Transmission Media

Quiz: ANGEL->Lessons->Quiz 2

Figure 1 Figure 2

Figure 3 Figure 4

Reading for next class

• Ch. 8.1 – 8.12

4

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

5

Review: Bandwidth-Limited Signals•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

Review: Bandwidth-Limited Signals

• Having less bandwidth degrades the signal8 sine waves

4 sine waves

2 sine waves

Lost!

Bandwidth

Lost!

Lost!

7

Receiver: Converting an Analog Signal back to Digital

1. (Sampling) The level of analog signal is measured repeatedly at fixed time intervals

2. (Quantization) A sample is then quantized by converting it into an integer value…

How many samples do we need?

8

• 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

9

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.

Example: At what rate should we sample this signal?

• Maximum frequency = 2Hz• Sampling rate: 2*2Hz = 4Hz

Exercise

• Q: At what rate should we sample the following signal?

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:

13

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

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?

A Taxonomy of Transmission Media by Forms of Energy

.

wired

Twisted Pair, Coaxial Cable, or Optical Fiber?

Figure 1 Figure 2

Figure 3 Figure 4

.

Copper (Electrical) Wiring vs. Optical Fiber

• Copper– 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.

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

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

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?

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)

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?