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Modulations/demodulations in Transmitters/Receivers

Amplitude modulation (AM)

Angle modulation – Frequency, phase

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AM modulation

AM has the advantage of being usable with very simple modulators and demodulators

Disadvantages include poor performance in the presence of noise and inefficient use of transmitter power

Applications: broadcasting, aircraft communications in the VHF frequency range

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Full carrier AM

V(t) = (Ec + em)sin(ωc x t)

Example 3.1

Modulation index m = Em / Ec

Over modulation

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Optical Carrier fc

Modulating signal em

DC bias

AM modulation circuits

RF modulation

Optical modulation

Modulating signal em

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Modulation index for multiple modulating frequencies

mT = sqrt (m12 + m2

2 + …)

Example 3.3

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Measurement of modulation index

m = (Emax – Emin) / (Emax + Emin)

Example 3.4

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Full carrier AM: frequency domain

V(t) = Ec sin(ωc t) carrier

+ mEc/2 cos(ωc - ωm )t left sideband

– m Ec/2 cos(ωc + ωm )t right sideband

Example 3.5

Ec

m/2Ec

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Bandwidth and power relationships

Bandwidth:

B = 2 fm

Power relationship:

Plsb = m2 /4 Pc

Pt = Pc (1 + m2/2)

Ec

m/2Ec

2fm

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Some observations

The total power in an AM signal increases with modulation, reaching a value 50% greater than that of the un-modulated carrier for 100% modulation

The extra power with modulation goes into the sidebands: the carrier power does not change with modulation

The useful power is rather small, reaching a maximum of 1/3 of the total signal power . For this reason, AM transmission is more efficient when the modulation index is as close to 1

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Measuring the modulation index in the frequency domain

M = 2 x sqrt(Plsb / Pc)

Example 3.11

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Quadrature AM

AM modulator

AM modulator

Phase shifter

Cos

Sin

Demodulation is the reverse process

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QAM demodulation

Carrier recovery

Phase shifter

Cos

Sin

To study the case when there exists phase shift from the carrier

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Suppressed-Carrier AM

In normal AM, two-third of the transmitted power is found in the carrier

Suppressed-carrier AM removes the carrier

Psb = 0.5 Pc = 1/3 Pt

Pc

1/6 Pt

Pt/21/6 Pt

Pt/2

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0

50

100

150

200

250

0 100 200 300

Time (ps)

Am

plit

ud

e (a

.u.)

0

50

100

150

200

250

0 100 200 300

Time (ps)

Am

plit

ud

e (a

.u.)

1

1.5

2

2.5

3

3.5

4

4.5

1551 1552 1553 1554 1555

Wavelength (nm)

Po

wer

(d

B)

1

1.5

2

2.5

3

3.5

4

4.5

1551 1552 1553 1554 1555

Wavelength (nm)

Po

we

r (d

B)

CSRZ RZ PW = 11.4 ps, ER = 13.7 dB PW = 9.2 ps, ER = 18.0 dB

Streak camera trace

Optical spectra

Practical examples: RZ and CSRZ

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Single-sideband AM

Two sidebands of an AM signal are mirror images

Removing one sideband reduces the bandwidth, and improves the signal-to-noise ratio

Pt/2 Pt/2 DSBSC SSB

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Power in suppressed-carrier signals

Peak envelop power is used for suppressed-carrier signals:

PEP = [Vp / sqrt(2)]2 / RL

Example 3.11

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Matlab simulation

P128, example of AM modulation

A simple AM modulator

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Angle modulation

Angle modulation can be divided into frequency (FM) and phase modulation (PM)

Both FM and PM are widely used in communication systems

The most important advantage of FM or PM over AM is the possibility of improved signal to noise ratio

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Frequency modulation

Frequency

Implementation

Amp VCO

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Frequency modulation

Cos(ωc t + θ), ωc is the modulating signal

Frequency deviation:

fsig = fc + kf Em(t)

Where kf is the modulator deviation constant

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Example 4.1

kf = 30 kHz/v, carrier frequency is 175 MHz, find out the frequency for an modulating signal equal to: 150 mV and –2V

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Frequency modulation index

Peak frequency deviation δ = kf Em

Fsig( fc + δ sin ωm t)

Frequency modulation index mf = δ / fm

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Example 4.3

An FM transmitter operates at its maximum deviation of 75 kHz, find out the modulation index for a sine modulation signal with a frequency of 15 kHz and 50 Hz.

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Phase modulation

kp = Φ/em

Kp: phase modulator sensitivity

Φ: phase deviation

em: signal amplitude

θ(t) = θc + kp em(t)

in case of sin signal: θ(t) = θc + mp sinωmt

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Relationship between frequency modulation and phase modulation

f

Phase shift

θ = ωt = Integral(ω dt)

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Implementation of a phase modulator

Amp VCO

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