Modulation (1): Amplitude Modulation

Luiz DaSilva Professor of Telecommunications dasilval@tcd.ie +353-1-8963660

What is modulation and what is it for? q Something we do to an information signal to

make it suitable for transmission

q The process of varying one or more properties of a periodic waveform, called the carrier signal, with a modulating signal that typically contains information to be transmitted

q It typically involves translating a baseband message signal to a bandpass signal at frequencies that are very high compared to the baseband frequency

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Types of modulation q  Modulation can be performed by varying the

Ø  Amplitude Ø  Phase Ø  Frequency of a high frequency carrier in accordance with the amplitude of the message signal

q  Demodulation is the inverse operation: extracting the baseband message from the carrier so that it may be processed at the receiver

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Analog and digital modulation q  Analog Modulation

Ø  Continuous signal Ø  Used in first generation mobile wireless systems such as AMPS (Advanced Mobile Phone System) in USA

q  Digital Modulation Ø  Time sequence of discrete-valued symbols or pulses Ø  Used in current and future mobile radio systems, WiFi, etc.

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Amplitude modulation: characteristics q  Changes the amplitude of the carrier signal

according to the amplitude of the message signal q  All info is carried in the amplitude of the carrier q  There is a linear relationship between the

received signal quality and received signal power q  AM systems usually occupy less bandwidth than

FM systems q  AM carrier signal has a time-varying envelope

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AM signal The amplitude of the carrier signal is varied according to the instantaneous amplitude of the modulating message signal m(t) Carrier signal: AM signal:

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Ac cos(2π fct)

AMModulatorm(t) sAM(t)

sAM (t) = (Ac +m(t))cos(2π fct)

AM signal (cont’d) We can also express sAM(t) as where g(t) = Ac + m(t) g(t) is called the envelope of the AM signal

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sAM (t) = Re{g(t)ej2π fct}

Modulation and demodulation

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Modulator Demodulator

Baseband Signal with frequency

fm (Modulating Signal)

Bandpass Signal with frequency

fc (Modulated Signal)

Wireless Channel

Original Signal with frequency

fm

Source Sink

fc>>fm

AM example Message signal: m(t) = 2 + 2 cos(t) Carrier signal: 4 cos(10t)

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-20

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0

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0 2 4 6 8 10 12 14

AM Double Side Band (DSB) The unmodulated carrier is described as: where

q  Ac = peak amplitude of the carrier

q  ωc = carrier (angular) frequency

q  θ = carrier phase at t=0 (we usually set it to 0)

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c(t) = Ac cos(ωct +θ )

AM DSB example in time domain

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AM DSB example in frequency domain

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-W W 0

0 fc -fc

LOWER SIDEBAND

UPPER SIDEBAND

CARRIER PRESENT

δ(f-fc)δ(f+fc)

modulated signal

message signal M(f)

AM power Consider a single tone modulating wave Power in carrier: Power in upper and lower sidebands:

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m(t) = Am cos(ωmt +θ )

Modulation index The ratio of the total sideband power to the total power in the modulated wave is dependent on the ratio k = Am/Ac We call this ratio the modulation index The fact that, in AM-DSB, so much power is wasted on the carrier is a bad thing

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