Amplitude modulation

Analog Modulation
Analog-to-analog conversion is the representationAnalog-to-analog conversion is the representation
of analog information by an analog signal. Oneof analog information by an analog signal. One
may ask why we need to modulate an analogmay ask why we need to modulate an analog
signal; it is already analog. Modulation is neededsignal; it is already analog. Modulation is needed
if the medium is bandpass in nature or if only aif the medium is bandpass in nature or if only a
bandpass channel is available to us.bandpass channel is available to us.

5.2
Types of analog-to-analog modulation

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

5.4
Amplitude Modulation
• A carrier signal is modulated only in amplitude
value
• The modulating signal is the envelope of the
carrier
• The required bandwidth is 2B, where B is the
bandwidth of the modulating signal
• Since on both sides of the carrier freq. fc, the
spectrum is identical, we can discard one half,
thus requiring a smaller bandwidth for
transmission.

5
AM Modulation/Demodulation
Modulator Demodulator
Baseband Signal
with frequency
fm
(Modulating Signal)
Bandpass Signal
with frequency
fc
(Modulated Signal)
Channel
Original Signal
with frequency
fm
Source Sink
fc >> fm
Voice: 300-3400Hz GSM Cell phone: 900/1800MHz

CSULB May 22, 2006 6
• The amplitude of high-carrier signal is varied
according to the instantaneous amplitude of the
modulating message signal m(t).
Carrier Signal: or
Modulating Message Signal: or
The AM Signal:
cos(2 ) cos( )
( ): cos(2 ) cos( )
( ) [ ( )]cos(2 )
c c
m m
AM c c
f t t
m t f t t
s t A m t f t
π ω
π ω
π= +

7
AM Signal Math Expression
• Mathematical expression for AM: time domain
• expanding this produces:
• In the frequency domain this gives:
( ) (1 cos ) cosAM m cS t k t tω ω= +
( ) cos cos cosc cAM mS t t k t tω ω ω= +
[ ])cos()cos(coscos:using 2
1 BABABA ++−=
2 2( ) cos cos( ) cos( )c c c
k k
AM m mS t t t tω ω ω ω ω= + − + +
frequency
k/2
k/2
Carrier, A=1.
upper sideband
lower
sideband
Amplitude
fcfc-fm fc+fm

CSULB May 22, 2006 8
AM Power Frequency Spectrum
• AM Power frequency spectrum obtained by squaring
the amplitude:
• Total power for AM:
.
2 2
2
2
4 4
1
2
k k
A
k
= + +
= +
freq
k2
/4k2
/4
Carrier, A2
=12
= 1
Power
fcfc-fm fc+fm

9
• 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).

CSULB May 22, 2006 10
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.
frequency
1.4 MHz
1,385,000Hz to
1,399,980Hz
1,400,020Hz to
1,415,000Hz
fc

CSULB May 22, 2006 11
Modulation Index of AM Signal
m
c
A
k
A
=
)2cos()( tfAtm mm π=
Carrier Signal: cos(2 ) DC:c Cf t Aπ
For a sinusoidal message signal
Modulation Index is defined as:
Modulated Signal: ( ) [ cos(2 )]cos(2 )
[1 cos(2 )]cos(2 )
AM c m m c
c m c
S t A A f t f t
A k f t f t
π π
π π
= +
= +
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.

CSULB May 22, 2006 12
Modulation Index of AM SignalModulation Index of AM Signal

CSULB May 22, 2006 13

CSULB May 22, 2006 14

15
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 ½ of the carrier amplitude.
Since power is proportional to the square of the voltage, each
has ¼ of the carrier power. ¼ x 1kW = 250W Total sideband
power = 2 x 250 = 500W. Total transmitted power = 1kW +
500W = 1.5kW

16
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.

Envelope/Diode AM Detector
When an AM signal is received, the receiver must
perform a converse process to get the original signal
(Information Signal ) back . This process is known as
detection or demodulation, the simplest process which
is used widely in AM radios is the Envelop Detector .
Envelop Detector is an electronic circuit which is used
to recover ( Demodulate ) the original signal in AM
systems, its constructed from just one diode, one
capacitor and one resistor .
This is essentially just a halfwave rectifier which
charges a capacitor to
a voltage = the peak voltage of the AM signal .

CSULB May 22, 2006 19
If the modulation depth is > 1, the distortion below occurs
K>1

• The output of the detector follows the envelop of the
modulated signal. On the positive cycles of the input
signal, the diode conducts and the capacitor charges
up to the peak voltage of the input signal. As the input
falls below this peak value, the diode is cut off,
because the capacitor voltage is greater than the input
signal voltage, thus causing the diode to open. The
capacitor now discharges through the resistor at slow
rate. The discharge process continues until the nest
positive half-cycle. When the input signal becomes
greater than the output across the capacitor, the diode
conducts again and the process is repeated.

CSULB May 22, 2006 21
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.

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

Demodulation
If we assume zero path delay between the modulator and
demodulator, then the ideal LO signal is cos(ωct).
Analysing this for a AM input =
( )( ) ( )tωtm+V cDC cos

CSULB May 22, 2006 24
Exercises: Draw the Spectrums
a) cos(ωct)cos(ω1t)
from cosAcosB= 1/2[cos(A-B)+cos(A+B)]
we get: cos(ωct)cos(ω1t)=1/2[cos(ωc-ω1)t + cos(ωc+ω1)t]
Hence the spectrum of this is:
b) cos2
ωt
from cos2
A=1/2[1+cos2A]
we get: cos2
ωt=1/2[1+cos2ωt]
The spectrum is thus:
ωc-ω1 ωc+ω1
1/2 1/2
frequency
amplitude
1/2
freq
2ω
1/2
DC=0Hz

Demerits of AM DSB FC
An unmodulated RF
carrier requires narrow
bandwidth
Modulation results in
creation of a carrier and 2
Sidebands. This
requires more power.
Moreover carrier contains
no information.

Why DSB SC?
 The carrier contains no information.
 So we can think of avoiding or suppressing

Why SSB?
 The carrier contains no audio information.
The sidebands contains duplicated information

Amplitude modulation

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Amplitude modulation