Physical Layer - CS331 Study Guide

01 · The job

What the physical layer actually does

Every layer above it thinks in messages, packets and frames. The physical layer is the only one that touches the real world: it turns bits into something that can travel through a wire, a glass fibre or the air, and turns it back into bits at the other end.

One sentence

Bits ⇄ signals

To be transmitted, data must be transformed to electromagnetic signals. Copper carries electrical signals; fibre carries light pulses; wireless carries radio, microwave or infrared waves.

Transmitter→communication channel→Receiver

Transmitter converts information into a signal and injects energy into the medium (a NIC turns bits into current or light; a phone turns voice into current).
Receiver takes energy from the medium and converts it back (current or light → bits; current → voice).

What it defines

The physical characteristics

How devices connect to each other and to the link (topology)
Shape, size and number of pins of connectors (e.g. RJ-45)
The voltages and currents used, and the type of medium
Transmission mode: simplex, half duplex, full duplex
Representation of bits: encoding into electrical or optical signals
Data rate (bits per second) and bit synchronisation of sender and receiver clocks

Devices that live here: NIC, hub, repeater.

02 · Signals

Analog vs digital, periodic vs aperiodic

Four words get mixed up all the time. Keep data (what you want to send) separate from signals (how it travels).

	Analog	Digital
Data	Continuous values: sound, light, temperature	Discrete values: text, integers, symbols
Signal	Continuously varying wave; infinite number of values over a period	Series of voltage pulses (square wave); limited number of values; holds a level, then jumps
Usually	Periodic (repeats in identical cycles)	Aperiodic (no repeating pattern)

Frequency and period

Meaning

Two views of the same wave

Period (T) = how long one cycle takes (seconds). Frequency (f) = how many cycles happen every second (Hz). They are the inverse of each other.

f = 1 / T · T = 1 / f

Frequency is the rate of change with time: changing in a short time = high frequency; changing over a long time = low frequency.

Picture it

Example 1 · home power (slide)

f = 60 Hz
T = 1 / 60 = 0.0166 s
  = 0.0166 × 1000 ms = 16.6 ms

Example 2 · period → kHz (slide)

T = 100 ms = 100 / 1000 s = 0.1 s
f = 1 / 0.1 = 10 Hz
  = 10 / 1000 kHz = 0.01 kHz

Example 3 · tutorial

f = 5 kHz = 5 × 1000 = 5000 Hz
T = 1 / 5000 = 0.0002 s
  = 0.0002 × 10⁶ μs = 200 μs

Example 4 · fast signal

f = 2 GHz = 2 × 10⁹ Hz
T = 1 / (2 × 10⁹) = 0.5 × 10⁻⁹ s
  = 0.5 ns

Simple vs composite signals

Simple

One frequency

A single sine wave; every cycle takes the same time. Example: a pure tone.

Composite

Many frequencies

Made of several sine waves with different frequencies, amplitudes or phases added together. Real data signals (voice, a digital square wave) are composite.

Part 1 · slide 7Analog vs digital signals: a continuous wave on the left, discrete levels on the right.

03 · Digital signals

Bit rate and bit interval

Most digital signals are aperiodic, so "frequency" isn't the right tool. We describe them with bit rate and bit interval instead.

Definitions

Two inverses again

Bit rate (digital bandwidth = transmission speed = link capacity): number of bits sent per second, in bps.

Bit interval (the digital "period"): time needed to send one bit, in seconds.

bit interval = 1 / bit rate · bit rate = 1 / bit interval

Here 1 = positive voltage, 0 = zero voltage.

Picture it

8 bits in 1 s → bit rate 8 bps → bit interval 1/8 s.

Example 1 · slide

Bit rate = 2000 bps
Bit interval = 1 / 2000 = 0.0005 s
             = 0.0005 × 10⁶ μs = 500 μs

Example 2 · tutorial

Bit interval = 50 μs = 50 × 10⁻⁶ s
Bit rate = 1 / 0.00005 = 20,000 bps
         = 20,000 / 1000 = 20 Kbps

Example 3 · fast link

Bit rate = 1 Gbps = 10⁹ bps
Bit interval = 1 / 10⁹ s = 1 ns

Example 4 · more levels (slide 15)

2 levels → 1 bit per level  → 8 bps
4 levels → 2 bits per level → 16 bps
bits per level = log₂(levels)

Part 1 · slide 16Bit rate and bit interval: eight equal bit slots in one second give 8 bps.

Part 1 · slide 15A two-level signal carries 1 bit per level; a four-level signal carries 2 bits per level, doubling the bit rate.

Why digital wins

Advantages of digital transmission

Low cost	Digital technology is inexpensive
Longer distances	Repeaters regenerate the signal
Security & privacy	Data can be encrypted
Noise removal	A clean signal can be regenerated
Multiplexing	Cheaper, easier: many sources share one link
One computer for all	Analog data (voice, video) and digital data can both be processed by computers

04 · Impairments

Why the received signal isn't what was sent

No medium passes every frequency safely: it may pass some, block others and weaken others. The differences between sent and received signals come from three impairments.

Attenuation

Loss of energy as the signal resists the medium; strength falls with distance and gets worse at higher frequency. The wire warms up.

Fix: amplifier (analog) · repeater (digital: regenerates a clean copy)

Distortion

The signal changes shape. Its frequency components arrive at different times, so neighbouring bits overlap. Example: a video call with smeared, delayed audio.

Noise

Unwanted energy added to the signal. Four kinds, below.

Noise type	Cause	Everyday example
Thermal	Random motion of electrons in a wire creates an extra signal	Always present, can't be removed entirely
Induced	Motors and electrical equipment	A cable running past heavy machinery
Crosstalk	One wire's signal leaks into the wire beside it	Hearing another conversation faintly on your phone call
Impulse	Short, high-amplitude spikes from power lines or lightning	The main source of errors in digital data

Part 1 · slide 21Attenuation: an amplifier boosts an analog signal (and its noise); a repeater regenerates a clean digital signal.

Part 1 · slide 23Noise added between two points changes the received signal.

05 · Performance

Propagation, transmission, latency, bandwidth–delay

These are the calculation marks. The trick is knowing which formula a question wants, so each one comes with a plain-words test.

Propagation time

How long ONE bit takes to travel

propagation time = distance / propagation speed

Depends on the length of the link and the medium, not on the message. Light travels at 3 × 10⁸ m/s in a vacuum, slower in air, and about 2/3 of that (≈ 2 × 10⁸ m/s) in a cable.

Plain-words test: "how far, how fast?" → propagation.

Transmission time

How long it takes to PUSH the whole message onto the link

transmission time = message size (bits) / bandwidth (bps)

Depends on the message size and the bit rate, not on distance.

Plain-words test: "how big, how fast a link?" → transmission.

Latency (total delay)

Everything added together

latency = transmission time + propagation time + queuing time + processing time

Queuing time is the time a message waits at each intermediate device before it is processed. Unless a question gives queuing or processing figures, latency is just transmission + propagation.

Worked examples

A · short e-mail, fast link (slides)

2.5-kbyte message, bandwidth 1 Gbps, distance 12,000 km, speed 2.4 × 10⁸ m/s.

Convert: 2.5 kbyte = 2500 bytes = 2500 × 8 = 20,000 bits
         12,000 km = 12,000 × 1000 = 1.2 × 10⁷ m
Propagation  = 1.2 × 10⁷ / 2.4 × 10⁸ = 0.05 s  = 50 ms
Transmission = 20,000 / 10⁹          = 0.00002 s = 0.02 ms

Propagation dominates (50 ms vs 0.02 ms): the message is short and the link is fast, so transmission can be ignored.

B · big image, slow link (slides)

5-Mbyte message, bandwidth 1 Mbps, same distance and speed.

Convert: 5 Mbyte = 5 × 10⁶ × 8 = 4 × 10⁷ bits
Propagation  = 0.05 s = 50 ms         (same link, same answer)
Transmission = 4 × 10⁷ / 10⁶ = 40 s

Transmission dominates (40 s vs 0.05 s): a long message on a slow link.

C · satellite (slide 31)

Computers A and B talk through a satellite. Bandwidth 1 Gbps, frame 2000 bytes, satellite 36,000 km above each ground station, speed 3 × 10⁸ m/s.

Distance = up 36,000 km + down 36,000 km = 72,000 km = 7.2 × 10⁷ m
Propagation  = 7.2 × 10⁷ / 3 × 10⁸ = 0.24 s = 240 ms
Transmission = 2000 × 8 / 10⁹       = 0.000016 s = 16 μs
Latency ≈ 0.24 s + 0.000016 s ≈ 0.240016 s

The trap: the signal goes up and back down, so the distance doubles.

D · tutorial questions

Propagation: 2,000 km at 2.0 × 10⁸ m/s
  2,000 km = 2 × 10⁶ m
  2 × 10⁶ / 2 × 10⁸ = 0.01 s = 10 ms

Transmission: 1 MB file on a 1 Mbps link
  1 MB = 8 Mb = 8 × 10⁶ bits
  8 × 10⁶ / 10⁶ = 8 s

Part 1 · slide 25Propagation time: the time for one bit to travel the distance d between t1 and t2.

Part 1 · slide 26Transmission time, queuing time and the full latency formula.

Part 1 · slide 31Satellite example: 36,000 km to the satellite, 2000-byte frame, 1 Gbps.

Bandwidth–delay product

Meaning

How many bits fill the link

bandwidth–delay product = bandwidth × delay (bits)

Think of the link as a pipe: bandwidth is how wide it is (bits entering per second), delay is how long it is (seconds to cross), so their product is how many bits fit inside — the length of the link measured in bits.

Picture it

Case 1 (slides)

bandwidth 1 bps, delay 5 s
1 × 5 = 5 bits fill the link

Case 2 (slides + tutorial)

bandwidth 5 bps, delay 5 s
5 × 5 = 25 bits fill the link

Real link

bandwidth 100 Mbps, delay 20 ms
10⁸ × 0.02 = 2 × 10⁶ bits
           = 2,000,000 bits in flight

Part 1 · slide 34Filling the link in case 2: 5 bps for 5 seconds puts 25 bits on the link.

Wavelength

Meaning

The distance one cycle occupies

λ = propagation speed × period = propagation speed / frequency

Depends on the signal's frequency and the medium. Higher frequency → shorter wavelength.

Example

f = 100 MHz in air, speed 3 × 10⁸ m/s
λ = 3 × 10⁸ / 10⁸ = 3 m

Same 100 MHz in a cable (2 × 10⁸ m/s)
λ = 2 × 10⁸ / 10⁸ = 2 m

06 · Conversions

The conversion table

Almost every lost mark in this chapter is a unit slip, not a wrong formula. Convert everything to base units first — seconds, metres, bits, bps, Hz — then use the formula, then convert the answer to whatever unit the question asks for.

Prefix	Symbol	Power of 10	As a number	To base unit	Used for
tera	T	10¹²	1,000,000,000,000	× 10¹²	THz (infrared)
giga	G	10⁹	1,000,000,000	× 10⁹	Gbps, GHz
mega	M	10⁶	1,000,000	× 10⁶	Mbps, MHz, Mbyte
kilo	k	10³	1,000	× 10³	kbps, kHz, km, kbyte
(none)	—	10⁰	1	base unit	s, m, bit, bps, Hz
milli	m	10⁻³	0.001	× 10⁻³ (÷ 1000)	ms
micro	μ	10⁻⁶	0.000001	× 10⁻⁶	μs
nano	n	10⁻⁹	0.000000001	× 10⁻⁹	ns

Time ladder

Each step is × 1000

s× 1000 →ms× 1000 →μs× 1000 →ns

ns÷ 1000 →μs÷ 1000 →ms÷ 1000 →s

0.05 s     = 50 ms    = 50,000 μs
0.0005 s   = 0.5 ms   = 500 μs
0.000016 s = 0.016 ms = 16 μs

Data size

Bytes → bits: × 8

1 byte = 8 bits

2.5 kbyte = 2.5 × 10³ × 8 = 20,000 bits
5 Mbyte   = 5 × 10⁶ × 8   = 4 × 10⁷ bits
1 MB      = 8 Mb

Capital B = byte, small b = bit: 1 MB = 8 Mb.

The course uses decimal prefixes: 1 kbyte = 1000 bytes (not 1024).

Rates, distance, frequency

Same prefixes, different units

1 Gbps    = 10⁹ bps
1 Mbps    = 10⁶ bps
20 Kbps   = 20,000 bps
1 km      = 10³ m
12,000 km = 1.2 × 10⁷ m
5 kHz     = 5000 Hz
2 MHz     = 2,000,000 Hz

The rule of thumb

Smaller unit → bigger number

Going to a smaller unit makes the number bigger (multiply); going to a bigger unit makes it smaller (divide).

2 MHz → Hz  : 2 × 10⁶ = 2,000,000 Hz
2 μs  → s   : 2 × 10⁻⁶ = 0.000002 s
500 μs → ms : 500 ÷ 1000 = 0.5 ms

Powers of 10 shortcut	Rule	Example
Multiply	Add the exponents	2 × 10⁶ × 10³ = 2 × 10⁹
Divide	Subtract the exponents	1.2 × 10⁷ / 2.4 × 10⁸ = 0.5 × 10⁻¹ = 0.05
1 over	Flip the sign of the exponent	1 / 10⁹ = 10⁻⁹ s = 1 ns
Write it nicely	Move the decimal, change the exponent to match	0.5 × 10⁻⁹ s = 0.5 ns = 500 ps

Live converter

Type a value, see every unit

Accepts plain numbers, 2.4e8 or 2.4 x 10^8.

07 · Transmission media

Guided (wired) media

The transmission medium is the physical path between transmitter and receiver. It sits below the physical layer and is controlled by it.

TRANSMISSION MEDIA
├── GUIDED (wired)
│   ├── Twisted pair ── UTP, STP
│   ├── Coaxial
│   └── Fibre optic
└── UNGUIDED (wireless)
    ├── Radio waves
    ├── Microwaves
    └── Infrared

Twisted pair

Two insulated copper wires, twisted

The pair acts as one link. Twisting makes interference hit both wires equally, so it cancels out: more twists = better quality (7.5–10 cm twist vs 0.6–0.85 cm). Used for the telephone subscriber loop and LANs. Connector: RJ-45.

	UTP	STP
Shield	None	Metal braid / foil
Cost	Cheapest	More expensive
Install	Easiest	Harder (thick, heavy)
EMI	Suffers from it	Reduced

UTP categories

Cat	Bandwidth	Max rate	Shielding
CAT5e	100 MHz	1000 Mbps	UTP or STP
CAT6	250 MHz	1000 Mbps	UTP or STP
CAT6a	500 MHz	10 Gbps	UTP or STP
CAT7	600 MHz	10 Gbps	Shielded only
CAT8	2000 MHz	25 / 40 Gbps	Shielded only (40 Gbps up to 24 m)

Notice: "bandwidth" here is in MHz (the cable's frequency range), while "max rate" is in bps.

Ethernet cabling

Straight-through vs crossover

Straight-through joins different kinds of device: PC ↔ switch/hub, router ↔ switch/hub.

Crossover joins similar devices: PC ↔ PC, hub ↔ hub, switch ↔ switch, hub ↔ switch, and router ↔ PC.

Why: a crossover cable connects one end's transmit pins (TD+/TD−) to the other end's receive pins (RD+/RD−). Two PCs both transmit on the same pins, so the wires must cross.

Coaxial & fibre

Copper core vs glass core

Coaxial: a copper core, insulation, a braided or foil copper shield and an outer jacket.

Optical fibre: three concentric sections — the core (thin glass or plastic strands), the cladding (a coating with different optical properties that keeps the light bouncing inside the core) and the jacket (protects against moisture and crushing). It carries light pulses.

Fibre advantages	Fibre disadvantages
Higher bandwidth (hundreds of Gbps) · smaller and lighter · lower attenuation, so repeaters can be farther apart (50 km or more without one) · no crosstalk · not affected by noise · highly secure (no light leaks)	Needs special skills to install · expensive interfaces compared with electrical ones

Issue	UTP	Fibre
Bandwidth	10 Mb/s – 10 Gb/s	10 Mb/s – 100 Gb/s
Distance	1 – 100 m	1 – 100,000 m
EMI / RF immunity	Low	High (completely immune)
Electrical hazards	Low immunity	High (completely immune)
Media and connector cost	Lowest	Highest
Installation skill	Lowest	Highest

Part 2 · slide 3Classes of transmission media: guided (twisted pair, coaxial, fibre) and unguided (radio, microwave, infrared).

Part 2 · slide 9UTP has a plastic cover only; STP adds a metal shield.

Part 2 · slide 15Straight-through cabling for different devices, crossover cabling for similar devices.

Part 2 · slide 17Optical fibre: core, cladding and jacket, with light reflecting along the core.

08 · Unguided media

Wireless: radio, microwave, infrared

Unguided signals travel through the air and reach anyone with a suitable receiver. Moving up the spectrum, frequency rises, wavelength shrinks, and the waves become more directional and worse at passing through walls.

Radio< 300 MHz

Microwave300 MHz – 300 GHz

Infrared300 GHz – 400 THz

lower frequency · longer wavelength · passes walls → higher frequency · shorter wavelength · line of sight

Wave	Direction	Strength	Used for
Radio	Omnidirectional (all directions)	Long distances	Multicast: AM/FM radio, TV
Microwave	Unidirectional, line of sight	High frequencies can't pass walls	Unicast: cellular phones, satellite, wireless LANs, point-to-point between buildings
Infrared	Line of sight	Short range, can't pass walls, unusable in sunlight	Remote controls, wireless keyboards and mice (IrDA: 75 kbps up to 8 m; 1.15–4 Mbps at 1 m)

Part 2 · slide 23The electromagnetic spectrum: radio and microwave, then infrared, then visible light.

09 · Cheat sheet

Everything on one card

Find	Formula	Answer unit	Convert first
Frequency	f = 1 / T	Hz	T into seconds
Period	T = 1 / f	s	f into Hz
Bit interval	1 / bit rate	s	rate into bps
Bit rate	1 / bit interval	bps	interval into s
Propagation time	distance / speed	s	km → m
Transmission time	size (bits) / bandwidth	s	bytes × 8; rate into bps
Latency	transmission + propagation + queuing + processing	s	all in seconds
Bandwidth–delay	bandwidth × delay	bits	bps and s
Wavelength	speed × T = speed / f	m	Hz, m/s

Light: 3 × 10⁸ m/s in a vacuum, ≈ 2 × 10⁸ m/s in cable. 1 byte = 8 bits. Prefixes are powers of 1000.

10 · Practice

Tutorial-style questions

Try each one on paper, then open the answer.

1. A signal has a period of 4 ms. Find its frequency.

4 ms = 4 / 1000 = 0.004 s
f = 1 / 0.004 = 250 Hz

2. A digital signal has a bit rate of 4 Mbps. What is the bit interval in μs?

4 Mbps = 4 × 10⁶ bps
bit interval = 1 / (4 × 10⁶) = 0.25 × 10⁻⁶ s = 0.25 μs

3. A sender and receiver are 3,000 km apart over a cable (speed 2 × 10⁸ m/s). Find the propagation time.

3,000 km = 3 × 10⁶ m
3 × 10⁶ / 2 × 10⁸ = 0.015 s = 15 ms

4. How long does it take to send a 2.5 MB file over a 10 Mbps link (ignore propagation)?

2.5 MB = 2.5 × 10⁶ × 8 = 2 × 10⁷ bits
2 × 10⁷ / 10⁷ = 2 s

5. A 1-kbyte frame travels 6,000 km over a 100 Mbps link at 2 × 10⁸ m/s. Find both times, the latency, and which one dominates.

Size: 1 kbyte = 1000 × 8 = 8000 bits
Propagation  = 6 × 10⁶ / 2 × 10⁸ = 0.03 s = 30 ms
Transmission = 8000 / 10⁸ = 0.00008 s = 0.08 ms
Latency ≈ 30.08 ms

Propagation dominates: a small frame on a fast link.

6. A link has a bandwidth of 10 Mbps and a delay of 3 ms. How many bits can fill it?

10⁷ × 0.003 = 30,000 bits

7. A 2 GHz signal travels in a cable at 2 × 10⁸ m/s. What is its wavelength?

λ = 2 × 10⁸ / 2 × 10⁹ = 0.1 m = 10 cm

8. Scenario: you hear another call faintly in the background. Name the impairment and its broader category.

Crosstalk, a type of noise: the signal on a neighbouring wire leaks into yours. Twisted pairs, shielding (STP) or fibre reduce it.

9. Scenario: a factory network beside heavy motors has many errors. Which impairment, and which medium would you choose?

Induced noise (electromagnetic interference). Choose fibre optic: it carries light, so it is completely immune to EMI. STP is a cheaper copper alternative that reduces it.

10. Why is a repeater better than an amplifier for a long digital link?

An amplifier boosts the weakened signal and the noise with it. A repeater reads the bits and transmits a freshly regenerated clean signal, so noise doesn't accumulate over distance.

11. Which cable joins a PC to a switch? A PC to another PC?

PC to switch: straight-through (different devices). PC to PC: crossover (similar devices, so transmit must be crossed to receive).

12. Which wireless wave would you use for a TV broadcast, for a link between two buildings, and for a TV remote?

TV broadcast: radio waves (omnidirectional, multicast). Between buildings: microwaves (line of sight, point to point). Remote control: infrared (short range, one room).