Physical Layer

Networks and Systems


Bandwidth is the physical property fo the transmission medium

The signal that runs from 0 to a maximum frequency. Has very narrow and near-zero frequency range. Used in wires
Signals that occupy the higher range of frequency and pass through frequency filter(s). Used in wireless spectrum

Signal Bandwidth

Bandwidth of analogue and digital signals are measured differently:

  • Analogue signal bandwidth is measured in terms of its frequency (Hz)

  • Digital signal bandwidth is measured in terms of bit rate (bps)

Digital Modulation

Digital signals (0,1) are encoded by low and high voltage

There are many digital encoding schemes

Digital Modulation

NRZ Encoding (Non-Return-to-Zero)

NRZ Encoding
  • A high voltage represents a 1 and a low voltage represents a 0
  • The voltage does not return to zero, it changes only when the bit value changes
  • Problem: having long runs of consecutive bits with the same value (no changes in voltage) the constant signal values can’t synchronize the communicating devices

  • Especially with long runs of either 0 or 1, there is no change to resynchronise so it is likely that the clocks would get out of sync

NRZI Encoding

  • NRZI attempts to alleviate the problem in NRZ scheme
NRZI encoding
  • 0 is encoded as no change in the level. 1 is encoded depending on the current state of the line
  • 1 is encoded as an inverting of the current state
  • This fixes the problem of sending consecutive 1s but not consecutive 0s

Bipolar Encoding

Bipolar Encoding
  • 0 is represented by a zero voltage, neither high nor low
  • 1 is represented by either positive voltage or negative voltage
    • It is inverted based on the last transmission of 1
    • It is represented by a negative voltage if it was represented by a positive voltage when it was last transmitted, and vice versa

For this, over a long enough message, the sum of the voltages is zero, this is called a “balanced encoding” and is desirable in some applications

Manchester Encoding

Manchester Encoding
  • A high to low voltage represents a 1 and a low to high voltage represents a 0
  • Uses signal changes to transmit a bit and achieves synchronisation
  • This is equivalent to an XOR of the clock signal and the NRZ encoding. The clock is at twice the frequency of the NRZ
  • Twice the bandwidth of NRZ is required


  • Channels are often shared by multiple signals

  • Different ways to accomplish multiplexing:

Frequency Division Multiplexing

  • Refactor the signals to start at different frequencies

  • Sit them side by side on the frequency spectrum on the same channel, so they don’t interfere with each other

  • Put a small region in-between adjacent frequency bands to avoid interference

Frequency Division Multiplexing

  1. The original bandwidths

  2. The bandwidths raised in frequency

  3. The multiplexed channel

Wavelength Division Multiplexing

  • The same as FDM but for optical fibres instead of wireless signals

Wavelength Division Multiplexing

Time division multiplexing

  • Intersperse the channels in some sequence, leave a guard time to be able to separate out information

Time division multiplexing

Code Division Multiple Access

  • Nice and clean mathematical method allows every transmitter to use the entire channel all the time

  • The individual transmissions are blended (or extracted by a receiver) using coding theory

  • Imagine that we have four transmitters called, from now on, stations

  • Each station has a chip (i.e. a code), which is a four bit vector

  • These codes are chosen so that the dot product of any of these codes with any other of the codes is 0 i.e. they are orthogonal to each other

  • Transmitting the stations chip sequence a 1

  • Transmitting the negation of a stations chip sequence is a 0