
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AM Power Distribution
Let’s go back to the original AM equation;
VAM = Vc sin 2fc t + (Vm sin 2fm t)( sin 2fc t)
Using trigo identity:
sin A sin B = cos (A-B) – cos (A+B)
2
2
And substituting this identity, the instantaneous signals
becomes;
VAM = Vc sin 2fc t + Vm cos 2(fc – fm)t - Vm cos 2(fc + fm)t
2
2
CaRriEr
LOWER
SiDeBAnd
UPPER
SiDEbaND
AM Power Distribution
NOW!! Remember that Vc and Vm are peak values of the
carrier and the modulating singnal.
So, How do we convert from ‘peak’ to ‘rms’???
VAM = Vc sin 2fc t + Vm cos 2(fc – fm)t - Vm cos 2(fc + fm)t
2
2 2
2 2
How do we calculate power??
P = V2 /R
Where do we get the ‘R’??? >> From the antenna (our load
impedance the resistive part)
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AM Power Distribution
PT =
Vc
2
R
2
+
REMEMBER:
Vm
2 2
R
2
+
Vm
2 2
R
2
Vm = mVC
That will makes
Power for
LSB
Power for
USB
Vc2 + mVc 2 + mVc 2
2R
8R
8R
This can be factored out giving,
PT =
PT =
Vc2
2R
1 + m 2 + m2
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4
Carrier
Power
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AM Power Distribution
Finally, we get a handy formula for computing the total
power in an AM signal when the carrier power and the
percentage of modulation are known:
PT = Pc 1 + m2
2
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Example : An AM transmitter has a carrier power of 30 W.
The percentage of modulation is 85%. Calculate:
a) the total power
b) the power in one sideband.
 In the real world, it is difficult to determine AM power by
measuring the output voltage and calculating power.
 However, it is easy to measure the current in the load.
 When the antenna impedance is known, the output power
is easily calculated using the formula;
PT = (IT)2 R
 Where,
IT = Ic  (1 + m2/2)
* Ic – unmodulated carrier current in the load
m – modulation index
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Suppressed Carrier
 In AM, 2/3 of the transmitted power is in the carrier
which itself conveys no information.
 Where is the real information?? Class??
It is in the sidebands where both sidebands
bring the SAME information.
DO we need BOTH sidebands than???
 One way to improve the efficiency of AM is to
suppressed the carrier and eliminate one sideband.
 This result a Single-Sideband (SSB) signal.
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A Frequency-domain Display
Suppressed Carrier
Sideband
Sideband
DSBSC
fc-fm
fc
fc+fm
Suppressed Carrier
Suppressed
Sideband
Sideband
SSB
fc-fm
fc
fc+fm
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DSB
 The first step in generating an SSB signal is
suppressing the Carrier, leaving the upper and lower
sidebands.
 This type of signal is referred to as a doublesideband suppressed carrier (DSBSC or DSB)signal.
 What is the benefit??
Of course, there will be NO power wasted
on the carrier.
 DSBSC modulation is simply a special case of AM
with no carrier.
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HOW DOES AM WAVEFORM IS OBTAINED??
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Where Does All the Power Go??
 Let's say we are running a 1 kilowatt (output) AM
transmitter, legally. When there is no modulation the
output power is 1,000 watts.
 When it is modulated to 100 percent the power in
the carrier does not change but additional power is
put into the sidebands.
 That means the power in each sideband is 250
watts. So the total for the carrier plus both sidebands
is 1500 watts.
 That extra power comes from the modulator
tubes.
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Figure below is a comparison of the envelopes of a
normal AM signal and a double sideband suppressed carrier (DSB) signal.
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Comparison of AM & DSB Signals
Both signals are modulated by the same frequency.
The carrier is missing in action and the two sidebands add
together to produce a signal apparently containing twice the
frequency.
 An attempt to detect this wave with a conventional diode
detector would result in a tone of twice the actual
frequency.
 It seems as though we need that carrier after all.
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Put the Carrier Back.
 It's no big deal to put the carrier back in, NOT at the
transmitter but at the RECEIVER.
 All we have to do is to run an oscillator at the center of the
IF band and let it combine with the incoming sidebands.
 If the receiver is not tuned perfectly there is an error in pitch
which makes a mess of music and makes speech sound
funny.
 This is why suppressed carrier has never become a part of
consumer equipment. If the person doing the tuning is a
skilled radio operator the signal can be tuned in close enough
for good intelligibility. It’s difficult to demodulate (recover) at
the receiver.
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SSB Signals’ Benefits
 The primary benefit – Spectrum space it occupies is only
half that of AM and DSB signals. This allows more signals to
be transmitted in the same freq range.
 All the power can be channeled into the single sideband,
producing STRONGER signal that should carry farther. The
transmitter can be made smaller and lighter than AM
transmitter.
 The amount of noise in the signal is reduced because SSB
occupy narrower bandwidth.
 Less fading over a long distances.
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Disadvantages???
 The main disadvantage of DSB and SSB signals is that they
are harder to recover or demodulate at the
receiver.
 So, we have to reinserted the carrier which MUST have the
same phase and frequency as the original signals. This is
difficult requirement.
 When SSB is used for voice transmission, the reinserted
carrier can be made variable but not possible with some kinds
of data signals.
 To solve this a low-level carrier (referred as pilot carrier) is
transmitted along with DSB or SSB. This technique used in FM
stereo transmission and TV broadcasting.
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Amplitude Modulator &
Demodulators Circuits
• Dozens of modulator circuits have been
developed that cause carrier amplitude to
be varied in accordance with the
modulating information signal.
• There are circuits to produce AM, DSB
and SSB at low or high power level.
• Also covered in this sub-chapter are
demodulator circuits for AM, DSB and
SSB.
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Amplitude Modulator
 Amplitude modulators are generally one of two types: low
level and high level.
 Low-level modulators generate AM with small signals
and thus must be amplified.
 High-level modulators produce AM at high power levels,
usually in the final amplifier stage of a transmitter.
 Although the discrete components circuits to be
discussed in the following sections are still used to a
limited extent, keep in mind that today amplitude
modulators and demodulators are in integrated circuit
(IC).
 There are two methods to generate AM – analog
multiplication and non-linear mixing.
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Multiplication Method
vm
Vc
0
t
*Note that the modulating signal uses the peak value of the
carrier rather than zero as its reference point.
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Multiplication Method
 Remember: The peak value of the carrier is the
reference point for the modulating signal; the value of the
modulating signal is added to or subtracted from the
peak value of the carrier.
 So, the instantaneous value of either the top or the
bottom voltage envelope, v1, can be computed using the
expression,
v1 = Vc + vm
= Vc + Vm sin 2fm t
 This express the fact that the instantaneous value of the
modulating signal algebraically adds to the peak value of
the carrier.
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Multiplication Method
 Thus, we can write the instantaneous value of the
complete modulated wave, v2, by;
v2 = v1 sin 2fc t
 Now, substituting the previous derived expression,
v2 = (Vc + Vm sin 2fm t ) sin 2fc t
= Vc sin 2fc t + (Vm sin 2fm t)( sin 2fc t)
 Are u familiar with this expression?
v2 is the instantaneous value of the AM waveform (vAM)
 The 1st term is the carrier and the 2nd term is the
‘product’ of sine-wave carrier and modulating signals.
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Multiplication Method
 So, it is clear that we need a circuit that can multiply the
carrier by the modulating signal and then add the carrier.
Analog multiplier
Modulating Signal
Summer
VAM
Carrier, Vc sin 2fc t
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Non-linear mixing
 One of the simplest amplitude modulator is the diode
modulator shown below.
Modulating
signals
Carrier
Signals
R1
R2
D1
R3
AM output
C
L
Diode modulator
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Low-level AM (Diode Modulator)
Waveform
at the diode
output
Modulating
Signal
+
Carrier
Waveform
at the diode
input
AM output signal
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Low-level Modulation System
Low level modulation systems use linear power amplifiers
to increase the AM signal before transmission.
Final RF
Power amplifier
Amplitude
modulator
Carrier
Oscillator
Voice
modulating
signal
Linear power amplifier
*The voltage is less than 1 V and power in milliwatts.
Usually the amplifier circuit – class A, AB or B.
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High-Level AM
 In high-level
modulation, the
modulator varies
the voltage and
power in the final
RF amplifier
stage of the
transmitter. This
result is high
efficiency in the
RF amplifier and
overall highquality
performance.
Carrier
Input
Final class C
RF power
amplifier
High power
audio amplifier
Microphone
Modulation
transformer
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Amplitude Demodulators
 Demodulators or detectors are circuits that accept
modulated signals and recover the original modulating
information.
AM
signal
D1
C2
R1
Original
Information
C1
Diode detectors
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Crystal Radio Receivers
 The crystal component of the crystal radio receivers that
were widely used in the past is simply a diode.
 Figure below is the diode detector which redrawn from
the previous detector showing an antenna connection
and headphones.
D1
C1
A crystal radio receiver
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Balanced Modulators
 A balanced modulator is a circuit that generates a DSB
signal, suppressing the carrier and leaving only the sum
and difference frequencies at the output.
 Then, the output of the balanced modulator can be
further processed by filters or phase-shifting circuitry to
eliminate one sideband which produce SSB.
 One of the most popular and widely used modulators is
the diode ring or lattice modulator.
 The carrier wave, which is higher frequency and
amplitude than the modulating signal is used as a source
of forward and reverse bias for the diode.
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Balanced Modulators
52
Balanced Modulators
+ve
+
-
53
Balanced Modulators
-
+
54
Output Waveform
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Balanced Modulator
Balanced Modulator Block Diagram
½ Vm(t)
DSB
MODULATOR 1

Vc cos 2fc t
- ½ Vm(t)
VDSBSC
DSB
MODULATOR 2
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DSBSC Mathematical Equation
Output from modulator 1;
VDSB = (Vc + ½ Vm(t) cos 2fct
-------- (1)
Output from modulator 2;
VDSB = (Vc - ½ Vm(t) cos 2fct
--------(2)
(1) – (2) will give us;
VDSBSC = [(Vc + ½ Vm(t)cos 2fct] – [(Vc - ½ Vm(t)cos 2fct]
Where;
Vm(t) = Vm cos 2fmt
So,
VDSBSC = Vm cos 2fmt cos 2fct
= Vm cos 2(fc – fm)t + Vm cos 2(fc + fm)t
2
2
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Balanced Modulators IC
 Another widely used balanced modulator circuit uses
differential amplifiers.
 The popular is 1496/1596 balanced modulator.
 This circuit can work at carrier frequencies up to
approximately 100 MHz and can achieve a carrier
suppression of 50 to 65 dB.
 It is the most versatile circuit available for communication
applications.
 It can reconfigured to perform as an amplitude
modulator or as a synchronous detector.
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Balanced Modulators IC
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SSB Circuits
 Generating SSB Signals: The Filter Method
Balanced
Modulator
DSB
Sideband
Filter
SSB
Carrier Oscillator
Suppressed
Carrier
Microphone
Audio
Amplifier
Lower
Sidebands
Upper
Sidebands
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SSB Circuits - The Filter Method
USB
Filter
Balanced
Modulator
Modulating
Signal
(a)
Balanced
Modulator
Modulating
Signal
LSB
USB
USB
Filter
SSB
Output
Sideband
Filter
(b)
SSB
Output
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SSB Circuits – The Phasing Method
 This method causes one of the sidebands to be
canceled out.
Modulating
Signal
Balanced Modulator
1
Carrier
Oscillator
SSB
Output
90 Phase
Shifter
90 Phase
Shifter
Balanced Modulator
2
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SSB Mathematical Equation
Output from balanced modulator 1;
VDSBSC1 = Vm sin 2fmt sin 2fct
= Vm cos 2(fc – fm)t - Vm cos 2(fc + fm)t ------------ (1)
2
2
Output from balanced modulator 2;
VDSBSC2 = Vm cos 2fmt cos 2fct
= Vm cos 2(fc – fm)t + Vm cos 2(fc + fm)t ------------ (2)
2
2
(1) + (2) will give us,
Vo = Vm cos 2(fc – fm)t ------- LSB
(2) – (1) will give us,
Vo = Vm cos 2(fc + fm)t ------- USB
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SSB Demodulator
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