# Modulation

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Modulation
Modulation is a process that causes a shift in the range of
frequencies in a signal.
• Signals that occupy the same range of frequencies can be
separated
• Modulation helps in noise immunity, attentuation - depends on
the physical medium
Figure 1 shows the diﬀerent kinds of analog modulation schemes
that are available

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Carrier Modulation
Communication System

Base−band        Carrier         Amplitude         Angle
Modulation       Modulation         (AM)

Frequency     Phase
(FM)        (PM)

Figure 1: A broad view of communication system

• Amplitude Modulation It is the process where, the amplitude of
the carrier is varied proportional to that of the message signal.
– Amplitude Modulation with carrier
Let m(t) be the base-band signal, m(t) ←→ M (ω) and c(t)
be the carrier, c(t) = Ac cos(ωc t). fc is chosen such that

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fc >> W , where W is the maximum frequency component
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of m(t).
The amplitude modulated signal is given by

s(t) = Ac [1 + ka m(t)] cos(ωc t)

Ac
S(ω) = π        (δ(ω − ωc ) + δ(ω + ωc )) +
2
ka Ac
(M (ω − ωc ) + M (ω + ωc ))
2

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m(t)
M( ω)

−f m               fm        ω
t

s(t)

S(ω )

A c /2

1/2 A/2 k M(0)
a

− fc                           fc
ω
t
2fm

Figure 2: Amplitude modulation

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Figure 2 shows the spectrum of the Amplitude Modulated
signal.
– ka is a constant called amplitude sensitivity. ka m(t) < 1 and
it indicates percentage modulation.
– Modulation in AM: A product modulator is used for
generating the modulated signal as shown in Figure 3.

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A c cos(2 π fc t)

+
s(t)
Product
m(t)          Modulator

Figure 3: Modulation using product modulator

– Demodulation in AM: An envelope detector is used to get
the demodulated signal (see Figure 4).

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r
C                v (t)
R       m
+
−

Figure 4: Demodulation using Envelope detector

– The voltage vm (t) across the resistor R gives the message
signal m(t)

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Double Side Band - Suppressed Carrier
(DSB-SC) Modulation
• In AM modulation, transmission of carrier consumes lot of
power. Since, only the side bands contain the information
about the message, carrier is suppressed. This results in a
DSB-SC wave.
• A DSB-SC wave s(t) is given by

s(t) =    m(t)Ac cos(ωc t)
Ac
S(ω) =     π    (M (ω − ωc ) + M (ω + ωc ))
2

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s(t)                                      S(f)

1/2 A M(0)
c

t               −fc                  fc   ω

2fm

Figure 5: DSB-SC modulation

• Modulation in DSB-SC: Here also product modulator is used as
shown in Figure 3, but the carrier is not added. Figure 6 shows
the spectrum of the DSB-SC signal.

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LPF

1/2 A M(0) cos(φ )
c

−2f             0                    2fc
c

Figure 6: Spectrum of Demodulated DSB-SC signal

• Demodulation in DSB-SC: A coherent demodulator is used.
The local oscillator present in the demodulator generates a
carrier which has same frequency and phase(i.e. φ = 0 in
Figure 7) a as that of the carrier in the modulated signal (see
Figure 7)
a Clearly  the design of the demodulator for DSB-SC is more complex than

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that vanilla AM
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v(t)                v o (t)
Product                            LPF
s(t)   Modulator

cos(2 π fc t + φ )

Local
Oscillator

Figure 7: Coherent detector

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v(t) = s(t). cos(ωc t + φ)
= m(t)Ac cos(ωc t) cos(ωc t + φ)
m(t)
=        Ac [cos(2ωc t + φ) + cos(φ)]
2

• If, the demodulator (Figure 7) has constant phase, the original
signal is reconstructed by passing v(t) through an LPF.

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Description: Modulation is converted into the baseband signal transmission signal technology. It will sample the analog signal after quantization, a binary digital signal "1" or "0" on-off modulated light carrier, and the pulse code (PCM). Digital modulation has the advantage of strong anti-interference relay when the impact of noise and dispersion does not accumulate, so you can achieve long distance transmission. The disadvantage is the need to wide band devices also are complex.