Chapter 2

(Week 3)
The Physical Layer

ANDREW S. TANENBAUM
COMPUTER NETWORKS
FOURTH EDITION
PP. 85-118
 The Purpose of the Physical Layer
• THE PURPOSE OF THE PHYSICAL LAYER
IS TO TRANSPORT A RAW BIT STREAM
FROM ONE MACHINE TO ANOTHER

The Hybrid Model of Computer Network

 Physical Layer’s Functions (1/2)
The Physical Layer is concerned with transmitting
raw bits over a communication channel. The
typical questions here are:
a) How many volts should be used to represent a 1
and a 0;
b) How many nanoseconds a bit lasts;
c) Whether transmission may proceed
simultaneously in both directions;
 Physical Layer’s Functions (2/2)
d) How the initial connection is established and
how it is torn down when both sides are
finished;
e) How many pins the network connector has and
what each pin is used for;
The design issues here largely deal with
mechanical, electrical, and timing interfaces of
the network.
The physical transmission medium, which lies
below the physical layer, is also studied in
scope of physical layer.
 The Theoretical Basis for Data
Communication (2/1)
• Information can be transmitted on wires by
varying some physical property such as voltage
or current.

• By representing the value of this voltage or

current as a single-valued function of time, f(t),
we can model the behavior of the signal and
analyze it mathematically.
 The Theoretical Basis for Data
Communication (2/2)

• Fourier Analysis
• Bandwidth-Limited Signals
• Maximum Data Rate of a Channel
 Fourier Analysis (1/4)
• INFORMATION CAN BE TRANSMITTED
ON WIRES BY VARYING SOME
PHYSICAL PROPERTY SUCH AS
VOLTAGE OR CURRENT.
• BY REPRESENTING THE VALUE OF
THIS VOLTAGE OR CURRENT AS A
SINGLE-VALUED FUNCTION OF TIME,
f(t), WE CAN MODEL THE BEHAVIOR OF
THE SIGNAL AND ANALYZE IT
MATHEMATICALLY
 Fourier Analysis (2/4)
• Any periodic function, g(t), with period T can
be constructed by summing a (possibly
infinite) number of sines and cosines:
1  
g (t )  c   an sin( 2nft )   bn cos( 2nft )
2 n 1 n 1
1
f  is the fundamental frequency; c is a constant;
T
an and b n are the sine and cosine amplitudes of the nth harmonics.

Such decomposition is called a Fourier series.

 Fourier Analysis (3/4)
• From the Fourier series, the function can be
reconstructed;
• That is, if the period, T, is known and the
amplitudes are given, the original function of time
can be found by performing the sums of g(t).
• A data signal that has a finite duration can be
handled by just imagining that it repeats the entire
pattern over and over forever (i.e., the interval
from T to 2T is the same as from 0 to T, etc.)
 Fourier Analysis (4/4)
1  
g (t )  c   an sin( 2nft )   bn cos( 2nft )
2 n 1 n 1
T
2
an 
T  g ( t ) sin( 2nft ) dt
0

2T
g (t) cos(2nft )dt
bn 
T 
0
T
2
c 
T 
0
g ( t ) dt
 Bandwidth-Limited Signals (1/8)
• Let us consider the relation of the Fourier Series
with data communication.
• Let us consider how to transmit the ASCII
character “b”, which can be encoded in an 8-bit:
01100010.
This signal is the
voltage output by
the transmitting
computer
 Bandwidth-Limited Signals (2/8)

The Fourier analysis of this signal is the voltage

output by the transmitting computer gives the
following coefficients:
an 
1
cos(n / 4)  cos( 3n / 4) cos( 6n / 4) cos( 7n / 4)
n
bn 
1
sin( 3n / 4)  sin( n / 4) sin( 7n / 4) sin( 6n / 4)
n
c  3/4
 Bandwidth-Limited Signals (3/8)

(a) A binary signal and its root-mean-square Fourier amplitudes.

(b) – (c) Successive approximations to the original signal.
 Bandwidth-Limited Signals (4/8)

(d) – (e) Successive approximations to the original signal.

 Bandwidth-Limited Signals (5/8)

• This figure shows the Root-Mean-Square a2  b2

n n
amplitudes for the first few terms.
• These values are proportional to the energy
transmitted at the corresponding frequency.
 Bandwidth-Limited Signals (6/8)
• Usually, the amplitudes are transmitted
undiminished from 0 up to some frequency fc .
All amplitudes above this cutoff frequency are
transmitted attenuated.
• The range of frequencies transmitted without being
strongly attenuated is called the bandwidth.
• Bandwidth is a physical property of the
transmission medium and usually depends on the
construction, thickness, and length of the medium.
 Bandwidth-Limited Signals (7/8)
• Assume that a bit rate is b bits/sec.
• Then the time required to send 8 bits (for example) 1
bit at a time is T=8/b sec.
• So frequency of the first harmonic is f=1/T=b/8 Hz.
• An ordinary telephone line, often called a voice-grade
line, has an artificially-introduced cutoff frequency
just above 3000 Hz.
• This restriction means that the number of the highest
harmonic passed through is roughly 3000/(b/8) or
24,000/b.
Bandwidth-Limited Signals (8/8)

Relation between data rate and harmonics.

Maximum Data Rate of a Channel (1/3)
• Nyquist Theorem: If an arbitrary signal has been
run through a low-pass filter of bandwidth H, the
filtered signal can be completely reconstructed by
making only 2H (exact) samples per second.

maximum data rate  2 H log 2 V bits/sec

V is discrete levels of signal, for binary signal V=2.

• For example, a noiseless 3-kHz channel can
transmit binary signals at a maximal rate 6000bps.
Maximum Data Rate of a Channel (2/3)
• There is always random (thermal) noise present due
to the motion of the molecules in the system.
• The amount of noise is measured by the ratio of the
signal power to the noise power, called the signal-to-
noise-ratio, or S/N.
• Usually, the ratio itself is not quoted; instead, the
quantity 10 log 10 S / N is given.
• These units are called decibels (dB)
• An S/N ratio of 10 is 10 dB, a ratio of 100 is 20dB.
Maximum Data Rate of a Channel (3/3)
• Shannon Theorem: The maximum data rate of a
noisy channel whose bandwidth is H Hz, and
whose signal-to-noise ratio is S/N, is given by:

maximum number of bits/sec  H log 2 (1 S / N )

• For example, a channel of 3000 Hz bandwidth

with a signal to thermal noise ratio of 30 dB can
never transmit much more than 30,000 bps.
 Transmission Media
• Various physical media can be used for the actual
transmission.
• Each one has its own niche in terms of bandwidth,
delay, cost, and ease of installation and maintenance.
• There are two groups of transmission media:
1) Guided media (copper wire, fiber optics, etc.)
2) Unguided media or wireless (terrestrial radio,
lasers through the air, satellite, etc.)
• This material will provide background information
on the key transmission technologies used in modern
networks.
Guided Transmission Data

• Magnetic Media
• Twisted Pair
• Coaxial Cable
• Fiber Optics
 Magnetic Media
• Magnetic tape;
• Removable media (e.g., recordable
DVDs);
• More cost effective, especially for
applications in which high bandwidth
or cost per bit transported is the key
factor.
 Twisted Pair (1/2)
A twisted pair consists of two insulated copper
wires, typically about 1 mm thick.

(a) Category 3 UTP.

(b) Category 5 UTP.
 Twisted Pair (2/2)
• Twisted pairs can run several kilometers
without amplification, but for longer distances,
repeaters are needed.
• Twisted pairs can be used for transmitting either
analog or digital signals.
• The bandwidth depends on the thickness of the
wire and the distance traveled, but several
megabits/sec can be achieved for a few
kilometers in many cases.
 Coaxial Cable
• A coaxial cable has better shielding than twisted
pairs, so it can span longer distance at higher
speeds.
• The bandwidth depends on the cable quality,
length, and signal-to-noise ratio of the data signal.

A coaxial cable: Modern cables have a bandwidth of close to 1 GHz.

 Fiber Optics (1/2)
An optical transmission system has three key
components: the light source, the transmission
medium, and the detector.

(a) Three examples of a light ray from inside a silica fiber impinging
on the air/silica boundary at different angles.
(b) Light trapped by total internal reflection.
 Fiber Optics (2/2)
• Multimode Fiber.
• Singlemode Fiber.
• Singlemode fibers are more expensive but are
widely used for longer distance.
• Currently available single mode fibers can
transmit data at 50 Gbps for 100 km without
amplification.
Transmission of Light through Fiber (1/3)
• The attenuation of light through glass depends on
the wavelength of the light (as well as on some
physical properties of the glass).
• The attenuation in decibels is given by the
formula:
Attenuatio n _ in _ decibels  10 log transmitted _ power
10
received _ power
Transmission of Light through Fiber (2/3)

Attenuation of light through fiber in the infrared region.

Transmission of Light through Fiber (3/3)
• Three wavelength bands are used for optical
communication.
• They are centered at 0.85, 1.30, and 1.55
microns, respectively.
• The last two have good attenuation properties
(less than 5 percent loss per kilometer).
• All three bands are 25.000 to 30.000 GHz.
 Fiber Cables (1/3)
Fiber optic cables are similar to coax, except
without the braid.

(a) Side view of a single fiber: the core is 8 to 10 microns in diameter.

(b) End view of a sheath with three fibers: the core is typically 50
microns in diameter.
 Fiber Cables (2/3)
• Fibers can be connected in three different ways.
• First, they can terminate in connectors and be
plugged into fiber sockets. Connectors lose about
10 to 20 percent of the light, but they make it easy
to reconfigure systems.
• Second, they can be spliced mechanically.
Mechanical splices take trained personnel about 5
minutes and result in a 10 percent light loss.
• Third, two pieces of fiber can be fused (melted) to
form a solid connection. A small amount of
attenuation occurs.
 Fiber Cables (3/3)

A comparison of semiconductor diodes and LEDs as light sources.

• The receiving end of an optical fiber consists of a photodiode, which

gives off an electrical pulse when struck by light.
• The typical response time of a photodiode is 1 nsec., which limits data
rates to about 1 Gbps.
 Fiber Optic Networks
Fiber optics can be used for LANs as well as for long-haul transmissions.

A fiber optic ring with active repeaters.

 Fiber Optic Networks (2)

A passive star connection in a fiber optics network.