1. Transmission Media

2. Review: Bandwidth of a digital signal
The bandwidth of a digital signal is infinite!
Accurate representation of a digital signal requires an infinite set of sine waves.
Transmitting/reproducing digital signals is impractical 2 2

3. Review: Bandwidth of a digital signal
The bandwidth of a digital signal is infinite!
Accurate representation of a digital signal requires an infinite set of sine waves.
Transmitting/reproducing digital signals is impractical
Engineers adopt a compromise:
generate composite sine waves that closely approximate the digital signal
the quality of approximation depends on the channel bandwidth 3 3

4. Review: Bandwidth-Limited Signals
Having less bandwidth degrades the signal
8 sine waves
Lost!
Bandwidth
4 sine waves
Lost!
2 sine waves
Lost!

5. Converting an Analog Signal back to Digital
(Sampling) The level of analog signal is measured repeatedly at fixed time intervals
(Quantization) A sample is then quantized by converting it into an integer value… 5 5

6. How many samples do we need?
too few samples: may only give a crude approximation of the original signal
too many samples: more digital data will be generated, which uses extra bandwidth

7. The Nyquist Theorem and Sampling Rate
A mathematician named Nyquist discovered exactly how much sampling is required:
fmax : the highest frequency in the composite signal.
Sample a signal at least twice as fast as the highest frequency that must be preserved.

8. Example: At what rate should we sample this signal?
Maximum frequency = 2Hz
Sampling rate: 2*2Hz = 4Hz

9. Exercise Q: At what rate should we sample the following signal?
Answer: 5/2 * 2 = 5Hz

10. Bandwidth to Channel Capacity
In practice, the maximum frequency of a signal is determined by the channel bandwidth B.
Nyquist Theorem: maximum symbol rate (baud) is 2B
Thus, if there are K signal levels, ignoring noise, the maximum bit rate is:

11. Example: Bit Rate of Telephone System
Audio bandwidth
Acceptable quality: preserving frequency up to 4k
Sampling rate (baud) = 2*4K = 8K
Quantization:
Reasonable quality reproduction: 8 bits / 256 levels

12. Exercise
If 8 signal levels are used, what is the data rate that can be sent over a coaxial cable that has an analog bandwidth of 6.2 MHz?
2 * 6.2MHz * log(8) = 37.2 Mbps

13. A Taxonomy of Transmission Media by Forms of Energy
Wired
(guided) .

14. Why Twisted Pair? .

15. Radiation And Electrical Noise
Facts:
“Random” electromagnetic radiation, called noise, is everywhere.
Light bulbs, electrical motors, paper shredders,…
When it hits metal, electromagnetic radiation induces a small signal.
“Random” noise can interfere with signals used for communication .

16. Noise induced is related to the spatial location of wires.
Altering the spatial locations of the pair can cancel out the noise.
When two wires are in parallel, there is a high probability that one of them is closer to the source of radiation than the other.
Twisting two wires makes them less susceptible to electrical noise than leaving them parallel.

17. Shielded vs. Unshielded Twisted Pair
Unshielded Twisted Pair (UTP)
Used in transmission where
Low-frequency signals are dominant.
Electrical noise are not very strong.
Wires are far away the source of noise.
Phone lines
Shielded Twisted Pair (STP)
Computer networks
Requiring high reliability

18. .

19. Categories of Twisted Pair Cable.

20. Coaxial Cable
Twisted pair, even shielded, tends to have problems with:
Very strong electrical noise
Close physical proximity to the source of noise
Close to a factory that uses electric arc welding equipment
Close to a transmission tower
High frequency signals
A fluorescent light fixture can interference signals.
We need something more resistant to electrical noise.

21. Coaxial Cable .

22. Optical Fibers Most popular type of media that uses light
Thin strand glass or transparent plastic encased in a plastic cover .

23. Copper (Electrical) Wiring vs. Optical Fiber
Less expensive
No need special treatment on wires
Ends of an optical fiber must be polished before being used.
Installation is easy.
Less likely to break if accidentally pulled or bent
Optical fiber
Immune to electrical noise
Higher bandwidth
Light traveling across a fiber does not attenuate as much as electrical signals traveling across copper. .

24. How fast can we send information over a channel with noise?
Key channel properties: The bandwidth (B), single strength (S), and noise strength (N)
B limits the rate of transmissions
S and N limit how many signal levels we can distinguish
Bandwidth B
Signal S,
Noise N

25. The Effect of Noise on Communication
In practice, the signal levels we can distinguish depends on S/N
Or SNR, the Signal-to-Noise Ratio
Shannon’s Theorem

26. Example
If a system has an average power level of 100, an average noise level of 33.33, and a bandwidth of 100 MHz, what is the effective limit on channel capacity?
100M * log(1+100/33.33) = 100M * 2 = 200M bps

27. Calculate Channel Capacity with S/N in dB
SNR often given on a log-scale in deciBels:
Example: the voice telephone system:
Signal-to-noise ratio: about 30 dB
An analog bandwidth: about 3 kHz
Calculation
Step 1: Converting the S/N in dB into a simple fraction: S/N = 10(dB/10)
30dB  1000
Step 2: Applying Shannon's Theorem
about 30,000 bps
dB = 10log10(S/N)

28. Exercise
If a telephone system can be created with a signal-to-noise ratio of 40 dB and an analog bandwidth of 3000 Hz, how many bits per second could be transmitted?