UNIT - 1

AMPLITUDE
MODULATION
Analog Modulation
The purpose of a communication system is to transmit information signals (baseband
signals) through a communication channel
The term baseband is used to designate the band of frequencies representing the original
signal as delivered by the input transducer
For example, the voice signal from a microphone is a baseband signal, and
contains frequencies in the range of 0-3000 Hz
The hello wave is a baseband signal:
 Need For The Modulation Process:

To reduce the height of the antenna

To avoid mixing signals
To increase the range of
communication
To improve quality of reception
Lastly to increase over all strength
 What is Modulation
Modulation
In the modulation process, some characteristic of a high-
frequency carrier signal (bandpass), is changed according to
the instantaneous amplitude of the information (baseband)
signal.
Why Modulation
Suitable for signal transmission (distanceetc)
Multiple signals transmitted on the same channel
Capacitive or inductive devices require high frequency AC
input (carrier) to operate.
Stability and noise rejection
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 About Modulation

Application Examples
broadcasting of both audio and
video signals.
Mobile radio communications, such
as cell phone.

Basic Modulation Types

Amplitude Modulation: changes the amplitude.
Frequency Modulation: changes the frequency.
Phase Modulation: changes the phase.

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 AM Modulation/Demodulation
Source Sink
Channel

Modulator Demodulator

Baseband Signal Bandpass Signal Original Signal

with frequency with frequency with frequency
fm fc fm
(Modulating Signal) (Modulated Signal)
fc >> fm
Voice: 300-3400Hz GSM Cell phone: 900/1800MHz
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 Amplitude Modulation
The amplitude of high-carrier signal is varied
according to the instantaneous amplitude of the
modulating message signal m(t).

Carrier Signal: cos(2 f ct ) or cos(ct )

Modulating Message Signal: m(t ) : cos(2 f mt ) or cos(mt )
The AM Signal: s AM (t ) [ Ac m(t )]cos(2 f ct )

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 * AM Signal Math Expression*
Mathematical expression for AM: time domain
S AM (t ) (1 k cos mt ) cos ct
expanding this produces:
S AM (t ) cos ct k cos mt cos ct
using : cos A cos B 1
2 cos( A B) cos( A B)
S AM (t ) cos ct k2 cos(c m )t k2 cos(c m )t
In the frequency domain this gives:
Carrier, A=1.
Amplitude k/2
k/2
frequency

lower fc-fm fc fc+fm

sideband upper sideband
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 AM Power Frequency Spectrum
AM Power frequency spectrum obtained by squaring
the amplitude:
Carrier, A2=12 = 1
Power

k2/4 k2/4

fc-fm fc fc+fm freq .

2 2
k k
A2
Total power for AM: 4 4
k2
1
2

CSULB May 22, 2006

 Amplitude Modulation

The AM signal is generated using a multiplier.

All info is carried in the amplitude of the
carrier, AM carrier signal has time-varying
envelope.
In frequency domain the AM waveform are
the lower-side frequency/band (fc - fm), the
carrier frequency fc, the upper-side
frequency/band (fc + fm).

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 Square-law modulator
v (t ) av (t ) bv (t ) 2
o i i

v ' (t ) [aA 2Abm (t )]cos 2 f t

o c

f c 3B To avoid overlap the spectrum of

m 2 (t ) and M (f f )
c
 Switching modulator

Assume m (t) = A , and diode an ideal switch

v o (t ) v i (t )w (t ),where
1 2 (1)n 1
w (t ) cos 2 f c (2n 1)t
2 n 1 2n 1
A 2
v o (t ) [ m (t )]cos 2 f ct
'

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 AM Modulation Example
The information signal is usually not a single frequency but a
range of frequencies (band). For example, frequencies from
20Hz to 15KHz. If we use a carrier of 1.4MHz, what will be the
AM spectrum?
In frequency domain the AM waveform are the lower-side
frequency/band (fc - fm), the carrier frequency fc, the upper-
side frequency/band (fc + fm). Bandwidth: 2x(25K-20)Hz.

1.4 MHz
frequency

1,385,000Hz to fc 1,400,020Hz to
1,399,980Hz 1,415,000Hz

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 Modulation Index of AM Signal
For a sinusoidal message signal m(t ) Am cos(2f mt )
Carrier Signal: cos(2 f ct ) DC: AC

Modulated Signal: S AM (t ) [ Ac Am cos(2 f mt )]cos(2 f ct )

Ac [1 k cos(2 f mt )]cos(2 f ct )
Am
k
Modulation Index is defined as: Ac
Modulation index k is a measure of the extent to
which a carrier voltage is varied by the modulating
signal. When k=0 no modulation, when k=1 100%
modulation, when k>1 over modulation.
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Modulation Index of AM Signal

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Modulation Index of AM Signal

CSULB May 22, 2006 16

Modulation Index of AM Signal

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 Modulation Depth
Amax = maximum peak-to-peak of waveform
Amin = minimum peak-to-peak of waveform

This may be shown to equal

U=Amax-Amin/Amax+ Amin

A
m
A
c 2Ami 2Amax
n

CSULB May 22, 2006 18

 High Percentage Modulation
It is important to use as high percentage of modulation as
possible (k=1) while ensuring that over modulation (k>1)
does not occur.
The sidebands contain the information and have maximum
power at 100% modulation.
Useful equation
Pt = Pc(1 + k2/2)
Pt =Total transmitted power (sidebands and carrier)
Pc = Carrier power

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 Example
Determine the maximum sideband power if the carrier output
is 1 kW and calculate the total maximum transmitted power.

Max sideband power occurs when k = 1. At this percentage

modulation each side frequency is of the carrier amplitude.
Since power is proportional to the square of the voltage, each
has of the carrier power. x 1kW = 250W Total sideband
power = 2 x 250 = 500W. Total transmitted power = 1kW +
500W = 1.5kW

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 Demodulation of AM Signals

Demodulation extracting the baseband message from

the carrier.

There are 2 main methods of AM Demodulation:

Envelope or non-coherent detection or demodulation.

Synchronised or coherent demodulation.

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 Envelope/Diode AM Detector

If the modulation depth is > 1, the distortion below occurs

K>1
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 Synchronous or Coherent
Demodulation

This is relatively more complex and more expensive. The Local

Oscillator (LO) must be synchronised or coherent, i.e. at the same
frequency and in phase with the carrier in the AM input signal.

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 Synchronous or Coherent
Demodulation
If the AM input contains carrier frequency, the LO or synchronous
carrier may be derived from the AM input.

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 Synchronous or Coherent
Demodulation
If we assume zero path delay between the modulator and
demodulator, then the ideal LO signal is cos(ct).

Analysing this for a AM input = VDC + mt cosct

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 Coherent Detection
Assume zero path delay between the modulator and demodulator:
VX = AM input x LO

= VDC + mt cosc t cosc t

= VDC + mt cos 2 c t
= VDC + mt 1 + 1 cos2ct
2 2

VDC m t VDC m t
Vx = + + cos 2ct + cos 2ct
2 2 2 2
Note the AM input has been 'split into two' red part' has
moved or shifted up to higher frequency: m t cos 2 t +V cos 2 t
c DC c
2
VDC m t
and blue part shifted down to baseband:
2 2
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 Diode v.s Coherent
1. Diode-: Unable to follow fast-modulation properly
2. Diode-: Power is absorbed from the tuned circuit by the
diode circuit.
3. Diode-: Distortion produced is not acceptable for some
communications.
4. Diode+: Obviously simple, low cost.
5. Coherent+: Low Distortion
6. Coherent+: Greater ability to follow fast-modulation.
7. Coherent+: The ability to provide power gain
8. Coherent-: Complex and expensive

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Double Side Band
Suppressed Carrier

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 Double Side Band Suppressed Carrier

From AM spectrum:
Carries signal c carries no information m.
Carries signal consumes a lot of power more
than 50%

Carrier

LSB USB

c - m c c + m
Single frequency

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 DSB-SC - Theory
General expression:c(t ) [k1m(t ) C ] cos (ct c )

Let k1 = 1, C = 0 and c = 0, the modulated carrier signal, therefore:

c(t ) m(t ) cos ct

Information signal m(t) = Em cos mt
Thus

c(t ) Em cos mt cos ct

MEc MEc
cos (c m )t cos (c m )t
2 2
upper side band lower side band
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 DSB-SC - Waveforms

Mixer
(Multiplier)

B = 2m

Notice: No carrier frequency

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 DSB-SC - Implementation
Balanced modulator

AM Ec (1+ 0.5 m(t) cos ct

0.5 m(t)
mod.
+
Carrier DSB-SC
Ec cos ct +
Ec m(t) cos ct
-
AM
-0.5 m(t)
mod. Ec (1- 0.5 m(t) cos ct

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 DSB-SC - Detection
Synchronous detection v(t ) 12 m(t )
Low pass
DSB-SC Multiplier filter
Message signal

Local oscillator y(t ) [m(t ) cos ct ] cos ct

c(t) = cos ct
y (t ) m(t ) 12 [1 cos 2c t ]
12 m(t ) 12 m(t ) cos 2c t
Condition:
Local oscillator has the same information high frequency
frequency and phase as that of the
carrier signal at the transmitter. Low pass filter

m 2c-m 2c+m 33
 DSB-SC - Synchronous Detection
Case 1 - Phase error v(t ) 12 m(t ) cos
Low pass
DSB-SC Multiplier Message signal
filter

Local oscillator y(t ) [m(t ) cos ct ] cos (ct )

c(t) = cos(ct+)
y (t ) m(t ) 12 cos (2c t ) m(t ) 12 cos ()
m(t ) 12 cos m(t ) 12 cos (2c t )
Condition:
Local oscillator has the same information high frequency
frequency but different phase
compared to carrier signal at the Low pass filter
transmitter.
m 2c-m 2c+m 34
 Phase Synchronisation - Costas Loop
In-phase
yip(t) 0.5Ec m(t) cos
X Recovered
DSB-SC LPF
signal
Ec cos (ct+)
Vphase(t) Phase
VCO
discriminator

90o
phase shift
Ec sin (ct+)
0.5Ec m(t) sin
X. yqp(t) LPF
Quadrature-phase
When there is no phase error. The quadrature component is zero
When 0, yip(t) decreases, while yqp(t) increases
The out put of the phase discriminator is proportional to 35
 DSB-SC - Synchronous Detection
Case 1 - Frequency error v(t ) 12 m(t ) cos
Low pass
DSB-SC Multiplier Message signal
filter

Local oscillator y(t ) [m(t ) cos ct ] cos (ct )

c(t)=Eccos(ct+)
y (t ) m(t ) 12 cos (2c t ) m(t ) 12 cos ()
m(t ) 12 cos m(t ) 12 cos (2c t )
Condition:
Local oscillator has the same information high frequency
phase but different frequency
compared to carrier signal at the Low pass filter
transmitter.
m 2c-m 2c+m 36
 DSB-SC - Square Detection
g(t)
Squaring
DSB-SC Band pass y(t)
Si(t)
circuit by 2
g =x2 C filter

Regenerated
carrier
2c z(t)
Multiplier

Low pass filter Message

signal

g(t) = Si2(t) = B2 cos2 mt cos2 ct

= B2 ( + cos 2 mt )( + cos 2 ct )
= B2/4 [1 + cos 2(c + m)t + cos 2(c - m)t + cos 2mt + cos 2 ct ]

y(t) = B2/4 cos 2wct z(t) = B2/4 cos wct

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 DSB-SC - Power
The total power (or average power):

2
2 MEc / 2
PT DSB SC
R 2
( MEc ) 2

4R

The maximum and peak envelop power

( MEc ) 2
PP DSB SC
R
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 DSB-SC - Summary
Advantages:
Lower power consumption

Disadvantage:
Complex detection

Applications:
- Analogue TV systems: to transmit colour information
- For transmitting stereo information in FM sound broadcast
at VHF

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