Analog Transmission

Chaiporn Jaikaeo

Department of Computer EngineeringKasetsart University

01204325 Data Communications and Computer Networks

Based on lecture materials from Data Communications and Networking, 5th ed.,Behrouz A. Forouzan, McGraw Hill, 2012.

Revised 2020-08-06

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Outline•Aspects of Digital-to-Analog Conversion•Amplitude Shift Keying• Frequency Shift Keying

•Phase Shift Keying•Quadrature Amplitude Modulation•Analog-to-Analog Conversion

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Digital-to-Analog Conversion•Required to send digital data over a band-pass channel

◦ Also known as modulation

(band-pass channel)

https://en.wikipedia.org/wiki/Modem

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Carrier Signals•Carrier signal is a high-frequency signal acting as a base for

information signal•Also known as Carrier Frequency

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• Simplest form of periodic signal

•General form: 𝑦(𝑡) = 𝐴×sin(2𝜋𝑓𝑡 + 𝜙)

periodT = 1/f

peakamplitude

time

signal strength

Sine Waves: Revisited

phase / phase shift

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Conversion Techniques

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Bit Rate vs. Baud Rate•Bit rate ® the number of bits per second•Baud rate ® the number of signal elements (symbols)

per second

• In the analog transmission of digital data, the baud rate is less than or equal to the bit rate

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Binary Amplitude Shift Keying• Or Binary ASK

• Represent bits by amplitudes; fix frequency and phase

• Simplest form ® On-Off Keying (OOK)

fc : Carrier frequency0 < d < 1

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Implementation of Binary ASK

•An everyday example: IR remote

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Frequency Spectrum of ASK (1)•Consider a digital signal of the form

•After modulation with the carrier frequency fc

𝑠 𝑡 = 𝐴! +&"#!

$

[𝐴" sin 2𝜋𝑛𝑓!𝑡 + 𝐵"cos 2𝜋𝑛𝑓!𝑡]

𝑣 𝑡 = sin 2𝜋𝑓%𝑡 ⋅ 𝑠(𝑡)

𝑣 𝑡 = 𝐴!sin 2𝜋𝑓"𝑡 +,#$!

%

[𝐴# sin 2𝜋𝑓"𝑡 ⋅ sin 2𝜋𝑛𝑓!𝑡 + 𝐵# sin 2𝜋𝑓"𝑡 ⋅ cos 2𝜋𝑛𝑓!𝑡]

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Frequency Spectrum of ASK (2)•Using trigonometric identities

𝑣 𝑡 = 𝐴!sin 2𝜋𝑓"𝑡 +,#$!

%

[ 𝐴#sin 2𝜋𝑓"𝑡 ⋅ sin 2𝜋𝑛𝑓!𝑡 + 𝐵# sin 2𝜋𝑓"𝑡 ⋅ cos 2𝜋𝑛𝑓!𝑡]

12𝐴#[cos 2𝜋𝑓"𝑡 − 2𝜋𝑛𝑓!𝑡 − cos(2𝜋𝑓"𝑡 + 2𝜋𝑛𝑓!𝑡)]

12𝐵#[sin 2𝜋𝑓"𝑡 − 2𝜋𝑛𝑓!𝑡 + sin(2𝜋𝑓"𝑡 + 2𝜋𝑛𝑓!𝑡)]

ffn

Bandband signal

ffcfc+fnfc– fn

Modulated signal

Demo on Desmos

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Example – ASK Bit Rate•Given bandwidth of 100 kHz, spanning from 200 kHz to

300 kHz•Modulate data using ASK with communication circuitry

that requires bandwidth of 2 Hz/baud•What is the carrier frequency and the bit rate?Solution:

𝑏𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ = 100 𝑘𝐻𝑧 = 2×𝑏𝑎𝑢𝑑 = 2×𝑏𝑖𝑡𝑟𝑎𝑡𝑒×1

𝑏𝑖𝑡𝑟𝑎𝑡𝑒 = 50 𝑘𝑏𝑝𝑠

𝑓% =300 𝑘𝐻𝑧 + 200 𝑘𝐻𝑧

2 = 250 𝑘𝐻𝑧

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Binary Frequency Shift Keying•Or Binary FSK•Represent bits by frequencies; fix amplitude and phase

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Implementation of Binary FSK

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Multilevel FSK•Use one frequency to send more than one bit at a time• E.g., the whole bandwidth divided into 8 frequency ranges

◦ Each frequency can represent 3 bits

000 001 010 011 100 101 110 111

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Binary Phase Shift Keying•Or Binary PSK•Represent bits by phase shifts; fix amplitude and frequency

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Implementation of Binary PSK

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Quadrature PSK• Each signal element carries 2 bits

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Example – QPSK Bandwidth• Find the bandwidth for a signal transmitting at 12 Mbps for

QPSK•Assume the communication circuitry requires 1 Hz/baud

Solution• For QPSK, two bits is carried by one signal element. This

means 1 baud = 2 bits per second

𝑏𝑎𝑛𝑑𝑤𝑖𝑑𝑡ℎ = 1×𝑏𝑎𝑢𝑑 = 1×12 𝑀𝑏𝑝𝑠

2 = 6𝑀𝐻𝑧

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Implementation of QPSKData Bits 00 01 10 11

Phase -135 135 -45 45

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Constellation Diagrams•A constellation diagram helps define the amplitude and

phase of a signal element

Phasor Visualization

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Example – Constellation Diagram• Show the constellation diagrams for OOK, BPSK, and QPSK

modulations

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Constellation Diagram for 8-PSK

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Quadrature Amplitude Modulation•QAM – Quadrature Amplitude Modulation•A combination of ASK and PSK

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QAM Modulation Process

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QAM Demodulation Process

Basic of Signal Demodulation

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Telephone Line Bandwidth

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V.32 and V.32bis Modem Standards

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Analog-to-Analog Conversion•Process of transmitting analog information by an analog

signal•Although the signal is already analog, modulation is

needed if a band-pass channel is available to us.

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Types of Analog-to-Analog Modulations

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Amplitude Modulation (AM)

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AM Band Allocation

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Frequency Modulation (FM)

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FM Band Allocation

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Phase Modulation (PM)•Considered a variation of FM

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Summary•Band-pass channels require signals modulated into specific

frequency range• Three properties of sine wave can be altered to represent

the original data bits◦ Amplitude-shift keying (ASK)◦ Frequency-shift keying (FSK)◦ Phase-shift keying (PSK)

•Quadrature Amplitude Modulation (QAM) combines both ASK and PSK•Analog-to-analog conversion: AM, FM, PM